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Best of Alan Krigman

Gaming Guru

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How do betting strategies affect your blackjack performance?

9 January 2012

Blackjack card counters can get an advantage over the casino by raising their bets when favorable ranks dominate what remains to be dealt from a deck or shoe. Given the rules dealers must follow and the options available to players, the house has a small edge when ranks are uniformly distributed. If cards taken out of action in earlier rounds leave low ranks in excess and therefore especially likely to be dealt, the house’s edge gets steeper. Conversely, if residual high ranks are in above-average proportion, these are most apt to be drawn and advantage shifts to the player.

Betting strategies in blackjack based other than on this principal, and those in games where probabilities don’t vary among rounds, have no effect on the edge. This isn’t to imply they don’t impact the chances associated with the possible outcomes of specific sessions, however.

Some betting strategies are designed to reduce the prospects of experiencing a losing session. The most widely known and simplest of these is the “Martingale” system. It’s most often used in games that pay even money. Players typically start with low wagers, say $5. If they lose, they double the bet for the next round. They continue to double the amount on every sequential loss, and drop back to the initial level when they win. The reasoning is that losing rounds can’t go on forever, and the ostensibly inevitable win will generate a profit for the set equal to their first bet.

Make believe a solid citizen employing this system loses four tries in a row, then wins on the fifth. The bets are $5, $10, $20, $40, $80. The four losses total $5 + $10 +$20 + $40 = $75. The $80 win on the fifth coup covers this loss and yield a $5 profit. What if there were nine losses in a row? Again starting at $5, the betting sequence would be $5, $10, $20, $40, $80, $160, $320, $640, $1,280. The weakness is that few players have the bankroll and tenacity to go this far, just to net $5. Among other issues, an individual would be $2,555 in the hole after the nine losses and the next bet would be $2,560. Ultimately, the chance of a major disaster is small, but not zero.

In blackjack, the probabilities of hands winning, pushing, and losing are roughly 43, 9, and 48 percent, respectively. Disregarding pushes, and ignoring the effect of 3-to-2 payoffs on naturals and of winning or losing multiples of the base bet owing to splits and doubles, this reduces to chances of approximately 47 percent to win and 53 percent to lose on a hand. The chance of four such losses in a row is about 79 out of 1,000. That of nine sequential letdowns is a bit over three out of 1,000. Both probabilities are low. But it makes little sense to wittingly take even these small risks to win a mere $5, especially when it’s necessary to bet $80 to try to recover in the first instance and $2,560 in the second – with the likelihood of failure being 53 percent in either case.

The flip side of the betting strategy coin comprises techniques to increase the size of possible wins on modest bankrolls. These involve what casino aficionados often refer to as “betting with the house’s money.” That is, pressing wagers using the proceeds of previous winning rounds. When it works, this modus operandi leads to greater profits than could be achieved solely with bets judiciously sized for a moderate stake. The fly in the ointment is that profits for successive wins don’t necessarily accumulate because they’re being put at risk and are returned to the house if a sequence proves to be shorter than the player fantasized it would.

Continuing with the simplified blackjack model, pretend a player starts with $5 and intends to go for three wins then drop back to the base bet. The sequence will be $5, $10, $20. Victory on the third round will yield a $40 return – the $20 bet plus a $20 payoff – of which $35 is the net profit on the initial $5 wager. A more aggressive application of the same concept might involve four in series before dropping back. The sequence is then $5, $10, $20, $40 – for a $75 net profit on the initial $5. The chances of ecstasy are 104 out of 1,000 for three in a row and 49 out of 1,000 for four. Of course, three straight wins at $5 flat only come to $15 and four to $20, as opposed to $35 and $75, respectively. But the progressions yield $5 net deficits if they fail at any point, while flat betting zeroes out on a win then a loss, and leads to a $5 gain on two successes followed by a failure and $10 profit on hit-hit-hit-miss.

You can devise an endless array of variations on betting strategy themes to reduce the risk of a losing session or pump your possible profits. In addition to extending or limiting the lengths of your sequences, you can use such approaches as putting your money on propositions that pay more than even money, locking-up profits before going for the gold, and spreading past winnings over more numbers at craps or roulette, or on multiple hands at blackjack. No matter how you choose to proceed, though, other than in exploiting the opportunities afforded in blackjack by withdrawal without replacement, you can’t circumvent the laws of probability. The inherent edge the bosses enjoy results from the offset between the odds of a win and the payoff – which don’t vary with betting patterns. The venerated versifier, Sumner A Ingmark, elegantly elucidated this reality when he rhapsodized:

How a good gambler wins is obscure and inscrutable,
But the math in casinos is known and immutable.

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.