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Can You Beat Blackjack by Betting on Streaks?

15 November 1999

Blackjack buffs lose more rounds than they win in the vast majority of sessions, including those which prove profitable. The reason is that bettors lose if their hands go over 21, even when the dealer subsequently also busts. Mathematically, the game is brought into relatively close balance by bonuses for doubles, splits, and ace-10 naturals. Optimum play helps, too.

Many solid citizens, however, think the key to gambling success lies in anticipating and acting on streaks. Some bet more after winning consistent with a belief that favorable hands tend to cluster. Others press after losing, convinced that the longer a past rout, the more the next event becomes due to win.

The precise chances a round will show a net gain depend on the rules in force and the way a person plays. Assume multiple-deck games with resplitting of pairs, doubling allowed on any two cards, doubling after splits, and strict basic strategy. Expected net win and loss rates are roughly 47.4 and 52.6 percent of all rounds, respectively, excluding pushes (no net win or loss).

Using these values, and ignoring possible round-to-round interactions, the chances of various length win and loss streaks are as shown in the accompanying list. As an example of interpreting the data, three consecutive net wins has 10.6 percent likelihood; three sequential net losses has 14.6 percent probability. Note, though, that after two wins or losses in a row, chances on the third hand are still 47.4 and 52.6 percent.

 length ofstreak probability (%) winning losing 2 22.5 27.7 3 10.6 14.6 4 5.0 7.6 5 2.4 4.0 6 1.1 2.1 7 0.5 1.1 8 0.2 0.6 9 0.1 0.3

These probabilities, combined with the amounts of money involved, show why players easily convince themselves that their faith in something special about streaks has a foundation. Either way.

Say you start with \$10 and parlay wins (let profits ride with the original bet). At even money, this earns \$150 in four wins. The figures show 5 percent probability by chance alone. So a \$150 sweep can be expected once every 20 tries -- enough gain sufficiently often to reinforce the religion of acolytes eager to believe. Failure on round five takes the bettor back to zero, while someone who wagered \$37.50 -- the average -- on each round would be \$75 ahead after three wins and one loss.

The converse is a "Martingale" bettor who doubles-up after losing in the hopes of recovery. The chance of six successive losses is 2.1 percent -- one out of approximately 48. Suppose you start with \$10 and are willing to risk as much as \$320. You'll recover in 97.9 percent of all cases, usually without having to go that high. To be sure, the downside is a 2.1 percent chance of dropping \$630. Someone betting \$105 -- the average -- per round would be \$420 behind after five losses and a win.

When each round is independent, streaks are random events which can be expected, but whose occurrence and duration can't be anticipated. Under these conditions, betting on streaks of wins leads to a small chance of a big payday. And betting against streaks of losses leads to a good chance at a modest gain.

Blackjack rounds aren't totally independent. One reason is that probabilities on each round depend on what's already gone from the available supply; "counters" try to exploit this demonstrable but small factor. A second reason is that patterns may occur in the discard pile, then persist after invariably imperfect shuffles, because completed hands tend to comprise a few high or multiple low cards; "clumpers" try to utilize this speculative but potentially large effect. Whether, or to what extent, these phenomena are reliable predictors is a topic of contention among gambling enthusiasts. I abstain from the arguments -- adhering to the agnosticism advocated by the poet, Sumner A Ingmark:

When passions run stronger than proof,
Unless you're involved, stay aloof.
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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.