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Best of Alan Krigman

Gaming Guru

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You Can Raise Your Chances of a Long Series of Winning Sessions

19 November 1996

I'm forever hearing about players who "must" have foolproof systems because they always - well, almost always - win. There are no such systems. Even card counting in blackjack and progressive jackpots so high they give players a slight edge don't guarantee a win... let alone a long queue of casino conquests.

My informants usually counter with something like, "It's gotta be more than luck. If someone comes to a casino once or twice a month, the odds of winning for a solid year must be minuscule."

It happens. The odds are small but not infinitesimal. And, yes, it's more than just luck. I call it intelligent gambling. Others sometimes call it wise money management.

Picture a "fair" even-money game where the house has no edge - like flipping coins. The player has a 50-50 chance on every bet and gets paid 1-1 for a win. Results won't be too much different on real casino games with low house edge.


In the fanciful fair game, the probability of winning a particular bet is 50 percent. But, this isn't necessarily the likelihood of being ahead after extended play. The chance of a successful session also depends on the depth of the downswing bettors are willing to brook and on the proceeds they demand before quitting. These figures are known, respectively, as "loss limit" and "win goal." In practice, they're rarely fixed amounts; however, using representative numbers helps put a handle on the odds.

Solid citizens can adjust their chances of successful sessions by changing their win goals relative to the loss limits they'll tolerate. Here's how to find the chance of reaching any win goal in a fair game, starting with a specified loss limit. Get out your calculator, or your pencil and paper, and use the formula: C=(100xL)/(W+L), where C is your chance expressed as a percent, L is your loss limit, and W is your win goal. As an example, a 20-unit loss limit offers 80 percent chance of winning five units, 66.7 percent chance of 10 units, 50 percent chance of 20 units, and 33.3 percent chance of 40 units.

The chances of having successful sessions visit after profitable casino visit drop the longer you go. But, modest win goals relative to your loss limits make it feasible. Here are examples of the chance you'll have a year of successive victories with one or two visits per month, for various session win probabilities:

1 win 12 wins 24 wins
66.7% 0.7% <0.1%
77.0% 4.3% 0.2%
80.0% 6.9% 0.4%
90.0% 31.8% 10.1%


Entries show that having will and wallet to outride normal downswings, and discipline to quit with nominal earnings, yield modest chances of repeated victories. For instance, an 80 percent chance of winning once - say because of a 25-unit win goal and 100-unit loss limit in the hypothetical game - means 6.9 percent chance of meeting the profit target 12 times in a row and a 0.4 percent shot at 24 successive successful sessions.

What about real games? Games where the house has an edge? Consider six-deck blackjack with resplitting of pairs and surrender of appropriate hands. Basic strategy and no card counting give the casino roughly 0.3 percent edge. Assume a 40-unit loss limit and 10-unit win goal. Players' chances of winning are 77 percent for any single game, 4.3 percent for a string of 12 and 0.2 percent for a series of 24 successes. These odds are the same as for a fair game with a loss limit of 40 and a win goal of 12 units.

The bottom line? You can manipulate the odds of achieving a series of profitable casino visits. How? First, by playing games with low edge, moderate fluctuation, and small or negative skew; next by conservatively setting win goals relative to loss limits. An aggressive bettor, who doesn't mind spending a day's gambling budget to buy a shot at a big score, may triumph spectacularly on occasion but not regularly. Sumner A Ingmark, the Chaucer of chance, summarized the situation succinctly in this insightful stanza about streaks:


Long winning runs are not so mystical,
When goals you set are realistical.


Table
Probability of achieving a desired win goal
before reaching a specified loss limit in a "fair" game

 
Loss Limits (in bet units)
Win
Goals
(in bet
units)
  10 20 30 40 50 60 70 80 90 100
5 66.7% 80.0% 85.7% 88.9% 90.9% 92.3% 93.3% 94.1% 94.7% 95.2%
10 50.0% 66.7% 75.0% 80.0% 83.3% 85.7% 87.5% 88.9% 90.0% 90.9%
15 40.0% 57.1% 66.7% 72.7% 76.9% 80.0% 82.3% 84.2% 85.7% 87.0%
20 33.3% 50.0% 60.0% 66.7% 71.4% 75.0% 77.8% 80.0% 81.8% 83.3%
25 28.6% 44.4% 54.5% 61.5% 66.7% 70.6% 73.7% 76.2% 78.3% 80.0%
30 25.0% 40.0% 50.0% 57.1% 62.5% 66.7% 70.0% 72.7% 75.0% 76.9%
35 22.2% 36.4% 46.2% 53.3% 58.8% 63.2% 66.7% 69.6% 72.0% 74.1%
40 20.0% 33.3% 42.8% 50.0% 55.6% 60.0% 63.6% 66.7% 69.2% 71.4%
45 18.2% 30.8% 40.0% 47.0% 52.6% 57.1% 60.9% 64.0% 66.7% 69.0%
50 16.7% 28.6% 37.5% 44.4% 50.0% 54.5% 58.3% 61.5% 64.3% 66.7%

 

 

Table
Probability of 12 and 24
successive wins
for games with the indicated
chance of a single win

 

1 win
12 wins
24 wins
66.7%
0.7%
<0.1%
77.0%
4.3%
0.2%
80.0%
6.9%
0.4%
90.0%
31.8%
10.1%

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.