Tuesday, July 23, 2013

Living the 10-7 dream at Jumer's Rock Island

My son has been taking summer classes at Northern Illinois U., coming home weekends, and Marcy and I have been driving him back to DeKalb each Sunday night. The pattern established, Marcy said to me, "One of these weeks, we should just keep driving past DeKalb and pick somewhere for an overnight. A little change of scenery."

I suggested we drive another couple of hours to Rock Island and take a look at the Jumer's casino. The last time we did that, Jumer's was on its old boat, which tells you how long its been. The new, modern Jumer's casino barge with its comfortable, up-to-date hotel opened in December 2008. I don't usually let so long pass between trips to any of the casinos reasonably close to home.

I'm not going to go into all the details, just a couple of impressions from our overnight.

**The casino had plenty of penny video slots to keep Marcy happy. For me, the real attraction was single-hand, 25-cent 10-7-5 Double Bonus Poker. There is very little playable single-hand quarter video poker in the Chicago area, where I live, so these games are a treasure, even if they are three hours from home.

They're not quite the same game you'd find in Vegas. Full-pay 10-7-5 Double Bonus pays 100.17 percent with expert play, and that's illegal in Illinois. Gaming regulations prohibit any game with a theoretical return of more than 100 percent. Never mind that very few players master the difficult Double Bonus strategy and most get 3 to 4 percent less than the break-even point. The state doesn't want any games in the casinos that will reduce its tax take, and somehow doesn't trust the bottom-line-driven operators to put profitable games on the floor.

Jumer's had full-pay 10-7-5 Double Bonus on its old boat, approved at a time gaming board test programs weren't really up to snuff. By the time the new casino barge opened, the Illinois Gaming Board was no longer approving the game. But the game was an attraction, and Jumer's wanted it in its casino. So it installed a version used as a $5 game in other markets. It's the same as full-pay Double Bonus up and down the pay table, except on the hands that pay 250 coins for a five-coin bet. On Jumer's Double Bonus, if you draw a straight flush or four 5s on up through four Kings, your payback is 239 coins instead.

On $5 machines, that means the dollar amount of the payback is $1,195 instead of $1,250, leaving it $5 below the $1,200 threshold at which IRS paperwork is required before a jackpot can be paid. More important for Jumer's quarter machines, it brings the overall theoretical payback percentage down to 99.79 percent with expert play. It's still a great game, but within Illinois' peculiar limits.

**New at Jumer's is the Blue Square Cafe, which features dishes such as the portabello fries served at Busch Stadium in St. Louis, the Stadium bratwurst with special sauce served at Miller Park in Milwaukee and the Monsters of the Midway chili served at Soldier Field in Chicago.

The connection is that all are ballparks with concessions from Delaware North, Jumer's parent company. I didn't know the connection at first, and was a little taken aback as I looked around the displays that lined the walls. There were jerseys and other memorabilia for the Chicago White Sox, Milwaukee Brewers, Detroit Tigers, Green Bay Packers ... and no Chicago Cubs. Made this old Cub fan feel quite out of place.

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.

Wednesday, July 10, 2013

Practice time brings a video poker strategy surprise

Practice may not make perfect in video poker, but it can spring some surprises on you.

I got a surprise of my own recently as I was practicing my strategy on Not So Ugly Deuces Wild. It's a game I hadn't played in some time, but I was planning a day at a casino that offered it. With expert play, NSUD pays 99.7 percent with expert play. That figured to be the best game I'd find on that trip, so I figured I'd better put in a little practice time on the WinPoker software I use.

Here's the hand I was dealt: Queen of clubs, 9 of diamonds, 8 of diamonds, 4 of spades, 3 of hearts.
High pairs don't pay off in Deuces Wild --- the pay table starts at three of a kind --- so I wasn't going to hold the low Queen. Straights in Deuces Wild pay only 2-for-1, so you need four cards before you start thinking about possible straight draws. The best straight possibilities here were only two-card sequences. Flushes pay 3-for-1 in NSUD, better than the 2-for-1 in full-pay Deuces Wild, so we do look for flushes often. Still, there were only two cards of the same suit in this hand.

Straight flushes pay 10-for-1, another step up from full-pay Deuces, which pays 9-for-1. But two cards to a straight flush? Not likely.

My conclusion: Toss the entire hand. Take a chance on five fresh cards.

The software's conclusion: A pop-up box, warning me I was making a mistake.
I changed my play to holding the 8-9 of diamonds, the only feasible play I could see here. At least it would give me starts on possible flushes, straights, and a long shot at a straight flush.

That, the computer accepted. It played out the draw, and then I clicked on the "analyze any hand" option to check out the numbers.

Sure enough, the calculations told me that holding the 8-9 of diamonds would bring an average return of 1.6075 coins per five wagered, while tossing the entire hand would bring only 1.6074 coins. I was wrong by one ten-thousandths of a percent.

Not a make-or-break hand obviously, and if you're playing in a casino and decide to toss the entire hand, well, I won't quibble. In order for holding the suited 8-9 to be the correct play, all the circumstances had to be in place.

To start with, the NSUD pay table had to be in place. In full-pay Deuces Wild, which pays less on flushes and straight flushes than the Not So Ugly variety, the best play is to discard all five cards. Even in Illinois Deuces, which matches NSUD in paying 3-for-1 on flushes but retains the full-pay return of 9-for-1 on straight flushes, the expert play is to toss the lot. The same hand in Illinois Deuces returns an average of 1.6012 coins with a five-coin discard, but only 1.5828 when holding the suited 8-9.

Beyond that, the situation regarding other possible straights and flushes had to be the same. Remember the hand: Queen of clubs, 8-9 of diamonds, 4 of spades, 3 of hearts.

If holding the two consecutive diamonds with a straight flush possibility meant tossing a third diamond, the percentages would shift. If the 3 of hearts was a diamond instead, the best play would be to throw away the entire hand. Three diamonds with no straight flush possibility wouldn't yield enough to hold them, and throwing away a third diamond would diminish flush possibilities enough that holding the 8-9 would no longer be worthwhile.

Same deal with straight possibilities. The only possible straight involving three cards in the original hand is 8-9-Queen. There are two gaps on the inside, so the only combinations that can complete the straight are 10-Jack, 10-2, Jack-2 or two wild deuces.

What if the Queen of clubs was a Jack instead? Then there would be only one gap, and the combinations that would result in a straight would increase to 7-10, 10-Queen, 7-2, Queen-2, or 2-2. Throwing away the Jack would decrease the chances of building 8-9 into a straight that here too, the best play would change to discarding all five cards.

It seems by random chance in practicing with the WinPoker software, I ran into the right hand on the right pay table to learn a little something. If I'm playing with the Not So Ugly Deuces Wild pay table, and if I'm dealt a hand with 8-9 suited, no other cards of the same suit, and no straight possibilities with less than two gaps, I'll be holding the 8-9.

That's a rare situation, and who knows when I'll run into it again. But it's a play I'll never forget, and one I'd never have noticed had I not taken the time for a little practice.

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.

Wednesday, July 3, 2013

Why video poker pros always bet max coin

Video poker games that pay in excess of 100 percent with expert play are practically non-existent in the Midwest, and even in Nevada they're getting scarcer all the time. A fellow named Jack games such as full-pay Deuces Wild and 10-7-5 Double Bonus Poker on his mind when he phone me recently.

"There are video poker pros in Nevada, right?"

Yes, I told him, although there are fewer opportunities for video poker advantage play than there used to be. And most video poker "pros" have other jobs or businesses. You have to be well-bankrolled and able to withstand the inevitable losing streaks to really press home the small edge you can get at some video poker games.

"It's that bankroll part I wanted to ask about. When a pro finds himself without enough money to bet five coins at a time, does he switch to one-coin play?"

No, I told him.

"Never? I mean, surely, it doesn't make any more sense for a pro to overbet their bankroll than it does for an average player."

Never. A short-bankrolled pro --- if he or she is smart --- is a pro who doesn't play until the bankroll is sufficiently padded.

"But surely a little one-coin play can help the pro through the tough times. Can't that help build the bankroll little by little so the pro has enough to bet it all again?"

It's more likely that one-coin play would erode the bankroll little by little until the pro hand nothing left.

"But these guys are experts, and the edge is the edge, right? They know all the expert strategy you like to write about."

Expert strategy is more than knowing which cards to hold and which cards to fold. It's also not overbetting your bankroll, and knowing that you can't get an edge on a video poker game unless you bet maximum coins. That's because of the huge jump in the royal flush payoff with five coins wagered. On most machines, a royal pays 250 coins for a one-coin wager, 500 for two, 750 for three or 1,000 for four. But on the fifth coin, the royal jumps to 4,000 coins --- essentially, you're getting 3,000 coins for the royal on that final coin wagered, but only getting 250 per coin on the first four coins.

"Royals are rare. Does that make that much difference, that a pro wouldn't even play for the smaller payoff?"

It makes all the difference in the world. Take 10-7-5 Double Bonus Poker, where full houses pay 10-for-1, flushes 7-for-1 and straights 5-for-1. With expert play, that's a 100.17 percent game. The pro squeezes out a small profit on the game, and cash back and comps are gravy. But when the royal is worth only 250 coins per coin wagered, the payback with expert play drops to 99.11 percent. It's not a beatable game.

Or take full-pay Deuces Wild. That yields a 100.76 return with expert play. But with four or fewer coins wagered, that return drops to 99.75 percent, under that magic 100 percent mark.

Betting fewer than five coins turns even the best video poker games into games that will pad the house's bankroll, not yours.

"So to get the edge, you have to bet five coins?"

Right. In video poker, the house makes ALL its money on coins Nos. 1 through 4. On the fifth coin, the player has an edge. That goes even for lower-paying games. On 8-5 Jacks or Better, the payoff on coins

Nos. 1-4 is only 96.06 percent. But on the fifth coin alone, we get back 102.26 percent, raising the overall return on the machine to 97.3 percent.

"I wish I could bet just the fifth coin."

So do I. If we got that payoff on every coin, we'd all be pros --- until the games disappeared.