WEDNESDAY MAY 22, 2013
 
More POKER
VARIANCE?
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The other day at a home game in Toronto I was complaining to my friend Carmenooch that I hadn’t seen pocket aces in over a month. “It’s statistically improbable,” I said. “The odds suggest that you should get pocket aces every 221 hands, or something like that. Well, between computer action and live games I’ve played more than a thousand hands and I haven’t caught a whiff of pocket aces. I think that’s fucked up.”

Carmenooch was bitterly amused. “You think that’s fucked up?” he said. “I haven’t seen pocket aces in over six months. And quite frankly, I’m tired of your whining.”

Well, that was a bit deflating, to say the least. I guess I wasn’t the only one running bad. But what explains such anomalies? I knew that Carmenooch was a math guy. Without further irking him – he is a big man with a big temper – I tried to ask him what accounted for this, mathematically speaking. “I really want to know,” I said.

We were between hands and Carmenooch thought about it for a moment and emerged from his gloom long enough to give me the following explanation, which he delivered in a baritone monotone: “Poker is essentially a game of mathematics and as a result players are subjected to what is called variance. In probability theory and statistics, the variance of a random variable, probability distribution or sample is a measure of statistical dispersion, averaging the squares of the deviations of its possible values from its expected value (mean). Mean describes the location of a distribution, the variance captures its scale or degree of being spread out. The unit of variance is the square of the unit of the original variable. The positive square root of the variance, called the standard deviation, has the same units as the original variable and can be easier to interpret for this reason. This definition encompasses random variables that are discrete, continuous or neither. Of all the points about which squared deviations could have been calculated, the mean produces the minimum value for the averaged sum of squared deviations. If a distribution does not have an expected value it does not have a variance either. The variance of a real-valued random variable is its second central moment, and it also happens to be its second cumulant. Just as some distributions do not have a mean, some do not have a variance. The mean exists whenever the variance exists, but not vice versa.”

Carmenooch stopped talking just as the cards arrived for the next hand. I understood not a whit of what he had just blathered. He smiled for a second. Then he looked at his cards and the smile disappeared. I checked my cards and when I saw two red aces I thought the poker gods must be listening. I promptly over-bet and everyone immediately folded. I took down the small pot and when I showed Carmenooch the aces he said, “Are you happy now? I don’t want to hear you complain for another month.”

Very next hand Carmenooch made a massive bet pre-flop and everyone folded. When he turned over black aces I started laughing. “Happy now?” I asked. Carmenooch shook his head with disgust, gathered the few chips in the pot and settled back into his gloom.

I knew something odd had just happened, though it’s difficult to define. I don’t know if it has anything to do with variance and all that math mumbo jumbo Carmenooch was spouting. But I sometimes get the feeling that the poker gods are watching and listening and that they send out funny messages now and again to let us know they are watching and listening and likely laughing at us.

Emile Frendo of the Honeymoon City is a semi-professional poker player and winner of the 2006 Pirate Poker Open Championship.

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