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Best of Alan Krigman

Gaming Guru

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Should You Lay Odds on "Don't" Bets at Craps?

27 December 1999

Craps players who follow "don't pass" or "don't come" strategies hotly debate whether it's preferable to lay odds after the come-out roll, or simply start higher and stick with their flat bets. Most dice doyens declare that laying as much as possible in odds is optimum because it minimizes the house advantage in the game. Bettors, however, sometimes find this counter-intuitive.

The reasoning behind the contrary opinion is twofold:

  1. Money laid as odds against a number returns less than is at stake. For instance, $30 yields $25 on points of six or eight, $20 on five or nine, and $15 on four or 10. So, why risk more to win less?

  2. The original flat bet is favored to win even money after a point is established. Chances are 6-to-5 on points of six or eight, 3-to-2 on five or nine, and 2-to-1 on four or 10. So, why not get 1-to-1 on more money flat, instead of fractional payoffs for the same amount laid as odds?

These arguments are reinforced by a third point. Namely, the relatively small sums represented by house advantage on every wager mean something to the casino. After all, the house earns a penny or two per dollar bet, roll after relentless roll, from player upon impassioned player. But individuals, in games of reasonable duration, don't really notice the effect. Generally, winning only a few bets over the statistically correct number more than covers the edge in craps.

An alternate way to view the options for don't pass or don't come bets is to consider how a set of solid citizens, using the two approaches, can anticipate finishing sessions of various lengths. For this purpose, say a thousand flat bettors drop $25 on the layout and quietly await their fate, while this many odds layers start with $5 and augment it with $30 regardless of which number the shooter is trying to repeat. The totals at risk are equivalent since the averages for every 36 come-out rolls will be $900 either way -- 36x$25 flat or 12x$5 plus 24x$35 with odds.

If break-even, $500 wins, and $500 losses are taken as reference levels, here's how the immutable laws of mathematics say the thousand stalwarts will fare after typical stints at the rail.

100 rounds: 445 flat bettors will be above break-even, 15 will be ahead by more than $500, and 29 be below $500; 489 odds layers will be above break-even, 19 will have won over $500, and 22 will have lost more than this.

200 rounds: 422 flat bettors will be above break-even, 52 will have won over $500, and 108 will have lost at least $500; 484 odds layers will be above break-even, 70 will have made in excess of $500, and 81 will be this deep in the hole.

500 rounds: 379 flat bettors will be above break-even, 112 will show profits greater than $500, and 275 will be wondering where the steam roller came from; 475 odds layers will be above break-even, 165 will be more than $500 to the good, and 198 will be this far down.

Purists should know that the casino's theoretical earnings on each player are $0.34 per round with $25 flat, compared to $0.07 per round with $5 flat and $30 odds. After 100-, 200-, and 500-round sessions, respectively, the totals are $34, $68, and $170 for flat fans and $7, $14, and $35 for odds buffs.

Applying the traditional criterion of house advantage to bets on don't pass or don't come, apportioning money between the flat and odds portions of a wager is clearly superior to betting an equivalent amount flat. And guess what, considering where you're likely to be after a session of representative duration, the conclusions are the same. Of course, if shooters happen to roll long runs of twos and threes on their come-outs, while sevens and elevens only appear after points are established, the flat bettors will be flush. But, that's where luck enters the picture.

All of which goes to show that the revered rhymer, Sumner A Ingmark, was right when he wrote:

While only fanatics deny mathematics,
A player perverse doesn't always do worse.
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.