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# What does edge cost you per hour at craps?

10 October 2011

Typical craps players out for the fun, excitement, and camaraderie of the game give little thought to the house advantage on the various bets. They put their pelf on propositions that seem to be hitting, their favorite or lucky numbers, or whatever lets them madly toss chips on table and bark orders at dealers they think make them sound like wiseguys straight from Damon Runyon stories.

More erudite solid citizens choose bets that minimize the house’s edge. They avoid hardways and one-roll wagers altogether. Instead, they focus on Pass or Come (or Don’t Pass and Don’t Come) – taking or laying the maximum Odds allowed – unless their fanny packs are too light to cover enough outcomes with this approach, in which case they Place the inside numbers.

Does it really matter whether a player pays attention to the math? On any particular hand or session, a person could rake in the dough bets having the most adverse edge on the layout, say by tossing \$5 on the 12 for role after and having it pop relatively often. Five consecutive 12s, a 60,466,175-to-1 shot that’s certainly occurred and will again, would net a player \$750. On statistically exemplary bets like \$5 on the line backed up by \$50 Odds, five successive miss-outs are a much more likely 29-to-1 prospect and would represent a \$275 loss.

Still, enquiring minds want to know the impact edge has on their action during a session or casino visit. To understand the answer to this question, they have to understand that edge isn’t – as conventional wisdom often spouted by civilians suggest – the likelihood of winning a bet. At the standard 30-to-1 payoff, the house has 13.89 percent edge on the 12. Were the payoff to be 33-to-1, edge would fall to 5.56 percent. The probability of winning is 2.78 percent either way.

But, 13.89 or 5.56 percent edge is 13.89 or 5.56 percent of what? Of the money at risk. In practice, the house figures that on a gross wager representing enough action – for instance, \$100,000,000 on ten million \$10 bets, it will earn close to the stated fraction – \$13,890,000 with 13.89 percent edge. So, on the average, individual patrons are worth the given percentage of their bets. Per round, at \$10, this would be \$1.39 for the \$12 at craps. Nobody actually forks this over as a charge on every round. It’s hidden in the offset between what some win and others lose.

Assume, arguendo, that the average number of decisions per hour – win or lose – is 35 on Pass (including come-out and point rolls), 55 on six or eight, 50 on five or nine, and 45 on four or 10. The house’s theoretical earnings due to edge for \$10 bet flat on 35 Pass line bets, regardless of the Odds taken, would be 1.42 percent of the \$10 or \$0.142 per decision, which comes to \$4.97 – just under \$5 per hour. For 55 \$12 bets on six or eight (for those not conversant with craps, you can only Place these numbers in multiples of \$6), edge would amount to 1.52 percent or \$0.182 per decision, which comes to \$10 per hour. For 50 \$10 on the five or nine, the joint’s average take is 4.00 percent or \$0.40 per decision, accumulating to \$20 per hour. And for 45 \$10 bets on four or 10, the fee in question is 6.67 percent or \$0.67 per decision, totaling \$30.00 per hour.

If you bet \$5 or \$6 instead of \$10 or \$12, these figures would be cut in half. And if you play longer than an hour, they’d be multiplied accordingly.
In the heat of the action, you’re not apt to notice the effect of the edge on your bankroll. This, because the volatility of the game overwhelms the edge in the short run. On fours and 10s, for instance, you either win \$18 or lose \$10 on every decision, while the casino’s covert commission is \$0.67. The fly in the ointment is that, over time, the \$18 gains and \$10 losses tend to offset one another while the \$0.67 fees mounts relentlessly.

You have to make up your own mind whether you think the house’s average earnings for letting you gamble are reasonable or excessive. It’s hard to argue with less than half a bet per hour on Pass or Come, especially when the \$5 per hour with \$10 flat applies no matter how much you take in Odds. On the other hand, the equivalent of three bets per hour, the case when you Place the four or 10, may seem rather high.

Of course, the bosses are going to have to assess their customers for the cost of running and banking the games. After all, they’re in business. Disney doesn’t let folks into its Magic Kingdom without paying for admission and use of the attractions or a mark-up on food and merchandise. But anyone who’s ever tried to tell a six-year-old that he or she can watch but can’t ride on the Big Thunder Mountain Railroad knows that the casinos offer a much greater opportunity to choose how much to pay for the experience offered. As the voluble versifier, Sumner A Ingmark, observed:

When planning your next gambling spree,