The Long and Short of All-or-Nothing Gambles

2 January 2002

By Alan Krigman

A venerable school of gambling thought advocates betting an entire bankroll all at once, then leaving - win or lose. The annals of casino fact and fancy describe gamblers who've done it, big time. Usually "in the good old days," whenever they were.

All-or-nothing bets aren't for everybody. In fact, they're hardly for anybody. Most people prefer to savor the action for extended periods. Many get queasy about risking more than a small portion, let alone all, of their pokes at once. Those who chiefly chase jackpots or other rich returns know that every try is another chance, never mind what that chance might be. Solid citizens who opt for wagers that pay close to 1-to-1 wait for streaks, betting moderately or starting small and pressing when they sense a run. Both groups realize the stars and planets may take time to align favorably, and size their bets to survive until it happens.

While you may never elect to go for broke, two key elements of legitimate logic underlie the approach. And understanding them can help you develop a more sophisticated gambling perspective.

The first factor involves the way the casino makes its money, and conversely, how bettors in the aggregate lose theirs. The house has an edge on every bet. Multiply that edge by the wager and you obtain the casino's theoretical profit. Over enough decisions, fluctuations caused by individual wins and losses get smoothed out and the casino coffers tend to fill with the forecast "take."

Say a million players start with $200 apiece and play games where house advantage is 1 percent. Were each to bet the $200 in one fell swoop, some would win and others lose but the casino would home in on 1 percent of $200 times a million, or $2 million. If the players each bet $5 per round, they'd likely be able to continue for hours, during which time they might average 200 bets. Now, the "handle" would be $5 times 200 rounds times a million players or $1 billion. The casino would earn 1 percent of the $1 billion, or $10 million. The bosses squeeze less from the all-or-nothing patrons, and the players accordingly fare better.

The second key element of the single-bet strategy has to do with the way wins and losses are distributed. Assume a million players make the same wagers repeatedly until they win, and then stop. More players will triumph on the first round than the second, on the second than the third, and so on. The accompanying table shows how many of the million are anticipated to succeed on the first three successive rounds for some representative bets - a lay ("no four" at craps: six ways to win and three to lose), a 50-50 proposition (the flip of a coin: equal chances), a longshot (a single spot at roulette: odds against winning are 37-to-1).

 

Maybe you're thinking, "Hold the phone! More rounds means more chances and more winners." Correct. But this addresses how many players are expected to win within some number of tries, not the number predicted to win on each subsequent round.

Here's one way to use the table. Imagine a million roulette players with $200 each. Were they to bet it in one lump sum, you'd expect 26,316 to win $7,000 each and 973,684 to go bust. Were they to bet $100 on the first spin and quit if they win or put the other $100 up for the second spin, you'd expect 26,316 to win $3,500 each, 25,263 to net $3,400 each, and 948,061 to bite the dust. You can see the trend and its implications for a longer shot at a bigger return versus a greater chance at less profit.

High rollers with million dollar bankrolls, who stake it all on one bet, are exceptional. But you've probably seen folks buy-in with a few hundred dollars, who bet it all on a single round, and wondered what these heretics had in mind by flouting rules the gurus said were sacred. Now you know. The punters' poet, Sumner A Ingmark, commented on the contradiction in this resonant rhyme.

Behavior that at first seems rash,
Looks foolish if it leads to trash,
And crafty if it gets the cash.