The Ups and Downs of Progressive Betting.

21 December 2005

By Alan Krigman

Many table games have 1-to-1 or other relatively low payoff ratios, and correspondingly close to 50-50 chances of success on any coup. But don't plan to get rich in these games betting $5, $10, or $25 round after round -- winning or losing like amounts and waiting for a miracle extended run of hits to break the bank.

Fine. Earning $25 or $50 with $5 bets at blackjack, minibaccarat, or whatnot -- on top of several hours of thrills and a coupon for the all-you-can-eat buffet -- may be what you want from a casino visit. Not everybody's out to parlay pennies into pig heaven.

Still, this doesn't force solid citizens bent on big bucks to begin with bulging bankrolls and head for the high-stakes pits, play table games with jackpot-oriented payoff schedules, or turn to the slots. Progressive betting is an alternative.

Progressions meant to escalate earnings are diverse. The common thread is to raise after bets win and return to the base after they lose. Broadly, series may be "arithmetic" with raises by fixed amounts such as $10, or "geometric" with increases being constant multiples such as two-times the previous wager. Another distinction is in the amounts or multiples, which may differ and may be constant or variable. And increases may continue until the string of wins ends or the table limit is reached, or bets may plateau or regress -- in full or part -- at some arbitrary level.

Most progressive bettors adhere to two articles of faith. First, they believe that luck occurs in streaks so one win implies another. Second, after a win, they think their own purses are protected because they're raising with the house's money. Faith, of course, doesn't need empirical evidence (that's why they call it faith). However, when a progression produces a plump profit, proof seems to be in the pudding and trust is reinforced in the primacy of pressing as a prudent punting principle. When a progressive scheme sends a player to the lockers, or -- worse -- the cash machines in the lobby, the rationale is something like "nobody wins every time" or "that's why they call it gambling."

Two mechanisms distinguish progressive systems from flat betting at some base level. 1) Progressions boost the average amount at risk during a session so players bet and accordingly win or lose more. 2) They magnify the volatility of the game and therefore increase the amplitudes of bankroll fluctuations up and down for the same average exposure.

Picture how this works in terms of two archetype progressions. Say that a blackjack buff is willing to risk a $500 bankroll to earn a $1,000 profit. Assume a $10 average wager.

Betting the $10 flat, the chance of earning $1,000 before losing $500 -- regardless of the number of rounds involved -- is 21 percent. And, independently, the likelihood of completing 400 hands without going belly-up is 97 percent.

Blackjack buffs who begin at $5 -- pressing indefinitely by $5 after every win and dropping back to $5 following a loss, will average just under twice the base bet, $10 per round. With this arithmetic progression, the chance of reaching $1,000 rather than forfeiting $500 improves to 25 percent. However, the probability of surviving 400 hands declines to 92 percent.

Players who double-up with what they consider the casino's dough upon a win then revert to $1 upon a loss, average about 10 times the base bet at blackjack. So averaging $10 per round means starting at $1. This geometric progression will hit the $1,000 zenith before dropping to the $500 nadir 33 percent of the time. But it will survive 400 rounds in only 2 percent of all tries.

Progressive betting modifies the dynamics of a game. Understanding how and why can help you decide whether the approach is right for you. And, if so, how to tailor a series as a trade-off between your fondest dreams and worst nightmares. For, as the balladeer of balance, Sumner A Ingmark, wrote:

'Tween devastation and a treasure,
There lies a point, though tough to measure,
Where you can optimize your pleasure.