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Best of Alan Krigman

Gaming Guru

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Playing it smart - When will the next streak start?

6 August 2007

Gambling is rife with misconceptions and bad advice about streaks. Misconceptions that they're special phenomena ongoing processes somehow sustained by inherent momentum. Bad advice telling players how to exploit the hot ones and blunt the cold.

Big bucks can obviously be made by continuing to press bets when they happen to keep winning. And, conversely, disaster can clearly be averted by cutting back or quitting rather than pile on losses when coups continue to run sour. Solid citizens might therefore look back on series of wins and be pleased at having had the foresight to go for the gold, or lament not doing so. Or, with 20/20 hindsight, review a string of adverse rounds and be happy for having dropped back, or sad about chasing losses.

Unfortunately, at any juncture, what's gone before doesn't anticipate what's to come. So you can start getting aggressive when you think you're on a roll, and give it all back in short order. Or quit to stem your losses while your luck is on the outs, and miss what would have been the redeeming rounds.

Ultimately, you can't know you're at the beginning, in the middle, or at the end of a sequence that in retrospect you'd call a streak. You can, however, consider the probability of a streak of any given duration, given the chance associated with each coup. This may be worthwhile in gauging the rarity of a streak about which you fantasize whenever you board the bus. Perhaps more cogently, it may be helpful in formulating a strategy for balancing your hopes and fears as a game ensues.

Assume you bet on a 50-50 proposition such as the flip of a balanced coin. The probability of two, three, four, and five wins in a row is 25, 12.5, 6.25, and 3.125 percent, respectively. That of a streak of 10 wins is 0.098 percent. At 50 percent per round, the likelihoods would be the same for losing streaks. Either way, chance falls off rapidly with duration. Figures differ for bets other than in 50-50 situations, but chances of streaks always decrease with length.

Say you play jacks-or-better video poker. Your shot at a return of any size on each hand is 45.440 percent. A run of five wins has only 1.937 percent chance; 10 wins drop you to 0.038 percent. A losing streak is slightly more likely. Five and 10 losses in a row finish at 4.835 and 0.234 percent, respectively.

With a "lay" bet, the promise is greater of winning than losing although, of course, you put more at risk than you can pick up. An example would be $1 each on 25 spots at double-zero roulette. Chances on any spin are 65.789 percent of winning $11 versus 34.211 percent of losing $25. The probability of five wins in a row is 12.235 percent; 10 in a row is 1.519 percent. On the losing side, prospects are only 0.469 percent of a five-spin cold streak and 0.002 percent of going down for 10 successive spins.

Don't be fooled by figures like these into thinking that series of wins or of losses are special classes of phenomena. A set of 10 consecutive heads, for instance, is simply a group of 10 arbitrarily specified events. Here, since possible outcomes of each flip are equally likely, the chance of 10 heads is the same 0.098 percent as that of any other designated ordering such as two heads, followed by three tails, followed by five heads.

Identical math governs the roulette case, where wins and losses aren't expected to occur with equal frequency. A series of five wins and five losses in any particular arrangement has 0.058 percent probability less than that of 10 wins, more than that of 10 losses. This is not to be confused with the chance of five wins and five losses in any unspecified order. This could be formed in 252 ways and would have 14.554 percent probability.

The next time you experience a streak, you may think to yourself (or someone will say) you should have started betting big when it began. Remember, then, the proverb of the poet, Sumner A Ingmark:

You can't know the future until it's the past,
So don't count your money before it's amassed.

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.