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Best of Alan Krigman

Gaming Guru

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Do the tortoise and hare teach you how to win at gambling?

21 December 2009

Everyone's heard of the tortoise and the hare. The plodder beat the sprinter. Does this apply to casino gambling? Are you apt to fare better wagering at the low end of the volatility scale with steady small returns or the high end with bursts of big payoffs?

There's no universal answer. It depends on your definition of "fare better." You may mean earn any profit at all. Perhaps you figure you can always get your paws on – say – $100 or $200, so you'll go all-in to shoot for a sizeable sum you're not apt to amass any other way. Or, conceiva-bly, your main goal may be a long run at a table or machine, win or lose but not go broke.

Consider the alternatives of $10 bets on Red or on one number at single-zero roulette. These choices have the feature that house edge and rounds per hour are equal in both cases so they don't complicate the comparison. However, similar principles apply to short- and long-odds proposi-tions within and across other games.

On the average, for huge numbers of solid citizens over extended periods, results would be the same either way. But individuals rarely think about averages. They focus on particular sessions or on casino visits involving statistically small numbers of trials.

Pretend, for this purpose, you'll play for an hour. Roulette will give you about 45 spins in this time span. With either of the prototype bets, the maximum loss is $450. On Red, this is also the most you can win. On one spot, you can go as high as $15,750. The chance is greater with the former, but both are minuscule.

Computer simulation of a million 45-spin sessions indicates what you can actually expect.

Betting $10 on Red, the likelihood of breaking even or earning a profit is 42.8 percent. The distribution is 38.1 percent under $100, 4.6 percent between $100 and $200, and 0.1 percent $200 to $300. Conversely, the overall chance of a loss is 57.2 percent. This includes 47.8 percent under $100, 9.2 percent between $100 and $200, and 0.2 percent between $200 and $300.

Betting $10 on a single spot, the good news is a 34.4 percent prospect of breaking even or being ahead. The breakdown shows chances of profits from $100 to $200 of 22.2 percent, $600 to $700 of 8.9 percent, $900 to $1,000 of 2.6 percent, and over $1,000 of 0.7 percent. The chance of ending with a loss is 65.6 percent. This includes probabilities of 36.4 percent of finishing under $100 in the hole and 29.2 percent of dropping $450.

Realistically, a $450 loss limit exceeds what most $10 table game aficionados would bear. Lowering this to $200 would increase the fraction of bettors who'd go belly-up before complet-ing 45 coups. Here's how the probabilities line up in this situation.

For $10 on Red, expectations with $200 or $450 loss limits are almost identical. Differences arise for $10 on a single spot. With $200, overall session chances are 26.7 percent to win and 73.3 percent to lose. For winners, likelihood is 16.0 percent of earning $200 to $300, 7.6 percent of making $600 to $700, 2.4 percent of grabbing $900 to $1,000, and 0.7 percent of snatching over $1,000 profit. The loss side includes 17.0 percent of finishing under $100 in the hole and 56.3 percent of busting out.

One implication is that higher volatility yields fewer but richer winning sessions. The roulette alternatives, though, show that with adequate funding, differences in chance of success may be smaller than might be imagined. For 1-to-1 and 35-to-1 bets on $450 stakes, the former lead to winning sessions less than 9 percent more often than the latter. Another ramification is that decreasing loss limits raise vulnerability to bottoming out, with impact becoming stronger as the volatility of the action rises.

You should decide which outlook you like better. But now you have more information to help make that decision. Or, as the bard beloved of passionate punters, Sumner A Ingmark, smartly said:

Much of gambling's a matter of what you prefer, But good gamblers to fact and not fancy defer.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.