In any casino game, there are myths and legends, things people believe that don't quite square with reality. Let's take on a few myths from a table games
player perspective.
MYTH: The third baseman is a team player, and shouldn't take the
dealer's bust card. A third baseman hitting 12 when the dealer has a 2,
for example, is hurting the entire table.
FACT: A player hitting in that situation helps the rest of the table
as often as he hurts it. Anyway, it's the best play for his hand.
Hitting 12 against 2 is what he SHOULD do.
Wouldn't it be nice if we knew whether or not the next card in the
deck would make the dealer's hand go bust? Problem is, we don't know
what the dealer has face down, and we don't know what the next card is.
Sitting at third base, I've drawn a 9 to my 12 for a 21, had the dealer
turn up a 10-value card, then draw another 10 to bust. The entire table
won, but if I hadn't hit, the dealer would have had a 9 and the whole
table would have lost.
I've also drawn a card that would have busted the dealer. Most often,
though, the dealer has something less than a 10-value face down, and NO
one-card draw can bust the dealer's hand.
Unless other players are willing to pay for losses, the third
baseman's responsibility is to make the play that's best for his or her
own hand.
MYTH: A hot craps table is likely to stay hot, a cold table is likely to stay cold.
FACT: Average results on a table after a hot streak are the same as
after a cold streak. Odds of the game don't change, regardless of how
hot or cold the shooters have bene.
Craps players are always looking for hot tables, and avoiding cold
ones. But unless you're dealing with controlled rollers, a la Frank
Scoblete and his Golden Touch Craps team, I've never really seen a
reason why a hot table should stay hot, or a cold table stay cold. We
are dealing with dice, after all, that don't know what the previous
results have been.
Several years ago, I put it to the test. For nearly a year, every
time I was in a casino in the Midwest, South and in Nevada, I stopped
by a craps table, waited until I saw two consecutive passes, then
tracked the result of the next decision -- not as good a sample as a
million-hand computer run, but a lot more time-consuming.
The result: Pass bettors won 489 wagers and lost 511 on the next
sequence after two consecutive wins. There was no tendency for the dice
to stay hot.
I also watched 1,000 trials that started with two don't passes, then
charted the next decision. The dice passed 496 times in those 1,000
trials a mere three more passes than the expected average. There was no
tendency for cold dice to stay cold, either.
Now, a thousand trials each way isn't enough to satisfy a
statistician, but if hot tables stay hot and cold tables stay cold,
well, you can't prove it by me.
MYTH: Just as in blackjack, counting cards can help you win.
FACT: Counting cards in baccarat doesn't help in any practical way.
Favorable situations in baccarat are really rare. The late Peter Griffin wrote in The Theory of Blackjack
that a baccarat player who doesn't bet unless he has an advantage can
squeeze an edge of about 0.7 percent of his maximum bets on banker and
player. However, that player might play only about three hands per eight
hours. That's watching, not playing.
For bets on ties, it's theoretically possible to count down to a 24
percent edge with six cards remaining, provided all the cards are dealt
out.
In the real world, nobody deals out all the cards, and with one-half
deck cut out of play, the bettor's potential edge on the last hand
shrinks to just 0.08 percent. With just a small reservation, we can say
the myth of the baccarat card counter is JUST a myth.
MYTH: An experienced roulette dealer can make the ball land where he pleases.
FACT: Dealers I know scoff at the notion they can hit a number at
will. With the wheel spinning one way, the ball going in the opposite
direction, bouncing on the surface and from fret to fret separating the
numbers, there are far too many physical variables for a dealer to
control where the ball will land.
Anyway, the last thing the casino wants is a dealer who can hit a
number at will. As long as the results are random, the casino makes its
money. However, if a dealer could control what numbers were coming up,
there'd be a chance someone would be in on the secret and take a lot of
money from the casino. Random games mean big profits for the operators.
Taking the randomness out increases operator risk.
Showing posts with label roulette. Show all posts
Showing posts with label roulette. Show all posts
Wednesday, August 28, 2013
Wednesday, July 17, 2013
How does the house edge work?
The house edge remains a mysterious thing to casino players, including the one who asked me recently about roulette.
"Does a 5.26 percent house edge mean the house wins 52.6 percent of all spins?"
That wouldn't be a bad guess if every wager paid even money, and the house edge was made up entirely of the difference between the frequency of house wins and the frequency of player wins. In the red-black wager at roulette, where winners are paid even money, the house wins 52.63 percent of rolls, the player wins 47.37 percent. Subtract 47.37 from 52.63 and you get the 5.26 percent house edge.
It is the difference between win percentage and loss percentage that's important, and you can't just multiply the house edge by 10 and get the percentage of losing wagers. Roulette is a bit of a coincidence that way.
Take craps and the pass line wager, another even-money payoff. The house has a 1.41 percent edge.
Obviously, it wins more than 14.1 percent of the time. Instead, if you want to know the frequency of house wins, divide that 1.41 percent house edge in half, then add the result to 50 percent. The house wins 50.705 percent of wagers, the player wins 49.295 percent. Do the basic subtraction, and you get a difference of 1.41 percent --- the house edge.
Things get more complicated when payoffs get bigger. Let's go back to roulette and single-number bets. A double-zero roulette wheel has 38 numbers, with 1 through 36 as well as 0 and 00. Any time you bet on a single number, you have one way to win, and 37 ways to loses.
Yet the house edge is the same 5.26 percent as it is on red-black, odd-even or first 18-last 18. On those wagers with even-money payoffs, the house wins 52.63 percent of the time, as we have already seen.
Obviously, the house wins far more than 52.63 percent of single-number wagers. It wins 37 of 38, or 97.37 percent of wheel spins.
The reason you're bucking a house edge of 5.26 percent even though you lose 97.37 percent of the time comes in the payoff, of course. Winning single-number bets are paid at 35-1 odds. If it was a truly even bet, you'd be paid 37-1.
The difference between the payoff and the true odds is the key to the house edge. Here's the way it works.
Let's say you bet $10 on 17 on each spin of a perfect sequence in which each number turns up once. You risk a total of $380. On your one win, you get back $360 --- $350 in winnings for the 35-1 payoff, plus the return of your $10 wager on that spin.
