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How do higher Odds multiples affect your chances at craps?

14 March 2011

Proficient craps players know that taking or laying odds behind their Pass and Come or Don't Pass and Don't Come bets reduces the overall edge the casino has on the dough at risk. The reason is that the house gets 1.4 percent on the flat portions of the bets and nothing on the Odds. So, if you start with $5 flat on Pass, the bosses figure you for $0.07 (1.4 percent of $5). Assuming you take double Odds, adding $10 after the shooter establishes a point, the bosses' theoretical earnings are still $0.07. However, that $0.07 is under half a percent of the $15 you have at risk with the point established. Take 10-times Odds, and the house still pencils you in for $0.07, but you have $55 up for grabs after the come-out roll; the $0.07 represents less than two-tenths of a percent of the $55 total.

Were edge the sole consideration, the optimum way to play would be to bet the minimum flat, Do or Don't as personal proclivities prescribe, then take or lay the maximum allowable Odds. Solid citizens with fat enough fanny packs could follow this strategy beginning, say, on Pass then adding to the numbers covered by using the same approach with Come bets on successive throws. The well-funded, of course, might begin above the minimum and still avail themselves of the maximum possible Odds in this manner – or run with the big dogs at higher limit tables.

Anyone having a finite budget or loss limit, for whom time in action and win goals are factors, has more to contemplate than just retarding the erosive effect of edge. On the average, after 100 decisions, edge on bettors who start with $5 flat – regardless of the Odds taken or laid – accounts for a mere $7 contribution to the casino coffers. But a craps aficionado can win or lose a bundle in this many coups. Credit or blame, as the case may be, falls to the volatility. And here, moolah earned or kissed goodbye on the Odds is as relevant as that on the flat portions of each wager.

Make believe you belly-up to the rail of a $5 craps game that offers 10-times Odds. To bracket the possibilities, consider the following alternatives with only one wager on the layout for any shooter: 1) Flat-bet $, period. 2) Flat-bet $55. 3) Flat-bet $5 and take $50 Odds when a point is established. 4) Flat-bet the equivalent of $5 coming-out (decided in 12 out of every 36 hands) and $55 during point rolls (resolved on the other 24 out of 36 hands), equal to (12/36) x $5 + (24/36) x $55 = $38.33 . Given these bets along with bankrolls presumed to be your loss limits, the probability you'll have the wherewithal to survive the normal downswings of sessions having at least some desired duration, and your chance of reaching one or another win goal before being benched, can be ascertained using a sophisticated "risk of ruin" analysis.

The accompanying table summarizes some representative results. The underlying analyses were based on bankrolls of $50 and $100 for the $5 flat bet with no Odds, and of $500 and $1,000 for the other cases. Comparisons across rows indicate the effect of different aspirations for longevity and profit at each combination of bet category and bankroll. Data up and down the columns show how expectations vary for the alternate bets and bankrolls. Of interest are both the probabilities for the various conditions and the rates at which they change for the different circumstances.

Probabilities associated with bets on Pass – flat only and flat with 10X Odds

                                   survive    survive  earn   earn   earn   earn     earn
bet                     bankroll  100 rnds   200 rnds   $50   $100   $250   $500   $1,000

$5 flat                 $50        64%       45%        43%   24%     7%    2%       >>1%          
                        $100       94%       80%        57%   36%    12%    3%        >1%	
$55 flat                $500       59%       41%        90%   81%    62%    44%       25%
                        $1,000     91%       75%        94%   88%    75%    58%       37%	
$5 flat & $50 Odds	$500       64%       48%        91%   83%    66%    49%       33%
	                $1,000     93%       80%        95%   91%    80%    66%       49%
$38.33 flat             $500       77%       58%        89%   80%    60%    41%       22%
                        $1,000     99%       91%        93%   87%    72%    54%       32%

Within each bet category and bankroll, reading across the rows shows that the chance of survival drops sharply with session duration, and the likelihood of reaching a given profit level before exhausting a stake similarly declines steeply as win goal rises. For alternate bets and bankrolls, and shifting money between flat and Odds portions of the wagers, read up and down the columns for comparisons. Larger bankrolls relative to bet sizes have a positive impact on chances of success. Taking Odds improves the outlook for earnings because of the lower house edge during the point phase of a hand, occasioned by payoffs greater than 1-to-1. In comparing $38.33 flat with equivalent $5 flat plus $50 Odds, the former offers the better chance of survival, possibly owing to the larger amount that can be won during the come-out when players are favored, although the latter is preferable with respect to achieving specified earnings levels. All of which was envisioned by the venerable versifier, Sumner A Ingmark, in this veracious verse:

A strategy superior,
Depends on your criteria.

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.