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Best of Alan Krigman

Gaming Guru

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How Much Should You Allocate for Place Bets at Craps?

30 August 1999

How Much Should You Allocate for Place Bets at Craps?

The majority of craps players start every round betting on the Pass line. This puts them at the heart of the hootin' and hollerin' on whichever of the numbers from four to six or eight to 10 becomes the shooter's point. Few dice doyens, however, stop with just a single number covered. And the way many solid citizens choose to get thicker into the fray is to make place bets on one or more additional boxes after the come-out.

Greenhorns and gurus all agree to disagree passionately about how many and which numbers to cover. The choice is an amalgam of hunch and individual bent, elevated to an article of faith. But, once a selection is made, the mathematics of the known universe -- including craps pits -- can help guide the amount to wager.

As with most table play, two contradictory factors govern bet sizing. The first objective is ability to bear the slings and arrows of outrageous sessions without going belly-up; smaller bets increase chances of survival. The second criterion is a win goal -- enough profit to contentedly color up and scamper away from the rail; larger bets raise the likelihood of reaching any designated gain before depleting a stake. "Risk of ruin" analysis based on odds and payouts yields the specifics for both criteria.

Folks who don't leave their better judgement at the casino door have predetermined gambling budgets. Surviving what they consider adequate playing time on the money that seemed sensible at home therefore usually outweighs win goal in bet sizing.

Say that players want to place as much as they can on their favorite numbers, yet be 85 percent sure their stakes will endure four hours of normal downswings. The following fractions of an initial bankroll, spread as uniformly as permitted across typical sets of numbers, will do the trick if no other bets are made.

 bet  fraction of  amount for
   bankroll  $500 bankroll
6 or 8  6.3%  $31.50 
5 or 9  5.5%  $27.50 
 4 or 10 4.8%  $24.00 
 6 & 8 7.2%  $36.00 
 5, 6, & 8 7.3%  $36.50 
4, 5, & 6  6.7%  $33.50 
4, 5, 6, 8, 9, & 10  7.1% $35.50 

Here's an example of interpreting the data. Players make only place bets. To be 85 percent sure of surviving four hours betting on four, five, and six, they can risk up to 6.7 percent of their initial bankrolls per round. For a $500 stake, this equals $33.50. A $10 four, a $10 five, and a $12 six would be close enough to the mark. Placing only the six and eight would meet the survival criterion at 7.2 percent -- $18 each on a $500 nest egg.

The next list reflects the win goal criterion. It shows the likelihood that players will earn profits equal to half and twice their initial stakes, betting the amounts shown previously for 85 percent confidence in surviving four-hour sessions.

 bet  chance of chance of 
  earning half  earning twice 
  the initial  the initial 
   stake stake 
6 or 8   60%  21%
5 or 9   48%  8%
 4 or 10  40%  3%
 6 & 8  58%  19%
 5, 6, & 8  53%  13%
4, 5, & 6   44%  6%
4, 5, 6, 8, 9, & 10   42%  4%

Here's an illustration of how to interpret these figures. Pretend players place the six, sizing their bets at the 6.3 percent level to meet the four-hour survival criterion. They have 60 percent chance of a profit equal to half their bankrolls and 21 percent chance of a gain twice their initial stakes. Starting with $100, with a minor conservative round-off, this means $6 bets with chances of 60 percent to earn $50 and 21 percent to earn $200 -- offset by 40 and 79 percent chances, respectively, to lose $100.

Players examining these figures are pleased to learn that they can bet a greater total across several boxes than on a single number, with the same chance of survival. They're displeased, though, when they discover that the added action cuts the odds they'll achieve their win goals. Such paradoxes may be what the punters' poet, Sumner A Ingmark, was pondering when he penned:

More than just the bets they make,
Winners know the give and take.
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.