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Best of Alan Krigman

Gaming Guru

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How Taking Odds Affects Your Chances at Craps

28 December 1998

Craps players have been debating whether or not to take odds when betting on the pass line since before time immemorial. I forget if they were arguing it earlier than that, although I suspect so.

One reason for the enigma is the tendency to compare apples with oranges when choosing between larger base bets and greater odds. That is, $10 on the line with $20 odds is usually contrasted with $10 or $30 flat, but neither represents commensurate risk.

Here's how to get "flat" risk equivalents to pass bets with odds. Of every 36 decisions, 12 are made during the come-out when only the base bet is up for grabs; the other 24 are made with a point established when odds are also in action. This makes the effective exposure $10x(12/36) + $30x(24/36) = $23.33 for $10 on the line with double odds. Risk counterparts to $10 with other common odds multiples are $43.33 at 5X, $76.67 at 10X, and $676.67 at 100X. To be practical, these values can be rounded-off to $25 at 2X, $50 at 5X, $75 at 10X, and $700 at 100X.

Another reason the odds polemic gets heated is that arguments focus on changes in house advantage. But edge is small either way and the impact isn't apparent in sessions of reasonable length.

It's more productive to compare the choices by examining the ranges of wins and losses which can be expected after games of appropriate duration. Imagine players wagering only on the pass line -- either $10 with odds or the rounded-off equivalent flat bets. The following limits on losses and profits should be exceeded in under 12.5 percent of all 100-decision sessions.

bet worst loss odds/flat equiv best profit odds/flat equiv
10+2X/25 343/322 315/252
10+5X/50 684/645 656/505
10+10X/75 1,257/968 1,229/757
10+100X/700 11,605/9,030 11,577/7,070

As an example of interpreting these figures, assume 1,000 players bet either $10 with 10X odds or the $75 rounded-off flat equivalent for 100 rounds. On the downside, 12.5 percent or 125 of these can expect to lose more than $1,257 with the odds and $968 with flat bets. On the upside, 125 can expect to win over $1,229 taking the odds and $757 betting flat.

These figures illustrate how taking odds or betting the flat risk equivalents affect expected bankroll swings in ordinary sessions. If luck runs sour, players subject themselves to slightly greater losses by taking odds. For instance, 125 out of every 1,000 bettors can anticipate being over $21 deeper in the hole betting $10 with $20 odds than $25 flat. However, the gain on the upside is relatively greater for those who take odds. At hot tables, 125 out of every 1,000 bettors can expect to have over $63 more profit betting $10 with odds rather than $25 flat.

Additional insight into the difference between the strategies is afforded by investigating the chance of being ahead by betting various ways. Again, consider a 100-decision session. Betting $25, $50, $75, or $700 flat on the pass line, players have 44.0 percent probability of being in the black. Betting $10 on the line with corresponding odds multiples of 2X, 5X, 10X, and 100X, chances of being ahead rise to 48.0, 49.0, 49.6, and 49.9 percent respectively. Distinctions are stronger after 900 decisions -- which might correspond to a weekend of play. Now, any of the flat risk equivalent bets gives solid citizens 33.7 percent probability of being ahead. With $10 on the line and odds multiples of 2X, 5X, 10X, and 100X, the chances of showing a profit rise to 44.3, 47.2, 48.5, and 49.8 percent, respectively.

Which approach is better? Decide for yourself. Taking odds improves your chances of finishing in the money. And, if the table is hot, you'll earn more for a comparable amount at risk. But the equivalent flat bet trims the loss you might suffer at a cold table. In making your choice, stay mindful of the odd observations of that prudent poet, Sumner A Ingmark:

The statisticians don't know how,
To buy stocks that will beat the Dow,
Or win at gambling here and now.
The weakness is their math depends,
On testing time that never ends.

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.