Considering a Progressive System? Weigh Chance, Not Just Amount

Aggressive craps players often start with small place bets, raising or lowering the amounts as a roll unfolds. Behind the mystique is the simple idea of locking up a small win as soon as possible, then pressing with "their money" to go for big payoffs.

Here's an example of how profits can mount. As soon as a shooter establishes a point, drop $12 on the six. If it hits, rack the $14 payoff and let the bet ride. Thereafter, double the bet after every hit, racking the difference. The worst that can occur is a $12 loss if the six never hits, followed by profits of $2, $4, $8, $16, $32, $64, $128, $256, $512, and up for successive hits.

The desirability of any such strategy depends on personal goals. You won't make a monster score betting $12 flat and getting $14 whenever a six appears. Progressive betting can pay big returns. But it leaves intermediate profits on the table, so rolls must be relatively long before this surpasses the conservative approach. Everybody remembers the solid citizen who grabbed over $1,100 starting with $6 by progressing to $192 on the six after five hits, then leaving the $192 and picking up $224 on each of the next five. But how often can you expect a six to hit 10 times before a roll ends? Roughly once in every 5,000 come-outs.

The accompanying chart is based on a computer simulation of a million shooters. It shows the chances of zero, one, or more hits on each number while a particular player is holding the dice, assuming bets work during come-out rolls after passes. Chances of more hits than those shown are under a tenth of a percent.

Note that regardless of number, the most likely result is no hits -- from two thirds of the time on four or 10 to somewhat over half for six or eight. In these instances, you'll lose the initial bet and grand plans for progressing become irrelevant.

Here's an example of how the chart can help evaluate a simple strategy. You can use the same idea on your own brainstorms.

Say you bet $5 on the four, intending to double up after every win and take it all down after three hits. The first hit gets you $9, $4 to the rack and $5 on the bet. The second gets you $18, $8 to the rack and $10 on the bet. The third hit gets you $36. You take it all, along with the $20 on the table. If you get all the way, your total profit on the initial $5 is a handy $63. But you have only 2.5 percent chance of success. If the shooter hit twice and then rolled the seven, you'd have put $12 in your rack, which would be a $7 profit because the house would get your original $5 along with the intermediate profits you left on the table. The chance this will happen is 7.4 percent. And if the shooter hit only once before sevening out, you'd lose $1 since you racked $4 and lost your original $5. The chance of this is 22.2 percent.

What if, instead, you bet flat? You'd have the same 66.6 percent chance of losing $5. But now you have 22.2 percent chance of a $4 profit on a single hit, a 7.5 percent chance of a $13 profit on two hits, and a 2.5 percent chance of $22 profit on three hits.

You can see the give-and-take. First, note that aggressive pressing can hurt on rolls with few hits but helps on those with many, while the converse holds for conservative strategies. Then, check how the chances fall for increasing hits per roll. Let your own gambling objectives and incentives guide your approach.

Ultimately, it's a matter of personal preference. But, don't choose the promise of big bucks on hot rolls without knowing how diminishing chances offset increasing returns on various schemes. Sumner A Ingmark, the dice denizens' Dryden, said it this way: