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Best of Alan Krigman

Gaming Guru

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How Should You Size Your Pass Line Bets at Craps?

16 August 1999

How Should You Size Your Pass Line Bets at Craps?

Craps offers diverse ways to wager on the outcome of a throw of the dice. And different numbers of throws are expected before dissimilar bets are resolved. As a result, guidelines for sizing craps bets depend on how individual players spread their money.

The most common and often the biggest wagers solid citizens are likely to make at craps are on the Pass Line, augmented with Odds after the come-out roll. Rules for what's prudent to risk on each shooter are therefore apt to start with and emphasize Line bets.

Further, as in most casino games, craps bet size is meaningful not in absolute dollars, but as a fraction of a bankroll that seemed sensible before leaving home. Two conflicting criteria apply: the confidence folks want that their stakes will outlast normal sessions of reasonable duration, and the profit levels or win goals at which they'd be glad to color-up and quit.

For most bettors, survival outweighs win goal. Ask yourself whether anything spoils a day at the casino quite as much as tapping out and making believe you had a good time anyway. And, for any given bankroll, it's usually more practical to set win goals consistent with survival rather than other way around.

In a representative craps game, a player is apt to experience approximately 25 come-out cycles per hour. A four-hour session will consequently comprise 100 or so such cycles.

Assume that players bet solely on the Pass Line -- taking single, double, or quintuple odds. Say they want to be 85 and 95 percent sure to survive 100 rounds on a certain buy-in. The following list shows the fraction of their budgets they can risk as the flat parts of their bets to meet this criterion. For reference, dollar values are given for bets corresponding to $500 bankrolls.

 Odds multiple  Fraction  $500
   of Bankroll  Bankroll
     
 at 85% confidence in surviving 100 rounds
single  3.5%  $17.00 
double  2.3%  $11.50 
quintuple  1.2%  $ 6.00 
     
 at 95% confidence in surviving 100 rounds
 single 2.6%  $13.00 
 double 1.7%  $ 8.50 
 quintuple 0.9%  $ 4.50 

Here's an illustration of how to interpret these figures. Players betting only the Pass Line with double odds would be 85 percent sure of surviving 100 rounds starting each come-out roll with 2.3 percent of their initial bankrolls. They'd be 95% confident of surviving if they started with 1.7 percent. With $500 stakes, these fractions mean bets of $11.50 and $8.50, respectively. Rounding off to $10 would put players midway between -- close to 90 percent sure of not going bust during the four hours. Note that quintuple odds cuts the optimum flat portion of the bet roughly in half for the same degree of confidence.

The chances of achieving various win goals with bets sized for survival vary only slightly among cases. With one pass line wager and double odds, sized for 85 percent survival in 100 rounds, players have the probabilities of success shown below. Smaller bets, sized for 95 percent survival, cut the chances of achieving the same relative profits by about 1 percent across the board.

 Win goal as  probability of success
 fraction of  1X  2X  5X
 bankroll  odds  odds  odds
 25%  77.7% 78.5%  79.3% 
50%  62.8%  64.1%  65.5% 
100%  44.4%  46.2%  48.3% 
200%  26.2%  28.5%  31.0% 

Here's an example of how to read the win goal numbers. Assume Pass Line bets with double odds, flat portions sized at 2.3 percent of a bankroll for 85 percent likelihood of surviving 100 rounds. This gives 64.1 percent shot at reaching a win of half a bankroll -- for instance, $500 profit on a $1,000 poke -- as opposed to going belly-up. To double a stake before going broke, perhaps earning $500 profit on a $500 nest egg, chance of success falls to 46.2 percent. Pondering predicaments like this, the perceptive punters' poet, Sumner A Ingmark, was moved to muse:

The more my aspirations soar,
The more my hopes drop through the floor.
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.