That means the house has kept $20 of your $380 in wagers. Divide 20 by 380, and you get .0526. Multiply by that by 100 to get percent, and you see the house has kept 5.26 percent of the money you've wagered.
That's the house edge on single number bets.
It's simple enough to do the same for place bets or proposition wagers in craps, or the player bet in baccarat, or spaces on the Big Six wheel. The house edge is not based on the frequency of winning hands alone, nor is it based solely on the payoffs on winning wagers. Nor is a game with frequent winners necessarily one with a low house edge, nor a game with low payoffs per win a high house-edge proposition.
From a player's perspective, it's not how often you win, nor how much that counts, it's how much how often, working together.
"Does a 5.26 percent house edge mean the house wins 52.6 percent of all spins?"
That wouldn't be a bad guess if every wager paid even money, and the house edge was made up entirely of the difference between the frequency of house wins and the frequency of player wins. In the red-black wager at roulette, where winners are paid even money, the house wins 52.63 percent of rolls, the player wins 47.37 percent. Subtract 47.37 from 52.63 and you get the 5.26 percent house edge.
It is the difference between win percentage and loss percentage that's important, and you can't just multiply the house edge by 10 and get the percentage of losing wagers. Roulette is a bit of a coincidence that way.
Take craps and the pass line wager, another even-money payoff. The house has a 1.41 percent edge.
Obviously, it wins more than 14.1 percent of the time. Instead, if you want to know the frequency of house wins, divide that 1.41 percent house edge in half, then add the result to 50 percent. The house wins 50.705 percent of wagers, the player wins 49.295 percent. Do the basic subtraction, and you get a difference of 1.41 percent --- the house edge.
Things get more complicated when payoffs get bigger. Let's go back to roulette and single-number bets. A double-zero roulette wheel has 38 numbers, with 1 through 36 as well as 0 and 00. Any time you bet on a single number, you have one way to win, and 37 ways to loses.
Yet the house edge is the same 5.26 percent as it is on red-black, odd-even or first 18-last 18. On those wagers with even-money payoffs, the house wins 52.63 percent of the time, as we have already seen.
Obviously, the house wins far more than 52.63 percent of single-number wagers. It wins 37 of 38, or 97.37 percent of wheel spins.
The reason you're bucking a house edge of 5.26 percent even though you lose 97.37 percent of the time comes in the payoff, of course. Winning single-number bets are paid at 35-1 odds. If it was a truly even bet, you'd be paid 37-1.
The difference between the payoff and the true odds is the key to the house edge. Here's the way it works.
Let's say you bet $10 on 17 on each spin of a perfect sequence in which each number turns up once. You risk a total of $380. On your one win, you get back $360 --- $350 in winnings for the 35-1 payoff, plus the return of your $10 wager on that spin.
That means the house has kept $20 of your $380 in wagers. Divide 20 by 380, and you get .0526. Multiply by that by 100 to get percent, and you see the house has kept 5.26 percent of the money you've wagered.
That's the house edge on single number bets.
It's simple enough to do the same for place bets or proposition wagers in craps, or the player bet in baccarat, or spaces on the Big Six wheel. The house edge is not based on the frequency of winning hands alone, nor is it based solely on the payoffs on winning wagers. Nor is a game with frequent winners necessarily one with a low house edge, nor a game with low payoffs per win a high house-edge proposition.
From a player's perspective, it's not how often you win, nor how much that counts, it's how much how often, working together.
Friday, July 5, 2013
Odd streaks, past results and future outcomes
For about a lifetime now, I've been telling gamblers that in most
games, past results have no effect on future outcomes. (Blackjack is an
exception, since each card dealt out changes the composition of the
remaining deck, altering the odds of the game.)
The roulette ball has landed on eight black numbers in a row? The chances of the next one being black are still 18 in 38. The craps shooter has gone a dozen rolls without a 7? Unless you're dealing with a controlled roller, the chances of the next roll being a 7 are 1 in 6, same as always. You've just hit a big slot jackpot? The odds against the big jackpot combination turning up on the next spin are the same as the spin before.
From time to time, I'm asked how that possibly can be. If in the long run, 18 of every 38 spins of the roulette wheel will be red, and there have been eight black numbers in a row, shouldn't you be betting on red? If there have been a dozen craps rolls without a 7, isn't 7 "due"? After all, in the long run, one of every six rolls will be a 7.
The answer is that there doesn't have to be any makeup time. In any game, there will be unusual streaks that seem to defy the odds. Casinos and their customers count on that. Without such streaks, there would be no winners --- we'd all just be handing over our money at a prescribed percentage.
Eventually, such streaks just fade into statistical insignificance, overwhelmed by the sheer number of trials that go on in casinos.
For a simple example of how all this works, I like to use another chance event: flipping a coin. Just as in rolling the dice, spinning the roulette wheel or pulling the slot handle, past coin flips have no affect on future outcomes. There's a 50-50 chance of heads or tails on every flip, regardless of what has gone on before.
This came up recently on an Internet message board in which I participate in the odd discussion --- the odder, the better. The manager of a softball team said a coin flip determined who was the home team, and that he'd lost 13 consecutive flips. What were the odds?
On a 50-50 event like flipping a coin, calculating the odds is easy. Your chances of losing a single flip are 1 in 2. Your chances of losing 13 in a row are 1 in 2 to the 13th power --- start with 2, then multiply by 2 12 times. The answer is 1 in 8,192. In 8,192 sets of 13 coin flips, on the average you'll lose all 13 of them once.
Another poster on this message board suggested you could improve your odds with some judicious selections. "If it hits seven heads in a row, isn't it more likely to come up tails the next time, because of the law of averages?"
No, the odds never change. If heads come up seven times in a row, the odds on the next flip are still even. There never has to be a makeup period --- in the long run, any unusual streaks just fade into statistical insignificance.
"But in the long run, things even out," the poster said. "That leads me to believe that, since you know things will even out, you're more likely to hit the other side if there's been a run on one side."
Recognize that train of thought? That's the same thing as a roulette player who thinks that after eight black numbers, red is due, or a craps player who thinks that after a dozen rolls without a 7, the shooter must be due to roll a 7.
But any evening out to be done is purely statistical, whether we're talking roulette, craps, slots or coin flips.
