How Does Varying Your Bet Affect Your Chances of Survival?

1 June 2005

By Alan Krigman

In games or on bets that pay close to even money, bankrolls normally tend to drift up or down slowly. Keeping bets uniform, players can rack up the dough on extended hot streaks; however, they often leave these sessions wishing they'd raised the ante when they were winning. Conversely, with the same bet on every round, they can go bust during cold streaks. Then, many solid citizens use the benefit of 20-20 hindsight to kick themselves for not increasing their wagers after each loss so, when that win finally popped, they'd have staged a meaningful recovery.

Everyone knows that winning is good and losing is bad. And that the pleasure and grief grow as amounts get larger. But few folks think much about the downside cutoff. Specifically, out of funds means out of action. Players who bust not only can't continue in the hope of a recovery, but may also have little to do for the rest of the time they'd planned for the casino except mope.

It's accordingly helpful to know how these betting strategies up after wins or up after losses impact the probability that a specified stake will be enough for a desired time duration. Consider a hypothetical game paying even money, while giving players a 49.78 percent chance of winning. The dynamics will be much like blackjack and baccarat, and not dissimilar to outside bets at roulette and many wagers at craps.

Whatever your base bet $5, $10, $100 call it one unit. Assume you press by increasing your bet by a unit for each subsequent round either when you win or you lose, depending on the strategy you select, and return to the base after a hand goes the other way. For instance, pretend you elect to press on a win and encounter the sequence win, win, win, lose, win, lose, lose. Your bets would be 1, 2, 3, 4, 1, 2, 1, 1. The same sequence, pressing on a loss, would lead to bets of 1, 1, 1, 1, 2, 1, 2, 3. Regardless of strategy, your average bet will be about two units.

What's your chance of outriding normal downswings for sessions you consider long enough on your original bankroll with either strategy? And, for reference, what would the be chance keeping your bets constant but at twice the base level so you'd be at the same average, although with less volatility, as had you pressed?

Consider a casino visit during which you'd like to be in the thick of things for 400 rounds. This would be about four hours of blackjack at a table with three other players, each person covering one spot. If you started with 25 units and bet two units flat every round, the probability you'd still be in action at the end of the 400 rounds would be about 37 percent. On a stake of 50 units, your chance of enduring would rise to 75 percent.

Instead, say you followed one of the indicated pressing models. With a 25-unit bankroll, your chances of staying alive for 400 rounds would be 38 percent raising after every win and 32 percent after every loss. Starting with 50 units, your prospects would be 74 percent press-on-win and 62 percent press-on-lose.

Note that chances of surviving normal downswings in sessions of the desired duration are nearly the same for pressing on a win and for betting the average two units flat. Both offer a somewhat greater likelihood of surviving the occasional run of bad luck than pressing on a loss. And, the figures show that adequate bankroll is a far more important factor than the choice of one or another of these betting strategies.

The lower survival rate in pressing after losses is a consequence of making large bets when you're behind, under the constraint of a finite cash reserve. If you had deep pockets, and the bosses put no upper limit on bet size, this approach would give you a good shot at a small profit. Under real casino conditions, however, raising after a loss has a tendency to knock players out of the box during cold streaks that would not be fatal to those betting flat or pressing after a win. The famed poet, Sumner A Ingmark, might have had just this quandary in mind when he mused:

Though major wins may seem a prize,
Finite stakes should make you nervous,
So systems that slight bankroll size,
May not help but be disservice.