PLAYING IT SMART by ALAN KRIGMAN

Whether Betting Progressions Work Depends on how "Work" Works

Strategies for varying bet size during a game are part of the gambling mystique. Not because, as some solid citizens believe, they're loopholes in the laws of chance. Rather, owing to the trade-offs they introduce between probabilities and amounts of wins and losses during sessions of reasonable duration.

Bet sizing strategies were once of interest only to table players. The reason was that slot buffs traditionally bet either the minimum number of coins to stretch their budgets, or dropped the maximum to earn the bonuses on critical winning combinations. Now, there are machines that take from one to 90 nickels, $0.05 to $4.50, per round. On these, folks who set realistic goals at various levels, rather than shoot only for the moon and accept a crash back to earth if they miss, can apply the same principles.

Effects of betting strategies on the likelihood of various session results depend on details of the game, propositions on which players bet when options are available, and the specific progressions employed. Definitive session profiles require each situation to be studied individually. And, answers would differ even for minor changes in conditions, such as whether "increasing a bet" meant raising it by one unit, doubling it, or whatever.

Still, some generalizations can help gamblers understand the concept and devise approaches suiting their personal preferences.

• Flat betting (keeping the same wager every round) most closely balances chances of finishing ahead or behind, with ever more extreme wins or losses becoming gradually less likely.
• Raising bets after every win widens the range over which sessions finish, while yielding small probabilities of large profits offset by greater chances of low to moderate losses.
• Raising bets after every loss also widens bankroll swings, but improves the chance of ending with a small to moderate profit, counterbalanced by greater prospects of large losses.
• Raising bets when you're ahead (playing with their money) narrows the range over which most players complete sessions, favoring more small losses and occasional big scores.
• Raising bets when you're behind (chasing) also tends to yield narrow ranges of outcomes -- characterized by most players earning small profits and a few getting badly hurt.

Some hard figures can be placed on these soft generalizations by analyzing a specific situation. For this purpose, I used a computer to simulate 1,000 baccarat sessions for each approach, always betting on Player. Wagers started at $1. Flat betting stayed at $1. With the other options, wagers increased by $1 whenever the condition applied, and returned to $1 otherwise. The session ended after 200 rounds, or when the simulated loss exceeded $100. Some key differences among the approaches are evident from the accompanying table. Scale up to your own tier by multiplying the dollar values by your base bet size.

Session characteristics for alternate betting strategies

?	highest profit	worst loss	% of players ending ahead
Flat	$??? 39	$ 49	42.9%
Press on win	??? 120	?? 82	38.6
Press on Loss	????? 82	?109	45.4
Press if ahead	?2,495	?110	4.7
Press if behind	????? 41	?136	81.7

The bankroll swings characteristic of each strategy are another factor. To compare the simulated sessions by this criterion, I converted some statistical mumbo jumbo into a volatility index and arbitrarily set it at 1.0 for flat bets. On this basis, the volatility index came out to 2.3 for press on win, 2.5 for press on loss, 7.1 for press if ahead, and 2.9 for press if behind.

Some players, in switching from flat to progressive betting, cut their initial wagers. This would make sense in the schemes evaluated, since the average bet is about $2 in progressions on wins or losses and "if ahead," and about $1.50 in "press if behind." If you halve your base bet to allow for this difference, divide the dollar values in the table and the volatility indices by two to estimate the impact. And, in deciding whether to adopt one betting strategy or another, recite this rhyme by the popular paragon of progressive poetry, the immortal Sumner A Ingmark:

---

Weigh the profits of prevailing,
'Gainst the penalties of failing.

(c) 2001, ICON/Information Concepts Inc

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