Let's say the coin flipper starts with 7 heads in a row. At that point, 100 percent of flips have been heads. The expectation is that 50 percent should be heads, so it appears there's evening up to do.
Now let's say future flips come up exactly 50 percent heads and 50 percent tails. (Things rarely come out quite so neatly, of course.) After another 100 flips, 57 have been heads, and 50 tails. Now only 53.3 percent of the flips have been heads, only 3.3 percent above expected average. On thousand flips after the first seven, we have 507 heads and 500 tails. 50.3 percent have been heads. One million flips after the first 7, 500,007, or 50.000035 percent, have been heads.
There has been no "making up," period, but we're right on 50 percent heads and 50 percent tails. The original streak of seven heads has just faded against the statistical background.
Streaks happen, and if you're on the winning side, streaks are meant to savor. But there doesn't have to be any equal but opposite streak to make the odds come out right. Given enough trials, normal results from the streak onward are enough to keep the games on track.
The roulette ball has landed on eight black numbers in a row? The chances of the next one being black are still 18 in 38. The craps shooter has gone a dozen rolls without a 7? Unless you're dealing with a controlled roller, the chances of the next roll being a 7 are 1 in 6, same as always. You've just hit a big slot jackpot? The odds against the big jackpot combination turning up on the next spin are the same as the spin before.
From time to time, I'm asked how that possibly can be. If in the long run, 18 of every 38 spins of the roulette wheel will be red, and there have been eight black numbers in a row, shouldn't you be betting on red? If there have been a dozen craps rolls without a 7, isn't 7 "due"? After all, in the long run, one of every six rolls will be a 7.
The answer is that there doesn't have to be any makeup time. In any game, there will be unusual streaks that seem to defy the odds. Casinos and their customers count on that. Without such streaks, there would be no winners --- we'd all just be handing over our money at a prescribed percentage.
Eventually, such streaks just fade into statistical insignificance, overwhelmed by the sheer number of trials that go on in casinos.
For a simple example of how all this works, I like to use another chance event: flipping a coin. Just as in rolling the dice, spinning the roulette wheel or pulling the slot handle, past coin flips have no affect on future outcomes. There's a 50-50 chance of heads or tails on every flip, regardless of what has gone on before.
This came up recently on an Internet message board in which I participate in the odd discussion --- the odder, the better. The manager of a softball team said a coin flip determined who was the home team, and that he'd lost 13 consecutive flips. What were the odds?
On a 50-50 event like flipping a coin, calculating the odds is easy. Your chances of losing a single flip are 1 in 2. Your chances of losing 13 in a row are 1 in 2 to the 13th power --- start with 2, then multiply by 2 12 times. The answer is 1 in 8,192. In 8,192 sets of 13 coin flips, on the average you'll lose all 13 of them once.
Another poster on this message board suggested you could improve your odds with some judicious selections. "If it hits seven heads in a row, isn't it more likely to come up tails the next time, because of the law of averages?"
No, the odds never change. If heads come up seven times in a row, the odds on the next flip are still even. There never has to be a makeup period --- in the long run, any unusual streaks just fade into statistical insignificance.
"But in the long run, things even out," the poster said. "That leads me to believe that, since you know things will even out, you're more likely to hit the other side if there's been a run on one side."
Recognize that train of thought? That's the same thing as a roulette player who thinks that after eight black numbers, red is due, or a craps player who thinks that after a dozen rolls without a 7, the shooter must be due to roll a 7.
But any evening out to be done is purely statistical, whether we're talking roulette, craps, slots or coin flips.
Let's say the coin flipper starts with 7 heads in a row. At that point, 100 percent of flips have been heads. The expectation is that 50 percent should be heads, so it appears there's evening up to do.
Now let's say future flips come up exactly 50 percent heads and 50 percent tails. (Things rarely come out quite so neatly, of course.) After another 100 flips, 57 have been heads, and 50 tails. Now only 53.3 percent of the flips have been heads, only 3.3 percent above expected average. On thousand flips after the first seven, we have 507 heads and 500 tails. 50.3 percent have been heads. One million flips after the first 7, 500,007, or 50.000035 percent, have been heads.
There has been no "making up," period, but we're right on 50 percent heads and 50 percent tails. The original streak of seven heads has just faded against the statistical background.
Streaks happen, and if you're on the winning side, streaks are meant to savor. But there doesn't have to be any equal but opposite streak to make the odds come out right. Given enough trials, normal results from the streak onward are enough to keep the games on track.
Monday, June 10, 2013
Do casinos make their profit from winning players?
Q. Sitting in the buffet, I caught a snippet of conversation that I was wondering if you could explain. (I wasn't listening in, they were so loud I couldn't help hearing.) One guy was saying that the casino really makes its money off the winners, and the other guy said something like, "Oh really? You mean we pay for all this when we win?" That doesn't really make sense to me.A. Kind of leaves you wondering what kind of gambling palaces they could build if everybody won, doesn't it? If the casino makes money off the winners, then more winners must mean more profits, right?
But seriously, there is a way of looking at how the casino makes its money that looks at casino profits as a tax on the winners. Casino games make money because they pay the winners at less than true odds. If 38 people are sitting at a double-zero roulette table and each bet $1 on a different number on a single spin, the 37 losers each will lose their buck, and the one winner will be paid at 35-1 odds and walk away with $36. If the casino was paying true odds, the one winner should be paid at 37-1 odds and walk away with $38. The casino profit is the $2 not paid to the winner that he'd get if true odds were paid.
Same deal with sports betting. In most sports books, you have to put down 10 percent vigorish on top of your bet. Let's say you and I are betting on the same football game, with me betting on Team A and you on Team B. We each intend to bet $100, but we have to pay the vig, so we actually each bet $110. When my team wins --- hey, it's my example; I get to win --- you lose your $110 bet, but I'm paid only $100, along with the return of my $110 wager. The casino profit is the $10 it didn't pay me on my winning bet.
Sometimes the paying of winners at less than true odds is disguised a bit. In baccarat, for instance, bets on banker win more often than they lose, and bets seem to be paid at even money. However, bettors have to pay a 5 percent commission on winning bets, so winners aren't really paid at 1-1; they're paid at (1 minus .05)-1, and that's less than the true odds of winning the wager.
So it goes with every casino game. There are going to be winners, and there are going to be losers, but the house will make money because it pays winners less than the true odds of winning the bet.
