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Best of Alan Krigman

Gaming Guru

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How Betting Progressions Affect Bankroll Swings

2 October 2000

Many table game players believe betting progressions are magical secrets of gambling success. While innumerable progressions are possible, all fall into four categories. 1) Raise bets randomly when you have a hunch you're going to win the next round, drop back when your extrasensory perception draws a blank. 2) Raise bets after a win or when you're ahead, drop back after a loss or when you're behind. 3) Raise bets after a loss or when you're behind, drop back after a win or when you're ahead. 4) Raise bets as probabilities change during the action and conditions get more favorable, drop back when they become more adverse.

Progressions increase the bankroll fluctuations apt to be experienced in the course of a game, relative to those projected for flat-betting the same average amount. I'll illustrate the phenomenon for random baccarat progressions. Assume a $25 average bet for a session comprising 87 hands -- half on Player, half on Banker. Expectation is to be $25 down at the end of this session owing to the house advantage, regardless of betting strategy.

About half of all players wagering $25 flat can figure on finishing the sessions between $175 in the red and $125 in the black -- a $300 range. Betting $10 and $40, each 50 percent of the time, this range grows to about $350 -- from a $200 loss to a $150 profit. A random progression, 50 percent at $10 and 25 percent each at $20 and $60, means that roughly half the solid citizens who try it will close from $225 down to $175 up -- a $400 range. The valleys and peaks expected during these sessions are about twice the final values. That is, with the $10-20-60 progression, nadirs exceeding $450 down and zeniths over $350 up can be anticipated in approximately half of all 78-session games.

What if bets are varied in accord with the apparent flow of the game? Raising on wins or bankroll surpluses tends to yield sessions with small chances of big hits. Raising on losses or bankroll deficits introduces bias toward high likelihoods of small wins. The extents of these effects are governed by the zeal with which bets are increased in each instance. Neither method reduces, let alone overcomes, house advantage. But both alter the characteristics of individual sessions. Players can accordingly opt to wager their wherewithal in long shots at big paydays, good odds of achieving modest gains, or something in between.

The fourth type of progression, pressing when probabilities become more propitious, is most often associated with counting cards in blackjack. Players who monitor what's been withdrawn from a shoe know when the remaining cards are particularly rich in 10-values. Under this condition, edge may be with the players rather than the casino and raising bets is mathematically beneficial. Still, just as a player can profit from normal upswings when the house is favored, a card counter can suffer from normal downswings when the situation is reversed. And, many would-be counters have learned the hard way that the wide spreads required to gain meaningful edge lead to violent fluctuations and therefore the possibility of serious short-term losses.

In essence, blackjack buffs who don't count cards but double down and split pairs properly also raise their bets under favorable conditions. This isn't the same as a card-counting progression, but it elevates expected earnings on given hands while escalating the inherent volatility. Similarly, craps players who take or lay odds on Pass or Don't Pass put extra money in action with no edge, offsetting part of the 1.4 percent house advantage on the base bet. Higher odds multiples lower the casino's juice on the total -- but, again, makes the roller coaster ride more severe.

After the dust settles on a session, everyone knows how he or she should have bet to exploit a string of wins or overcome a run of losses. Good gamblers understand in advance how alternate betting progressions affect the magnitude and direction of the swings to be expected, and follow strategies consistent with their goals and resources. The poet, Sumner A Ingmark, put it this way:

Gambling is more than just winning or losing,
Bettors have options and skill's in the choosing.

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.