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Best of Alan Krigman

Gaming Guru

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Every System Works When You're Lucky

8 October 1996

Admit it. You've fantasized about sure-fire casino gambling systems. So consider this. 1) How you play can affect how you do, but can't violate the laws of probability for the bets you make. 2) Every system works when you're lucky. 3) Mobs of mathematicians have tried and failed to find fool-proof systems; worse, they can prove why any postulated plan other than cheating or exploiting oversights by casino personnel is flawed; 4) Even card counting, which tells blackjack believers when they have a temporary slight edge, carries no guarantees.

Some systems don't bear on how bankrolls are apt to behave during sessions. For instance, looking for patterns on machines or tables, then following perceived trends or betting on events which seem "due," don't vary the characteristics of a game.

Other systems do influence projected fiscal dynamics. They occasionally reduce house edge, but never below the theoretical minimum for a bet; more often, they raise the edge to give the casino more advantage than necessary. Systems of this type can also amplify or attenuate expected bankroll fluctuations. And, they can skew the game to favor more small wins with a few larger losses, or a few larger wins with more small losses.

Craps abounds in opportunities for such systems. Here's an example. Most players bet on "pass" during the come-out then "take odds" on the point. A few bet on "don't pass" during the come-out then "lay odds" against the point. Occasionally, the craps gods inspire someone to make equal flat bets on both sides then lay odds on don't pass. Coming-out, the bettor can't win but can only lose one unit, on a 12, which seems fairly safe. Subsequently, the flat bets cancel each other so just the odds are at stake; the odds give the house no edge and lays win more than they lose, although the payoffs are less than what's at risk.

What does the system achieve? Say two solid citizens play through 1980 decisions which turn out to have the statistically-correct distributions. One bets $5 don't pass, then lays double odds. The other bets $5 pass and $5 don't pass, and also lays double odds. Laying double odds with $5 flat means $12 to win $10 on points of six and eight, $15 to win $10 on fives and nines, and $20 to win $10 on fours and tens. The accompanying table gives overall and per-hand expected loss due to house edge, overall and per-bet bankroll fluctuation, and skew characterizing each strategy.

The system doubles expected loss. The flat bets may seem self-cancelling, but the casino "earns" its commission on their sum, not their difference. The bad news is exacerbated because the house's toll rises while the player's potential payout plummets from $5 to zero on the come-out, from $15 to $10 on the point.

The system decreases fluctuation by one third. Since fluctuation is what puts players over the top, cutting this quantity hones the hope of climbing out of a hole and also trims the total take during a normal upswing. Players with shallow pockets, though, for whom volatility represents risk, may regard reduced fluctuation as a boon because it lessens the likelihood of going belly-up during a normal downswing.

The system makes skew nearly twice as negative. This induces more smaller wins and a few larger losses. Aggressive bettors, who are not happy with modest gains, find this a detriment. Conservative players, who can quit with small profits, think it a benefit.

The verdict? The system hurts all players' chances by increasing expected loss. And it limits the potential for bettors financially and emotionally prepared to outride the valleys and pump the peaks. But it may help those who want to decrease bankroll fluctuations and enhance their chances of small wins. As the beloved bettor's bard, Sumner A Ingmark, vacillatingly versified:

Some gamblers like their action brisk,
And aren't afraid to take the risk,
But not all players can afford,
The wagers with the best reward.

TABLE
Expected Loss, Fluctuation, and Skew
for 1980 Craps Decisions
with Two Modes of Play
Result $5 don't pass, $5 pass,
lay 2X odds $5 don't pass,
lay 2X odds
Overall expected loss $135.00 $275.00
Expected loss per decision 0.07 0.14
Overall bankroll fluctuation 634.76 446.47
Bankroll fluctuation per decision 14.26 10.03
Skew -0.33 -0.56
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.