Friday, May 17, 2013
My roulette system? Play for fun
Over the years, I've debunked a fair number of roulette systems.
There's the Martingale, where you double your bet after each loss. Hazardous to your bankroll. Bets get very large, very fast. Even if you can afford the action, you'll will bump up against table maximums often enough to sink the system.
There's the cancellation, where you start by writing three numbers, the sum equaling your win goal for the sequence. In a three-number cancellation with a win goal of three units, you'd write 1, 1, 1. Your first bet is the sum of the end numbers, so you start with a two-unit bet. A win cancels the end number --- that's the cancellation part --- so your next wager ins the remaining bet. Win that, cancel out the number, and you've won your goal.
What if you lose? You then write your wager in units at the end of your number sequence. Start with 1, 1, 1, wager two units and lose, and you're left with 1, 1, 1, 2. Your next wager is three units --- the sum of the two end numbers.
The problem? You're still increasing wagers as you lose. It's not as dangerous a system as the Martingale, but a few losses in a row stretches out the sequence, and it's not unusual for your row of numbers to get so long it'd take an unusual hot streak to get you back to even.
One close friend likes to extend play at roulette by betting on black plus an equal amount on the third column. Eight of the numbers in the third column are red, so my friend covers 26 of the 38 numbers --- all 18 black numbers plus eight red. If a black in the first two columns shows up, he breaks even, winning on black but losing the column bet. If one of his eight reds turns up, he makes a one-unit profit, winning a 2-1 payoff on the column while losing on black. But if the ball lands on one of the four third-column blacks, he wins triple --- even money on black, plus 2-1 column.
Of course, there's the pesky matter of the 10 red numbers he doesn't cover, plus 0 and 00. Any of those dozen numbers bring a double loss.
Undermining all roulette systems is that the house edge never rests. Whether you're betting red or black, dozens or columns, single numbers or three-number streets, that 5.26 percent house edge is always working against you. The exception is if your system includes the five-number bet on 0, 00, 1, 2 and 3. Then a little higher house edge is working against you, since the house has a 7.89 percent advantage on that bet.
Still, few players just throw their chips out willy-nilly when they play roulette. Nearly everyone uses a system of some sort, whether it's in how they choose their numbers, or in how they raise or lower their bets.
My friend who likes the black-plus-third-column system pressed me for my system. "Come on," he said.
"Everybody has a system. What do you do?"
And I do have a system. A really easy one. I play family birthdays. So does my wife. When we play together, we're usually on different numbers. I play her birthday, and she plays mine.
Given a balanced wheel, no number is any more likely than any other to come up, so why not have some fun? It might even produce a memorable moment.
It did for me one day in Las Vegas, playing at a wheel with a $1 minimum bet, and with 25-cent chips available. It was my birthday, so I was betting on myself. I put a chip on No. 29, and surrounded it with a chip on each of the corners and splits surrounding it.
I had a nice streak. No 29s, but the two-number splits, paying 17-1, and four-number corners, paying 8-1, were hitting regularly. My stack was growing, and I increased to two chips on each bet.
I heard the ball drop, and the dealer said, "Uh-oh. Here we go."
It was No. 29.
The four corner bets each brought me 16 chips in winnings. The four splits each brought 34. The single number bet brought 70. Suddenly I had 270 extra chips in front of me, and my nine two-chip bets were still on the table.
The next number: 29. I raked in another 270 chips.
That was the end of the streak. The second 29 was followed by an 11. I exchanged my roulette chips for casino chips, tipped the dealer and left with a profit of more than $125.
When I told my systems-playing friend that story, he said, "Don't you wish you were playing with dollar chips? Too bad it was only quarters."
I told him I had no such wishes. I play roulette for relaxation, and I play only at low-limit tables. I was thrilled to walk away with such a profit.
Besides, I told him, I know what the house edge is on that system, and I don't care to bet too much money against that kind of an edge.
In roulette, the magic number for the house is almost always 5.26.
There's the Martingale, where you double your bet after each loss. Hazardous to your bankroll. Bets get very large, very fast. Even if you can afford the action, you'll will bump up against table maximums often enough to sink the system.
There's the cancellation, where you start by writing three numbers, the sum equaling your win goal for the sequence. In a three-number cancellation with a win goal of three units, you'd write 1, 1, 1. Your first bet is the sum of the end numbers, so you start with a two-unit bet. A win cancels the end number --- that's the cancellation part --- so your next wager ins the remaining bet. Win that, cancel out the number, and you've won your goal.
What if you lose? You then write your wager in units at the end of your number sequence. Start with 1, 1, 1, wager two units and lose, and you're left with 1, 1, 1, 2. Your next wager is three units --- the sum of the two end numbers.
The problem? You're still increasing wagers as you lose. It's not as dangerous a system as the Martingale, but a few losses in a row stretches out the sequence, and it's not unusual for your row of numbers to get so long it'd take an unusual hot streak to get you back to even.
One close friend likes to extend play at roulette by betting on black plus an equal amount on the third column. Eight of the numbers in the third column are red, so my friend covers 26 of the 38 numbers --- all 18 black numbers plus eight red. If a black in the first two columns shows up, he breaks even, winning on black but losing the column bet. If one of his eight reds turns up, he makes a one-unit profit, winning a 2-1 payoff on the column while losing on black. But if the ball lands on one of the four third-column blacks, he wins triple --- even money on black, plus 2-1 column.
Of course, there's the pesky matter of the 10 red numbers he doesn't cover, plus 0 and 00. Any of those dozen numbers bring a double loss.
Undermining all roulette systems is that the house edge never rests. Whether you're betting red or black, dozens or columns, single numbers or three-number streets, that 5.26 percent house edge is always working against you. The exception is if your system includes the five-number bet on 0, 00, 1, 2 and 3. Then a little higher house edge is working against you, since the house has a 7.89 percent advantage on that bet.
Still, few players just throw their chips out willy-nilly when they play roulette. Nearly everyone uses a system of some sort, whether it's in how they choose their numbers, or in how they raise or lower their bets.
My friend who likes the black-plus-third-column system pressed me for my system. "Come on," he said.
"Everybody has a system. What do you do?"
