How to Win an Unbeatable Game

You frequently hear non-gamblers grumbling that players can't win because the odds favor the house or the casino has the edge. Were that not annoying enough, you also read experts describing casino games as "unbeatable." Yet the same gurus tell everyone how to win. And solid citizens who follow this advice, not to mention some who flout it, often do. Such apparent contradictions are not mutually exclusive. They differ in the time frames from which they are viewed, with reconciliation complicated by results being matters of probability rather than certainty.

I'll use single-zero roulette and a $100 bankroll to illustrate. Similar reasoning applies to other games and amounts.

Imagine the shortest conceivable roulette session. You wager your wad on a single spin, then walk -- regardless of outcome.

You could put all the money on an "outside" bet such as "red" or "odd." Your chances are then 18 out of 37 of earning $100 and 19 out of 37 of blowing $100. That's a 48.6 percent shot at winning versus 51.4 percent at losing -- the same amount either way. Considered from another angle, if 1,000 players made this bet, 486 would be expected to hit and 514 to miss.

Alternately, you could bet the entire $100 on a single number. Now, your chances would be one out of 37 to pick up $3500 and 36 out of 37 to drop the $100. That's 2.7 percent versus 97.3 percent, but it's $3500 to $100. Again thinking of those 1,000 players, 27 are projected to win $3500 and 973 to lose $100.

Other one-spin possibilities let you improve your prospects of pleasure by shaving the size of the prize. An example might be to bet $50 on each of two 12-number columns. This gives 24 chances out of 37 to win $50 and 13 out of 37 to lose the $100. That's 64.9 percent likelihood of $50 profit contrasted with 35.1 percent of $100 loss. When the 1,000 hypothetical players try it, 649 should strut home $50 richer and 351 slink away $100 poorer.

Maybe you prefer longer games with less exposure per spin. Start with the same $100, bet $10 per round on each of the two 12-number columns, and quit when the well runs dry or clear $50. Analysis based on "risk of ruin" shows that your chance of triumph is 57.6 percent. Had you bet only $5 per column, your chance of reaching the goal before losing your stake would be 48.5 percent. Back to the 1,000 players, 576 will achieve the $50 target the first way, and 485 will get there with the lower bets.

There are further trade-offs. The longer you play, and the larger the fraction of your bankroll you bet per round, the more apt you are to bite the proverbial dust. Begin with the $100 and bet $5 on each of two 12-number columns. You have a 30.8 percent chance of going bust within 100 rounds and a 65 percent chance of hitting bottom before 200 rounds are finished. This is equivalent to 308 and 650 of the 1,000 players losing their bankrolls within 100 and 200 rounds, respectively. Betting $10 per column drops your chance of outlasting 100 rounds below 1 percent, and having money for 200 rounds close to -- but not quite -- zero.

Some conclusions can be drawn from these examples. (1) You can adjust your play to enhance your chances of winning sessions in beatable games. (2) Chances of winning rise as earnings amounts drop. (3) Chances of reaching specific targets rise as bet sizes increase. (4) Chances of surviving sessions of arbitrary duration with given bankrolls grow as bet sizes decline. (5) As a group, players lose more than they win. (6) The longer you play, the greater the chance you'll lose your entire stake.

This shows how and why bettors can and do have winning sessions, even strings of successive successful casino visits, playing games that are supposedly unbeatable. That elusive entity, luck, lurks under the tables and behind the machines. But, as Louis Pasteur said, "Luck favors the prepared mind." Goals and matching betting strategies are key elements of that preparation for gambling. As the poet of perplexity, Sumner A Ingmark, put it: