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.

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