And I do have a system. A really easy one. I play family birthdays. So does my wife. When we play together, we're usually on different numbers. I play her birthday, and she plays mine.
Given a balanced wheel, no number is any more likely than any other to come up, so why not have some fun? It might even produce a memorable moment.
It did for me one day in Las Vegas, playing at a wheel with a $1 minimum bet, and with 25-cent chips available. It was my birthday, so I was betting on myself. I put a chip on No. 29, and surrounded it with a chip on each of the corners and splits surrounding it.
I had a nice streak. No 29s, but the two-number splits, paying 17-1, and four-number corners, paying 8-1, were hitting regularly. My stack was growing, and I increased to two chips on each bet.
I heard the ball drop, and the dealer said, "Uh-oh. Here we go."
It was No. 29.
The four corner bets each brought me 16 chips in winnings. The four splits each brought 34. The single number bet brought 70. Suddenly I had 270 extra chips in front of me, and my nine two-chip bets were still on the table.
The next number: 29. I raked in another 270 chips.
That was the end of the streak. The second 29 was followed by an 11. I exchanged my roulette chips for casino chips, tipped the dealer and left with a profit of more than $125.
When I told my systems-playing friend that story, he said, "Don't you wish you were playing with dollar chips? Too bad it was only quarters."
I told him I had no such wishes. I play roulette for relaxation, and I play only at low-limit tables. I was thrilled to walk away with such a profit.
Besides, I told him, I know what the house edge is on that system, and I don't care to bet too much money against that kind of an edge.
In roulette, the magic number for the house is almost always 5.26.
Monday, May 6, 2013
Time, money and the house edge
If you've been my casinos columns for very long, you've seen the
numbers a hundred times: The house has a 5.26 percent edge on American
double-zero roulette, a 1.41 percent edge on the pass line at craps, a 2
to 2.5 percent edge against the average blackjack player, but only a
half-percent or so edge against a basic strategy player.
Chances are you use those numbers as a rough comparison of games. Which give you the better shot to win? Which are nothing more than "house" games? And that's fine. You do have a much better shot to win if you're betting the pass line at craps than if you're playing roulette.
But those numbers are also statistical averages. They don't mean that every time you bet $100 on the pass line, you're going to lose $1.41, or even that every 100 times you bet $100 on pass, you'll lose $141.
If the losses were that regular, and that certain in the short term, no one would play. Even on the casino games with the highest house edges, results are volatile enough that players will win sometimes.
Given enough trials, though, the house edge will hold up, and the more trials there are, the closer the results will be to giving the casino its expected profit.
One of the more colorful descriptions of how this all works came from the late Peter Griffin, author of the classic The Theory of Blackjack. I'd been invited to spend a week as a student at the Harrah's Institute for Casino Entertainment in Las Vegas, a crash course in casino operations designed to give gaming basics to non-gaming employees Harrah's had marked as up-and-comers. Griffin was a guest instructor.
Imagine a situation, he told us, in which a busload of roulette players have finished for the day and are in the waiting room, waiting to board for the trip home. They decide they have time for one last spin of the wheel if each of the 100 players gives $100 to a casino manager with instructions to place the bets. (This takes place in a jurisdiction with a particularly lenient gaming board, I might add.)
The manager puts all the money --- $10,000 worth --- in a big box, and climbs a staircase to a balcony overlooking the waiting room. He then takes out $526 --- more or less --- and dumps the rest of the money back over the railing to the waiting bus group.
Players scramble for the money. Some get back their $100. Most get back less. Some get more --- a few get considerably more.
There are winners. There are losers. And the house has its 5.26 percent.
Slot machines work the same way. When we say quarter slots at a given casino return an average of 93 percent to players, that's just another way of saying the house edge on those machines is 7 percent. If you play $100 through a quarter slot at that casino, are you likely to wind up with precisely $93? No, most of the time you'll wind up with less. Much of a slot machine's long-term return is tied up in larger jackpots, so sometimes you'll win hundreds, or even thousands of dollars for that $100 in play. You may win big, or more often lose fast, but on balance over hundreds of thousands of plays, the house will get its 7 percent.
If you go to the casino and play a couple of hours on a three-reel quarter slot, you might spin the reels 1,000 times --- 500 plays per hour is a busy, but not hectic, pace. With a three-coin maximum bet, you're risking $750. If the machines in that casino return 93 percent, your expected average loss is $52.50, but you won't land precisely on that figure very often. Most of the time, you'll lose somewhat more than that. Less often, you'll get a big hit or a few medium-sized wins and walk away a winner. In one short trip to the casino, there's no telling what your results will be.
But let's take a page out of Griffin's book and say you're on a bus trip with 100 players all spending a couple of hours on those 93-percent, quarter slots, all betting 75 cents a spin for a total of 1,000 spins each. Now your group is setting the reels spinning a total of 100,000 times, and the casino can almost count on getting something close to its 7 percent take.
There almost certainly will be a winner, or several winners, in your group. There also almost certainly will be those who lose fast and wind up dropping a couple of hundred dollars. The majority will lose some of their money. All told, your group is likely to leave behind a total very close to $5,250 on its $75,000 worth of wagers.
There are winners. There are losers. And the house has its 7 percent.
That's the way it is when you look around any busy casino. A few are winning. Most are paying for their day's entertainment. It's the hope that this time we'll be one of the winners that keeps us going.
Chances are you use those numbers as a rough comparison of games. Which give you the better shot to win? Which are nothing more than "house" games? And that's fine. You do have a much better shot to win if you're betting the pass line at craps than if you're playing roulette.
But those numbers are also statistical averages. They don't mean that every time you bet $100 on the pass line, you're going to lose $1.41, or even that every 100 times you bet $100 on pass, you'll lose $141.
If the losses were that regular, and that certain in the short term, no one would play. Even on the casino games with the highest house edges, results are volatile enough that players will win sometimes.
Given enough trials, though, the house edge will hold up, and the more trials there are, the closer the results will be to giving the casino its expected profit.
One of the more colorful descriptions of how this all works came from the late Peter Griffin, author of the classic The Theory of Blackjack. I'd been invited to spend a week as a student at the Harrah's Institute for Casino Entertainment in Las Vegas, a crash course in casino operations designed to give gaming basics to non-gaming employees Harrah's had marked as up-and-comers. Griffin was a guest instructor.
