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Best of Alan Krigman
Playing it Smart - How do you figure what you earn in comps at Craps?12 November 2007
Most casino gamblers know the house has an edge on every bet. That edge is usually expressed as a percentage. You can picture it as the average the joint will earn per dollar wagered over an extended period. This is important to the bosses because it's the source of their profit. It's also significant for players. Indirectly because it has a mathematical influence on the sizes and probabilities of wins and losses; directly because the casinos base their comp and other rewards programs on it.
Say the edge on a certain bet is 1 percent. If a solid citizen gambles with a $100 bankroll, this doesn't mean the house expects to earn 1 percent of the $100 which would only be $1. The player might feed a slot machine $1 at a time, but by recycling returns could easily bet $2,500 during a session. The casino would then figure its potential for earnings from this person at 1 percent of $2,500, which would be $25.
Bankroll, itself, is not a critical factor. You may exhaust your stake and go bust. But doing so in a session of reasonable duration is more a result of volatility than edge. And the casino offsets your losses with someone else's wins, ending up close to the average based on percentage and gross amount wagered.
Most people realize that bet size and edge are key elements in casino gambling. Less well appreciated is the number of times wagers are resolved during a session. This depends not only on how long you play, but also on the game's decision rate.
In many cases, the decision rate can be fairly easily determined because it's simply the number of rounds per unit time. For instance, a motivated machine maven might get 15 spins per minute, say 900 per hour. Betting $1 per spin for an hour, the gross wager would be $900. At a game with 5 percent edge, the house would earn a theoretical 0.05 x $900 or $45. The player would recover about a third of this, $15, in some form of reward.
Blackjack decision rate is a bit trickier to find. It depends on how many spots are being dealt at a table. A good estimate for hand-shuffled shoes is 420/(n+1) rounds per hour where n is number of spots. With four positions, this would be 420/5 or 84 rounds per hour. A $10 bettor at such a table would risk a total of $840 per hour. With Basic Strategy, edge would be 0.5 percent. So the house's theoretical take in the hour would be 0.005 x $840 or $4.20; one third back would be $1.40 in comp credits.
Craps is far more complex. The reasons are that a) ignoring one-roll "sucker bets," decisions aren't made on every throw of the dice; b) alternate bets have different decision rates; and c) the frequency at which Pass, Come, Don't Pass, and Don't Come bets are resolved depends on the come-out roll if there's a win or loss then and there, or otherwise which number becomes the point.
The accompanying table gives decision rates for the most common craps bets based on a computer simulation of 10 million throws. Place bets are presumed made as soon as a point is established and don't "work" during come-outs. The 1.4% for edge on Pass and Don't Pass is on the flat portion only; Odds are irrelevant.
Decision rates for common bets at craps
Bet decisions edge per 100 throws Pass or Don't Pass 29.6 1.4% Place the four or 10 17.5 6.7% Place the five or nine 19.5 4.0% Place the six or eight 21.5 1.5%
A fast table might have 100 throws in an hour. So, pretend you always bet $10 on Pass then Place the five for $10 and the six for $12. The house's theoretical profit from you will be (29.6 x 0.014 x $10) + (19.5 x 0.04 x $10) + (21.5 x 0.015 x $12), or $15.81 per hour. Casinos that knew their math and monitored the action accurately would give you back a third of this $5.27 in rewards. Action at this level is apt to get you more in comps, though. Suggesting either how highly the bosses esteem you or how poorly they did in grammar school arithmetic. A situation the punter's poet, Sumner A Ingmark, described as follows:
Know what you're doing, receive what you've earned; Thrash about blindly, you're bound to get burned.
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