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Best of Alan Krigman

Gaming Guru

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Does Pascal's Wager Have a Counterpart in Gambling

30 May 2006

In 1660, the French philosopher and mathematician, Blaise Pascal, formulated what's considered an infamous wager. A bet on the existence of God. Absent real proof, he asserted, four conditions are possible. 1) Bet that God exists and are right, you gain the infinite reward of eternal bliss. 2) Bet that God exists and are wrong, you lose nothing. 3) Bet that God doesn't exist and are right, you gain nothing. 4) Bet that God doesn't exist and are wrong, you suffer the infinite loss of eternal damnation.

Pascal concluded that the best bet was on existence. It had an upside with no downside. The opposite wager would have a downside with no upside. The choice, he thought, was obvious.

Parallel reasoning has been applied on more earthy planes to situations in which empirical evidence is impossible or impractical to obtain. In gambling, for instance, say you play the slots. You overhear someone who looks like an insider remark that one machine in every row is set to return more than 100 percent. The idea is that most solid citizens will be lured by the Lorelei sounds accompanying wins on the high-payout device, and think all the machines are loose because they can't distinguish among them. What the casino sacrifices on the loss leader, it therefore recovers handsomely elsewhere along the line. You jot down who's doing what, and when the hot machine you identify gets free, you jump on it. Similar logic may be used in gambling for everything from assuming patterns in various games, biased roulette wheels, controlled dice throws, and so on.

Here's the analogy to Pascal's wager. First, there's no way you can get data proving that one machine is set differently from any other. Moreover, the lack of such data doesn't prove it isn't so. Also, your observations won't be extensive enough for you to draw legitimate statistical conclusions, no matter how long you watch.

Given these conditions, the following situations pertain. 1) You monitor the action then grab the machine that seems intrinsically hot, and it really is, so you score. 2) You monitor the action then grab the machine that seems intrinsically hot, and it really isn't, so you're no worse off than just sitting down at random. 3) You figure the idea of one machine being the bait is nonsense so you take the first empty seat, and the theory was really nonsense, so you haven't sacrificed a shot at an edge over the house. 3) You figure the idea of one machine being the bait is nonsense so you take the first available seat, and the theory was really valid, so you miss the chance to play at an advantage.

Theologians have found plenty of fault with Pascal's wager as it was meant to apply. Is anything fundamentally amiss with its extension to casino gambling? That is, playing under the assumption that you're ahead if you try some strategy and it's reliable, and no further behind if it isn't.

There is, if you act on it in a manner that exposes you to a penalty you might not else face. Mainly by betting more than you might otherwise deem sensible -- and losing, or chasing your losses in confidence that a turn-around is inevitable -- and it doesn't happen. Further, in games involving decisions, by making choices that give the house more edge than you ordinarily would, or that change the volatility such that normal bankroll upswings become too small for your fantasies and downswings too great for your fanny pack. Pascal's theological wager ostensibly offers a reward with no risks; in gambling being wrong can cost you money.

Still, under some circumstances, this tactic may be worth trying. For instance, pretend you play craps and always make one Pass and two Come bets. You read in a book how to set and throw dice so, on the average, sevens supposedly occur less often than six out of 36 times while fives and nines come up more frequently than four out of 36 each. If you play as you did before, a Pass and two Comes with bets of your usual amounts, there's no apparent disadvantage to giving the dice setting idea a shot. Subject, of course, to the caveat of the punter's poet, Sumner A Ingmark:

Oft consequences unintended,
Result from plans ill comprehended.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.