Imagine a situation, he told us, in which a busload of roulette players have finished for the day and are in the waiting room, waiting to board for the trip home. They decide they have time for one last spin of the wheel if each of the 100 players gives $100 to a casino manager with instructions to place the bets. (This takes place in a jurisdiction with a particularly lenient gaming board, I might add.)
The manager puts all the money --- $10,000 worth --- in a big box, and climbs a staircase to a balcony overlooking the waiting room. He then takes out $526 --- more or less --- and dumps the rest of the money back over the railing to the waiting bus group.
Players scramble for the money. Some get back their $100. Most get back less. Some get more --- a few get considerably more.
There are winners. There are losers. And the house has its 5.26 percent.
Slot machines work the same way. When we say quarter slots at a given casino return an average of 93 percent to players, that's just another way of saying the house edge on those machines is 7 percent. If you play $100 through a quarter slot at that casino, are you likely to wind up with precisely $93? No, most of the time you'll wind up with less. Much of a slot machine's long-term return is tied up in larger jackpots, so sometimes you'll win hundreds, or even thousands of dollars for that $100 in play. You may win big, or more often lose fast, but on balance over hundreds of thousands of plays, the house will get its 7 percent.
If you go to the casino and play a couple of hours on a three-reel quarter slot, you might spin the reels 1,000 times --- 500 plays per hour is a busy, but not hectic, pace. With a three-coin maximum bet, you're risking $750. If the machines in that casino return 93 percent, your expected average loss is $52.50, but you won't land precisely on that figure very often. Most of the time, you'll lose somewhat more than that. Less often, you'll get a big hit or a few medium-sized wins and walk away a winner. In one short trip to the casino, there's no telling what your results will be.
But let's take a page out of Griffin's book and say you're on a bus trip with 100 players all spending a couple of hours on those 93-percent, quarter slots, all betting 75 cents a spin for a total of 1,000 spins each. Now your group is setting the reels spinning a total of 100,000 times, and the casino can almost count on getting something close to its 7 percent take.
There almost certainly will be a winner, or several winners, in your group. There also almost certainly will be those who lose fast and wind up dropping a couple of hundred dollars. The majority will lose some of their money. All told, your group is likely to leave behind a total very close to $5,250 on its $75,000 worth of wagers.
There are winners. There are losers. And the house has its 7 percent.
That's the way it is when you look around any busy casino. A few are winning. Most are paying for their day's entertainment. It's the hope that this time we'll be one of the winners that keeps us going.
Monday, April 29, 2013
Does the house make its money off winners?
Q. Sitting in the buffet, I caught a snippet of conversation that I was wondering if you could explain. (I wasn't listening in, they were so loud I couldn't help hearing.) One guy was saying that the casino really makes its money off the winners, and the other guy said something like, "Oh really? You mean we pay for all this when we win?" That doesn't really make sense to me.A. Kind of leaves you wondering what kind of gambling palaces they could build if everybody won, doesn't it? If the casino makes money off the winners, then more winners must mean more profits, right?
But seriously, there is a way of looking at how the casino makes its money that looks at casino profits as a tax on the winners. Casino games make money because they pay the winners at less than true odds. If 38 people are sitting at a double-zero roulette table and each bet $1 on a different number on a single spin, the 37 losers each will lose their buck, and the one winner will be paid at 35:1 odds and walk away with $36. If the casino was paying true odds, the one winner should be paid at 37:1 odds and walk away with $38. The casino profit is the $2 not paid to the winner that he'd get if true odds were paid.
Same deal with sports betting. In most sports books, you have to put down 10 percent vigorish on top of your bet. Let's say you and I are betting on the same football game, with me betting on Team A and you on Team B. We each intend to bet $100, but we have to pay the vigorish, so we actually each bet $110. When my team wins --- hey, it's my example; I get to win --- you lose your $110 bet, but I'm paid only $100, along with the return of my $110 wager. The casino profit is the $10 it didn't pay me on my winning bet.
Sometimes the paying of winners at less than true odds is disguised a bit. In baccarat, for instance, bets on banker win more often than they lose, and bets seem to be paid at even money. However, bettors have to pay a 5 percent commission on winning bets, so winners aren't really paid at 1:1; they're paid at (1 minus .05):1, and that's less than the true odds of winning the wager.
So it goes with every casino game. There are going to be winners, and there are going to be losers, but the house will make money because it pays winners less than the true odds of winning the bet.
Tuesday, April 23, 2013
Sheep bones, gum logos and other gambling trivia
In the race to see which is more cluttered, my home office or the
corner of my mind that collects little pieces of gambling history,
well, I guess my home office wins hands down. Nonetheless, bits of
trivia are trying to escape, so let's empty a little of the clutter:
**The slang expression rolling the bones has an origin that is quite literal. Dice were carved from bones for thousands of years. It was not at all unusual in Roman times for dice to be fashioned from sheep's knuckles.
Dice have been made from wood, clay, stone, peach pits, animal horns, teeth, ivory, bronze, porcelain, even jewels. The oldest known dice with regular sides were found in northern Iraq. They're made of baked clay and date to about 3,000 B.C.
**Coin-operated gaming devices in the late 1800s included games with large revolving wheels divided into color segments. Players wagered on which color the wheel would stop. They're considered the forerunners of modern slot machines, even though they didn't have reels. The first recognizably modern three-reel slot was the Liberty Bell, invented by Charles Fey in San Francisco in 1899. The machine was so popular that for many years all slot machines were referred to as bell machines.
The bar symbol used on modern slot machines is derived from a Bell Fruit Gum logo. The gum was dispensed in slots designed by Herbert Mills in Chicago in 1910, and other fruit symbols on slots were derived from the gum flavors.
Among the most popular early slots were poker games, although the machines did not usually pay out coins. Payoffs had to come from the operator. After the introduction of the Liberty Bell, poker-based slots waned in popularity, until the invention of video poker in the 1970s.
**The game of 21 got its common nickname, blackjack, from a practice in illegal casinos in the early 1900s. Some casinos paid a bonus if a two-card 21 was made up of an ace and jack of spades. Others paid bonuses if an ace of spades was accompanied by a jack of either clubs or spades. The black jack was the key to the bonus, and became the name of the game.
