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Best of Alan Krigman

Gaming Guru

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You Can Win More Often… By Shooting for Less Profit

30 November 1998

Gamblers love "systems" and frequently elevate their favorites to articles of faith. Any number have been developed over the years, and I'd hate to estimate how many hopefuls are working on more.

Details vary with the game. However, systems employ three general principles - singly or combined. Some involve multiple results on which wagers of varying amounts are placed at any one time. Others entail sequences of differently sized bets. The rest utilize decisions based on previous outcomes.

No systems can eliminate the casino's inherent edge on bets in independent-trial games. But edge isn't the whole story. Systems can affect the chances of winning or losing various amounts in sessions of reasonable length. There's a catch, of course. Assume your worst-case loss is set by a fixed bankroll. Then systems trade-off the gain at which you're happy to quit with the likelihood you'll reach the goal before going broke. That is, you can shoot for lower profits and raise your chance of success, or aim for higher returns but lower the odds of getting there.

"Martingale" negative progressions are especially attractive to solid citizens looking for small but frequent profits. Many variations are possible, mainly focusing on even-money wagers with close to 50 percent chance of winning. The idea is to double your bet after every loss, beginning the cycle again after every win. Each successful series of such bets will net one unit - an amount equal to the original wager.

Say you start with $5. The Martingale sequence is $5, $10, $20, $40, $80, and so on. At each stage, accumulated loss is $5 less than the current bet. So winning any round yields $5 profit.

The mantra Martingale bettors chant is "I've never seen it lose five (or whatever number) times in a row." And, in fact, bets recommended for Martingale systems rarely run long strings of losses. Rarely, but not never. And, that's the problem. When bet after bet does go down, a player can suffer a serious setback from which it's tough to recover one unit at a time.

Martingale progressions are often applied at craps to flat bets on Pass or Don't Pass and to the Field. The chart below shows the chances of these wagers losing from once to 11 times running, along with amounts bet at each stage. Pass and Don't Pass win 1?to-1; fruitful cycles starting with $5 earn $5. The Field pays 2-to-1 on two or 12 and 1-to-1 on other winners, so successful sequences can yield more than $5. For instance, the chart shows that $160 is bet after five losses; two or 12 on the sixth roll nets $165 ($320 - $155) while other wins return $5 ($160 - $155).

No of
rounds
Amt
bet
Probability of losing
($)
Pass/Don't Pass
(%)
Field
(%)
1
5
50.71
55.56
2
10
25.71
30.86
3
20
13.04
17.15
4
40
6.61
9.53
5
80
3.35
5.29
6
160
1.70
2.94
7
320
0.86
1.63
8
640
0.44
0.91
9
1280
0.22
0.50
10
2560
0.11
0.28
11
5120
0.06
0.16

As a further example of using the chart, the chance of losing six successive Pass or Don't Pass bets is 1.70 percent and calls for a $320 wager at the seventh step. If 1.70 percent probability seems negligible, consider this. When 1,000 players try the system, 17 are expected to go this far and be $315 in the hole - seriously questioning whether they should, or can afford to, face a 50.71 percent chance of dropping another $320 behind.

The chart also shows how table limits mitigate Martingale mania. Many games with $5 minima have $500 maxima. Few $5 tables have over $2,500 at the high end. These limits hold the series to seven and nine trials, respectively. Chance of nine losses in a row is small. But five out of every 1,000 well-heeled Martingale Field bettors can be expected to get this far, then hit the wall. As Sumner A Ingmark, the retrogressive rhymer, said:

On jackpot wins when odds are low,
You're sure you've got a shot at it.
With equal odds of losing dough,
You know you won't get caught at it.


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.