What are the Chances?

Posted on Dec 4 2012 by pomomojo in Backgammon, Board Games, Poker

A large part of the joy of playing designer or luxury games is found in their visceral qualities – the beauty of the pieces or the weight of a component in your hands – but when you play a game you can also get quite involved in the mental calculations of finding the best move. In fact, if you enjoy math, then gaming is probably the hobby for you.

The most obvious place to look for numerical gymnastics would be in world of gambling or casino games and not just so you can add up all the money you’ve lost. If you are playing roulette you’ll find that all the bets available on the board are carefully calculated by odds. You can bet black or red and have close to a fifty percent chance of winning or losing, just like on a coin flip. Same goes for betting odd or even. If you pick a single number your odds are 1 in 38 on an American double zero wheel. You can double the odds by making a split bet (2 adjoining numbers) or quadruple the odds by betting a corner (4 adjoining numbers). Of course, if you want to be totally logical about the wheel, you’ll recognize that all the payouts fail to account for the two zero spaces on the wheel and, thus, always favor the house.

Math skills can actually help you win, however, in other parts of the casino. Many people think that card counting in Blackjack involves amazing feats of memorization, but all it really involves, for most people, is adding or subtracting one for each high or low card, respectively. The card counter just keeps a running count in their head of how many good cards have already been burned and, thus, the probability of the next hand containing a face card or ace that they need. Poker players, too, calculate probabilities for facedown cards based on the little information they have in their hand or the flop. In addition, it helps to be able to quickly calculate the value of your opponent’s stack of chips.

You might be surprised to see similar calculations in more traditional board games. Backgammon players are at the mercy of the dice, so one might think that they just have to constantly adjust to random data. However, probabilities show that with one man on the bar you have a very good chance of entering him into play unless your opponent has closed all but one point, whereas with two men on the bar you need five points open to have a good chance of getting them both in. For the serious Backgammon player, this means sending two men to the bar is much more powerful than sending them there one at a time.

What about in family games, like Monopoly? Sure you have to count money and roll dice, but obviously the game is simple enough for children. We all want to buy Boardwalk and Park Place, right? Well, actually, because there are several ways to get sent to Jail, there is actually a much higher probability of a player landing on the orange or red properties. In fact Park Place is the property least likely to get landed on. To come to these conclusions, statisticians had to employ complex computer algorithms that take into account dice rolls, spaces on the board, and the Community Chest and Chance decks. It turns out that the math of Monopoly is more complex than anything in the casinos!

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