Less commonly used nicknames for the game of 21 include Pontoon and Van John. Both arose in the South, probably around illegal casinos in New Orleans. Both nicknames probably are corruptions of the pronunciation of the French game vingt-un, which means "21" and is believed by some to be a blackjack forerunner.
**Horizontal gaming wheels, such as those used in roulette, were invented in England in 1720 for a game called roly-poly. Roly-poly was similar to roulette, except there were no numbers on the wheel. There were alternating white spaces and black spaces, along with a "bar black" space and a "bar white" space. The "bar" spaces were the equivalents of zero and double-zero -- if the ball landed in either space, bets on black or white lost.
Roly-poly was banned in England in 1745, but the horizontal wheel traveled well. By 1796, modern roulette was being played in France.
**The kings in decks of playing cards represent real leaders and conquerors from history, although not all had the title of king. The deck we use today is based on cards designed in 15th-century France. The king of spades represents the Biblical King David, the king of clubs represents Alexander the Great, the king of hearts represents Charlemagne and the king of diamonds represents Julius Caesar.
The four suits represent civilizations that have influenced our culture. Spades represent the Middle East of Biblical times, clubs represent Greece, diamonds represent the Roman Empire, and hearts represent the Holy Roman Empire.
Perfect for Caesars Palace, don't you think?
**The slang expression rolling the bones has an origin that is quite literal. Dice were carved from bones for thousands of years. It was not at all unusual in Roman times for dice to be fashioned from sheep's knuckles.
Dice have been made from wood, clay, stone, peach pits, animal horns, teeth, ivory, bronze, porcelain, even jewels. The oldest known dice with regular sides were found in northern Iraq. They're made of baked clay and date to about 3,000 B.C.
**Coin-operated gaming devices in the late 1800s included games with large revolving wheels divided into color segments. Players wagered on which color the wheel would stop. They're considered the forerunners of modern slot machines, even though they didn't have reels. The first recognizably modern three-reel slot was the Liberty Bell, invented by Charles Fey in San Francisco in 1899. The machine was so popular that for many years all slot machines were referred to as bell machines.
The bar symbol used on modern slot machines is derived from a Bell Fruit Gum logo. The gum was dispensed in slots designed by Herbert Mills in Chicago in 1910, and other fruit symbols on slots were derived from the gum flavors.
Among the most popular early slots were poker games, although the machines did not usually pay out coins. Payoffs had to come from the operator. After the introduction of the Liberty Bell, poker-based slots waned in popularity, until the invention of video poker in the 1970s.
**The game of 21 got its common nickname, blackjack, from a practice in illegal casinos in the early 1900s. Some casinos paid a bonus if a two-card 21 was made up of an ace and jack of spades. Others paid bonuses if an ace of spades was accompanied by a jack of either clubs or spades. The black jack was the key to the bonus, and became the name of the game.
Less commonly used nicknames for the game of 21 include Pontoon and Van John. Both arose in the South, probably around illegal casinos in New Orleans. Both nicknames probably are corruptions of the pronunciation of the French game vingt-un, which means "21" and is believed by some to be a blackjack forerunner.
**Horizontal gaming wheels, such as those used in roulette, were invented in England in 1720 for a game called roly-poly. Roly-poly was similar to roulette, except there were no numbers on the wheel. There were alternating white spaces and black spaces, along with a "bar black" space and a "bar white" space. The "bar" spaces were the equivalents of zero and double-zero -- if the ball landed in either space, bets on black or white lost.
Roly-poly was banned in England in 1745, but the horizontal wheel traveled well. By 1796, modern roulette was being played in France.
**The kings in decks of playing cards represent real leaders and conquerors from history, although not all had the title of king. The deck we use today is based on cards designed in 15th-century France. The king of spades represents the Biblical King David, the king of clubs represents Alexander the Great, the king of hearts represents Charlemagne and the king of diamonds represents Julius Caesar.
The four suits represent civilizations that have influenced our culture. Spades represent the Middle East of Biblical times, clubs represent Greece, diamonds represent the Roman Empire, and hearts represent the Holy Roman Empire.
Perfect for Caesars Palace, don't you think?
Monday, April 22, 2013
Can playing the streaks help in roulette?
Q. When I play roulette, I wait until the same color hits three times in a row, then I bet the opposite color. If there have been three black colors, I bet red, and if there have been three red colors, I bet black. My friend says he'd go the opposite way, that if there are three red numbers in a row, he'd think red was hot and stay with it. Who's right?A. To use one of the favorite phrases of gaming analysts, the wheel has no memory. It doesn't know if the last three numbers have been red, black, mixed or polka dotted. Past results have no effect on future outcome. Regardless of what happened in the last few spins, on the next spin there's a 47.37 percent chance the number will be red, 47.37 percent that it will be black and 5.26 percent that it will be a green 0 or 00.
Is there an advantage to your system? Sure. If you wait to bet until three numbers of the same color turn up, you do a lot more watching than betting.Watching costs less.
Thursday, April 18, 2013
Separate gambling fact from fiction
Casino lore is full of myths, legends and superstitions.
That's natural enough. Few players understand the math, the odds and percentages that explain what's really going on in the casino. It's easier to blame that losing streak on someone else's poor play, and more fun to claim our own smart play led to a big win, than to make sense of the eternal tide of random results.
I try to bust casino myths from time to time, but they're persistent. Rarely does a week go by in which I don't hear from a reader about one long-held misconception or another. Let's take a look at some of the most common casino myths:
MYTH: Other players hurt you at the blackjack table.
FACT: Other players sometimes hurt you, but help you just as often. Their play has no effect on your long-term results.
No one knows what cards are coming next, nor do we know what card the dealer has face down. The player you think is taking the dealer's bust card may actually be taking a card that would have given the dealer a pat hand.
Let's say the player at third base - the last player to make a hit/stand decision - has a hard 16, and the dealer has a 6 face up. If the player follows basic strategy, he'll stand and the dealer will get the next card. If he makes a bad play and hits instead, the dealer gets the second card down.
Which would you rather the dealer have, the next card or the second one? Answer: It makes no difference. You don't know what the cards are, and either is just as likely to be the one that busts the dealer - or makes his hand.
MYTH: Hot craps tables are likely to stay hot; cold craps tables are likely to stay cold.
