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Best of Alan Krigman

Gaming Guru

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If Anything Can Happen in a Single Session, Why Sweat the Details?

9 March 2005

Place and buy bets at craps are wagers on one or more of the numbers four, five, six, eight, nine, or 10. The bets win if the dice show the indicated total; they lose if a seven appears.

Chances of winning, payoffs, and house advantage differ among the choices. Buying the four or 10 for $29 and paying $1 "vigorish," a total outlay of $30, for instance, should generate results an average of nine out of every 36 tosses. Of these, three should yield profits of $58 and give the house 2.2 percent edge. Placing the five or nine for $30 should produce decisions an average of 10 out of 36 throws. These should include four $42 winners, with an edge of 4.0 percent. Betting $30 on the six or eight, players can anticipate action an average of 11 out of 36 throws. Here, they expect to win $35 five times and face 1.4 percent edge.

Of course, such figures aren't the sum and substance of craps, or any casino game. If they were, think what would happen during a 360-throw session, about four hours, in which a solid citizen had a single bet on the layout for every toss. Buying the four or 10, this individual would collect $58 x 30 = $1,740 and lose $30 x 60 = $1,800, finishing $60 in the hole. Someone making Place bets on the five or nine in such a game would pick up $42 x 40 = $1,680 and drop the same $1,800, ending $120 to the bad. And a person with $30 on the six or eight would take in $35 x 50 = $1,750 while also sacrificing $1,800, suffering a net zonk of $50.

In practice, over what may seem a marathon session but is really a statistically short 360 throws, bettors can succeed or fail to degrees that diverge widely. This, even under the hypothetical condition that they persist uniformly for 360 throws. The effects can be pictured from the results of a computer simulation of 10,000 360-throw sessions, in each of which players put up $30 to bet on either the four or 10, five or nine, or six or eight.

Simulated session averages were close to what the math predicts for the long run. The virtual bettors lost $59 on fours and 10s, $121 on fives and nines, and $51 on sixes and eights. And the effective edges were 2.2 percent for fours and 10s, 4.1 percent for fives and nines, and 1.5 percent for sixes and eights.

The $30 outlays for Buys on the four or 10 have the intermediate edge for the three options, the least action during the session, and the longest odds with the highest payoffs. Of the 10,000 simulated bettors, 4,342 won and $5,613 lost while 45 broke even. Further, 4,049 won more than $30 and 5,347 lost over this amount while 604 were within $30 either way. The biggest win was $1,778 and the worst upset was $1,560. The median was a loss of $62, meaning that as many players fared better as did worse than this.

The 10,000 digital dice devotees on the five and nine got more decisions with somewhat better odds of winning, but the payoffs were smaller and the house advantage larger. Totals of 3,583 won and 6,358 lost while 59 broke even. Likewise, 3,263 won more than $30 and 6,021 took bigger hits than this while 716 were within $30 either way. The greatest profit was $1,206 and the deepest loss $1,488. The median for these bets was a loss of $126.

Place bets on six or eight had the most action, the best chance of winning, and the least edge to overcome, but the smallest payoffs. Overall, 4,406 winners contrasted with 5,525 losers and 69 players who broke even. This included 4,035 who earned more than $30, 4,172 who lost over this much, and 793 who finished up or down within $30. Here, the median was a $50 deficit.

Overall, edge had a clear effect. More players lost and fewer won on fives and nines, with the steepest edge, than on the others. Higher volatility, manifest by less frequent but larger wins on fours and 10s, is reflected by greater maximum losses and wins as well as fewer finishes within $30 either way. And getting more action had a moderating effect because edge applied more often. Still, in the end, the approaches all had winners and losers. That's what gambling's all about. As the beloved bard, Sumner A Ingmark, clearly contemplated in composing this telling triplet:

If every conclusion were known in advance,
We'd only take actions we knew would enhance,
But it would be boring with naught left to chance.

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.