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Best of Alan Krigman

Gaming Guru

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Getting the Odds to Work for You at Blackjack

11 August 1997

Players can get an edge over casinos at blackjack. But few are willing to meet the rigors imposed by card counting and the like. Further, the benefits are statistically significant only after more shuffles than most solid citizens are ever likely to see.

Adverse edge notwithstanding, players can easily get favorable odds of winning over the short term. And it's not even essential to go strictly "by the book" to achieve this happy state. In fact, it actually helps to violate a few rules of basic strategy.

You can shift the odds to your side by grouping wagers into rounds comprising progressively-increasing bets. Each bet covers losses on previous hands in the round plus an allowance for a profit. After a win, or when you've lost the predetermined series, end the round and quit or begin again with your lowest bet. The accompanying table shows how odds favor the player starting at two hands, and rise sharply as rounds become longer.

Here's how it works. I'll temporarily neglect doubles and splits.

Say you're aiming for $5 profit in a two-stage round. Bet $5 on the first hand. Win, and the round's over; you've made $5 - $7.50 on an uncontested blackjack. If you lose the first hand, bet $10 on the second. A win now nets you $5 - $10 on an uncontested blackjack. Repeat any hand that pushes. The table shows you're favored 2.6-to-1; that's 72.4 percent chance you'll win from $5 to $10, offset by 27.6 percent chance you'll lose $15.

Maybe your goal is $10 profit on a four-hand round. Start with $10 and progress, as needed, to $20, $40, and $80. The table shows you have 92.4 percent chance, 12.1-to-1 odds, of earning $10 - more if you win with a 3-to-2 payoff for a blackjack. The downside is a small 7.6 percent chance you'll lose a hefty $150.

The Devil may get its due if you take this concept too far. The table shows whopping 89.9-to-1 odds you'll win a seven-hand round. But if you're after $10, the sixth loss puts you $630 down and needing $640 for the final try. Big bucks for a $10 return. This may exceed what you care to risk. It may also top what the house will book at $10 games - a casino custom which keeps deep-pocketed players from fully exploiting techniques of this type.

Doubles and splits assume extra meaning when you use progressive betting to manipulate odds. Either tactic can raise the ante for a round if it leads to hands which lose more than single bets.

There's more to it, though. Correct doubling enhances expected gain by letting players bet more money under advantageous conditions. However, because doubling involves taking a single card, this move reduces or doesn't alter but never increases the probability of a win. Therefore, you sacrifice the amount but improve the chances of a profit if you double only when doing so doesn't lower the probability of winning. This occurs with player 10, 11, or soft 17 versus dealer four, five, or six. For other normally-doubled hands, stand on soft 18 and hit on everything else.

Proper splits likewise boost expected gain, or trim expected loss, but generally also raise the probability of a win or push. Exceptions are nine-nine versus dealer two through six. Stand in these cases; follow basic strategy for all other splits.

The caveat: don't mistake odds for edge. They're not the same. Raising the odds for yourself leverages a strong shot at a small gain with a weak chance at a disproportionately greater loss. Still, if your aim is a modest profit and you have the discipline to quit when you're ahead, this approach may appeal to you. As the poet of parity, Sumner A Ingmark, poignantly prattled:


There are laws of compensation,
Gambling folks too oft forget,
Targets set in moderation,
Are most likely to be met.

 

TABLE
Chance of Winning Multi-Hand
Blackjack Rounds of Various Lengths
Following Basic Strategy
Hands per
round
probability
of winning
probability
of losing
odds of
winning
1
47.5%
52.5%
0.9-to-1
2
72.4
27.6
2.6-to-1
3
85.5
14.5
5.9-to-1
4
92.4
7.6
12.2-to-1
5
96.0
4.0
24.0-to-1
6
97.9
2.1
46.6-to-1
7
98.9
1.1
89.9-to-1
8
99.4
0.6
165.7-to-1
9
99.7
0.3
332.3-to-1

 

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.