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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Taking it or laying it at the craps table

5 May 2009

Some craps buffs bet identical amounts on Pass and Don't Pass (or Come and Don't Come), then take or lay Odds on the former or latter, respectively. Their "theory" is that the flat bets cancel on the come-out one wins when the other loses so only money on the Odds, where the house has no edge, is at risk. The fly hits the ointment when 12 pops on the come-out, since Pass loses while Don't Pass pushes. And the average net loss caused by this effect equals the edge times the sum of the two flat bets.

Based on edge alone, dice doyens dictate choosing one side or the other and adding the Odds when the point is established. Betting both on the come-out, however, offers solid citizens the option of picking sides after the point is known. But, so what?

Since edge on the Odds is zero, if the sides differ, it's because of volatility and/or skew. To illustrate, say the flat bets are each $10 and the player goes for 5X Odds.

  • Fours or 10s: $50 Odds on Pass must overcome a 2-to-1 handicap to win $100; $100 Odds on Don't Pass is favored by 2-to-1 to win $50. Volatility, measured by standard deviation (picture it as average bankroll change per decision) is $70.70 on either side; skew (the degree to which results show few large wins versus many small losses, and conversely) is +0.71 for Pass and -0.71 for Don't Pass.

  • Fives or nines: $50 Odds on Pass is an adverse 1.5-to-1 shot for $50 to win $75; $75 Odds on Don't Pass is a 1.5-to-1 favorite to win $50. Volatility is $61.20 on either side; skew is +0.41 on Pass and -0.41 on Don't Pass.
  • Sixes or eights: $50 Odds on Pass fights 1.2-to-1 to win $60; $60 Odds on Don't Pass has the best of 1.2-to-1 to win $50. Volatility is $54.80 either way; skew is +0.18 on Pass and -0.18 on Don't Pass.

Over many decisions, these effects are balanced. But only the bosses operate in the long-term. Mere mortals muddle in the short, where 1) focus is on individual sessions or casino visits, typically involving several hundred throws and fewer decisions; 2) bettors have finite bankrolls and drop out if they bust out; 3) players can choose how much to bet; 4) gamblers can quit if they're happy with their haul or want to cut their losses.

In theory, absent edge, players opting to double their money or bust out trying have 50 percent chance of success or failure. This would certainly hold, given enough trials. Betting the Odds on Pass or Don't Pass would be equivalent. What about the more pragmatic short-term? Ignoring come-outs and evaluating only point rolls, pretend players with $500 stakes go for broke to win $500 or run out of time, taking or laying 5X Odds on $10 flat bets. Say they have two hours, about 200 point-roll throws.

Simulations of 10,000 sessions show that on sixes or eights, taking Odds on Pass yields chances of 23 percent of earning $500, 22 percent of busting out, and 55 percent of never reaching either limit. Chances laying 5X Odds on Don't Pass are 22 percent of earning $500, 23 percent of busting out, and 55 percent of doing neither. On fours or 10s, the other extreme in terms of prospects and payoffs, chances are 30 percent of reaching either $500 limit and 40 percent of never getting this far, regardless of the side on which the Odds were bet. Fives and nines yield results falling between these figures.

The margin of error in 10,000-session simulations is 1 percent, so the likelihood of agony or ecstasy is the same Pass or Don't Pass for any particular point. Skew, which differs on opposite sides of each number, is irrelevant. The choices diverge across numbers in the magnitude of the expected bankroll swings, evidenced by the 55 and 40 percent likelihoods of never hitting the limits with sixes/eights and fours/10s, respectively. This phenomenon is a consequence of the volatility differences among bets on the alternate points. All of which vividly validates this vital verity proclaimed by the punters' poet, Sumner A Ingmark:

Often fact intrudes and shatters,
Myths about what you think matters.

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.