FACT: Unless you've found a rare player who can control the dice, every roll is an independent trial. Past outcomes have no affect on future results.
Several years ago, I tried an experiment in which I waited for two consecutive passes, then tracked the next decision. Of the next 1,000 sequences, 489 were passes - almost dead on the 494 average expected by random chance. No evidence there of hot streaks continuing. At the same time, I charted 1,000 sequences starting with two don't passes. The result: 470 wins for don't bettors, 493 losses and 37 pushes on 12. No evidence for cold tables, either.
Do hot and cold streaks occur at the craps table? Sure, just as they do in any game of chance. That's a natural outgrowth of probability. Can we predict when the streaks are coming? No. All a hot streak means is that the table has been hot in the past. That streak has no value in predicting future results. If it did, we could all stand and watch, waiting for a hot roll, then jump on and get rich.
MYTH: If the same roulette number comes up three or four times in a row, it's time to jump off that number - it's not "due" again for hours.
FACT: Numbers are never "due" or "not due." On an American wheel with both a 0 and a 00, the odds against any given number turning up on the next spin are 37-1. That's true whether the number just hit on the last spin, the last four spins, or if it hasn't hit at all in a couple of hours. Just as at the craps table, each trial is independent, and past outcomes have no effect on future results.
Rarely, a wheel may be biased, with some numbers turning up more often than expected by random chance. The wheel may be off balance, there may be a warp or a loose fret. In such cases, a number that has been showing up frequently may continue to hit more than once per 38 spins. Finding a wheel bias is painstaking work that most of us won't do. Still, the long shot that a wheel is biased gives us more reason to stay with a repeating number than to jump off.
MYTH: The casino can reward slot players by pushing a button to let them win a jackpot.
FACT: There is no jackpot button in the casino front office, the surveillance room or anywhere else. The casino has no control over when jackpots hit.
The closest the casino has to control is in programming it orders from the slot machine manufacturer. The manufacturer offers chips that will make a game pay out at different levels - the casino might order an 89 percent chip, or a 92 percent chip on the same penny game. Some games might pay the top jackpot an average of once per 10,000 pulls; on others the jackpot might hit only once per 20,000, 100,000, even 1 million or more pulls.
All those are long-term averages. Given millions of pulls, those averages will hold up. But there's no way to predict, or change, what will happen on any specific spin of the reels. Each spin is as random as humans can program a computer to be. A casino can't make a jackpot appear on the next spin. There will be winners and losers. The casino can't determine who will be which. It just knows the losers will more than balance out the winners.
That's natural enough. Few players understand the math, the odds and percentages that explain what's really going on in the casino. It's easier to blame that losing streak on someone else's poor play, and more fun to claim our own smart play led to a big win, than to make sense of the eternal tide of random results.
I try to bust casino myths from time to time, but they're persistent. Rarely does a week go by in which I don't hear from a reader about one long-held misconception or another. Let's take a look at some of the most common casino myths:
MYTH: Other players hurt you at the blackjack table.
FACT: Other players sometimes hurt you, but help you just as often. Their play has no effect on your long-term results.
No one knows what cards are coming next, nor do we know what card the dealer has face down. The player you think is taking the dealer's bust card may actually be taking a card that would have given the dealer a pat hand.
Let's say the player at third base - the last player to make a hit/stand decision - has a hard 16, and the dealer has a 6 face up. If the player follows basic strategy, he'll stand and the dealer will get the next card. If he makes a bad play and hits instead, the dealer gets the second card down.
Which would you rather the dealer have, the next card or the second one? Answer: It makes no difference. You don't know what the cards are, and either is just as likely to be the one that busts the dealer - or makes his hand.
MYTH: Hot craps tables are likely to stay hot; cold craps tables are likely to stay cold.
FACT: Unless you've found a rare player who can control the dice, every roll is an independent trial. Past outcomes have no affect on future results.
Several years ago, I tried an experiment in which I waited for two consecutive passes, then tracked the next decision. Of the next 1,000 sequences, 489 were passes - almost dead on the 494 average expected by random chance. No evidence there of hot streaks continuing. At the same time, I charted 1,000 sequences starting with two don't passes. The result: 470 wins for don't bettors, 493 losses and 37 pushes on 12. No evidence for cold tables, either.
Do hot and cold streaks occur at the craps table? Sure, just as they do in any game of chance. That's a natural outgrowth of probability. Can we predict when the streaks are coming? No. All a hot streak means is that the table has been hot in the past. That streak has no value in predicting future results. If it did, we could all stand and watch, waiting for a hot roll, then jump on and get rich.
MYTH: If the same roulette number comes up three or four times in a row, it's time to jump off that number - it's not "due" again for hours.
FACT: Numbers are never "due" or "not due." On an American wheel with both a 0 and a 00, the odds against any given number turning up on the next spin are 37-1. That's true whether the number just hit on the last spin, the last four spins, or if it hasn't hit at all in a couple of hours. Just as at the craps table, each trial is independent, and past outcomes have no effect on future results.
Rarely, a wheel may be biased, with some numbers turning up more often than expected by random chance. The wheel may be off balance, there may be a warp or a loose fret. In such cases, a number that has been showing up frequently may continue to hit more than once per 38 spins. Finding a wheel bias is painstaking work that most of us won't do. Still, the long shot that a wheel is biased gives us more reason to stay with a repeating number than to jump off.
MYTH: The casino can reward slot players by pushing a button to let them win a jackpot.
FACT: There is no jackpot button in the casino front office, the surveillance room or anywhere else. The casino has no control over when jackpots hit.
The closest the casino has to control is in programming it orders from the slot machine manufacturer. The manufacturer offers chips that will make a game pay out at different levels - the casino might order an 89 percent chip, or a 92 percent chip on the same penny game. Some games might pay the top jackpot an average of once per 10,000 pulls; on others the jackpot might hit only once per 20,000, 100,000, even 1 million or more pulls.
All those are long-term averages. Given millions of pulls, those averages will hold up. But there's no way to predict, or change, what will happen on any specific spin of the reels. Each spin is as random as humans can program a computer to be. A casino can't make a jackpot appear on the next spin. There will be winners and losers. The casino can't determine who will be which. It just knows the losers will more than balance out the winners.
Subscribe to:
Posts (Atom)