# Variance

If the casino has such an advantage over the player, why on Earth does anyone play the game? My guess is that most people don't have a clue they're playing a losing game. Others are so arrogant they think they can outplay the casino and turn a negative expectation into a positive, even over the long term. Others know they'll lose, but play anyway for fun and excitement. As a knowledgeable player, why should you even bother playing a game you know will beat you? As a knowledgeable player, is there any hope you can walk away a winner, at least once in a while, even though you're at a statistical disadvantage?

Craps is a game of numbers and statistics, with the house having a built-in advantage. Since craps is based on statistics, let's find a way to use statistics to our advantage. You'll never beat the casino over the long haul, but you can, indeed, beat it in the moments of time when the distribution hiccups and things go your way.

Let's talk about "variance," which is the average squared deviation of each number from the mean of a data set. Huh? Don't worry; we don't need a Harvard math degree to understand this. It's simply a measure of how spread out the data is. Let's consider the familiar coin-flip example.

Suppose we flip a coin 10,000 times. We expect heads to appear about 5,000 times and tails to appear about 5,000 times. Suppose we bet $1 on heads for each flip. If these are even-money bets, we expect to break even--or close to it after those 10,000 flips. As illustrated in one of my other articles, the house doesn't give us even money when it loses. In our coin-flip example, instead of paying us $1 for each loss, suppose they pay us only $0.96. With this built-in house advantage, our negative expectation is to lose about $200 after 10,000 flips. Here's the math. If we expect about 5,000 heads and about 5,000 tails to appear, then we expect to lose 5000 x $1 = $5000; and win 5000 x $0.96 = $4800. $5000 - $4800 = $200. This is called "negative expectation."

Now, of those 10,000 flips, suppose we focus on only 30 of them, and we continue betting on heads. Of those 30 flips, we might see heads 25 times and tails only 5 times. This data fluctuation shows that, for a limited number of flips over a short period of time, we can get lucky and experience Nirvana where things go our way. I call it a "Nirvana hiccup" in the distribution that causes a relatively high variance. In this example of only 30 flips, we win $24 for the 25 heads (i.e., 25 x $0.96 = $24), and lose $5 for the 5 tails (i.e., 5 x $1 = $5), which gives us a net win of $19. This short term variance temporarily removes the long-term negative expectation, which means there are, indeed, times when we can walk away a winner.

Although you'll lose in the long-term, there are times when you'll win because of variance. Suppose you take a three day vacation in Vegas once a year and play four one hour craps sessions each day (i.e., a total of 12 hours for the trip). You could conceivably get extremely lucky and hit that Nirvana hiccup during each session, and then go home a big winner. In that case, you go home thinking you're a genius, a craps god, invincible, a world-class gambling stud. Yeah, sure, okay. I don't recommend quitting your day job.

Now, suppose you're a Vegas local who plays an hour every day after work. In this case, it's clear that whatever few Nirvana hiccups you experience will be properly adjusted over time such that you'll lose your shirt in the long-term.

Therefore, the infrequent craps player can, indeed, consistently win if she's lucky enough to hit those Nirvana hiccups. However, the frequent long term player has no chance of coming out a winner at the end of his craps life. Part of the secret to craps is knowing how to be around for those occasional Nirvana hiccups where the dice fall your way.