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Best of Alan Krigman

Gaming Guru

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Playing smart - If you think doubling earns twice as much as hitting, think again

17 September 2007

Most blackjack players know that properly doubling down raising an initial wager then taking one and only one new card is an advantage bet. When ordained by Basic Strategy, players not only have an edge, but are projected to earn more, on the average, than by following any of the alternatives.

Twice the money is at stake, and can be lost as well as won. But few solid citizens are aware of how this translates into expected profit, or what restriction to drawing a single card implies.

Picture the effect in terms of doubles on 10 versus upcards of two through nine. When the dealer shows two through six, doubling has the same chance of success or failure as hitting. Against seven through nine, doubles win less and lose more often than hits. This, because players would stop after one card against two through six anyway, even with a total under 17 (ignoring a small discrepancy for 12 vs two). Against seven through nine, totals under 17 can sometimes be pulled from the fire by hitting again.

Everything important about doubling on a 10 is presented in the accompanying table. Except the secret to predicting when you'll be flooded with stiffs and when with the cards of your prayers.

Chance of winning, losing, and pushing when doubling or hitting a 10 against two through nine (hits on 12 vs 2 are ignored)

  Upcard	Hitting	 Doubling
		win	lose	push	win	lose	push
	2	55.06%	37.11%	7.83%	55.06%	37.11%	7.83%
	3	56.44%	35.97%	7.59%	56.44%	35.97%	7.59%
	4	57.85%	34.80%	7.35%	57.85%	34.80%	7.35%
	5	59.26%	33.64%	7.10%	59.26%	33.64%	7.10%
	6	61.00%	32.22%	6.78%	61.00%	32.22%	6.78%
	7	57.83%	32.14%	10/03%	56.07%	36.44%	7.49%
	8	54.89%	35.09%	10.02%	53.46%	39.13%	7.41%
	9	50.14%	38.49%	11.37%	49.26%	42.04%	8.70%

The probabilities are identical for hitting and doubling against two through six. Expected earnings for either is the amount at risk times the difference between the chances of joy and sorrow. Doubling is then twice as profitable as hitting, averaged over many hands, simply because twice as much moolah is up for grabs.

Here's how this works for a $10 bet. Say the dealer has a two-up. Hitting, earnings average $10 x (0.5506 - 0.3711), or $1.80. Doubling yields $20 x (0.5506 - 0.3711), or $3.60. Profitability improves either way as the dealer's upcard rises to six because you'll win more and lose less often. Amounts for six-up are $10 x (0.6100 - 0.3222) or $2.88 for hitting and $5.75 for doubling.

For dealers' seven through nine, win and lose percentages differ for doubling and hitting. Doubling, you expect to win less often 56.07 vs 57.83 percent for seven, 53.46 vs 54.89 percent for eight, and 49.26 vs 50.14 percent for nine. The shortfall worsens on chances of a loss 36.44 vs 32.14 percent for seven, 39.13 vs 35.09 percent for eight, and 42.04 vs 38.49 percent for nine.

As an illustration, consider a $10 bet with 10 vs eight-up. Hitting, you expect to earn an average of $10 x (0.5489 - 0.3509) or $1.98. Doubling, it's $20 x (0.5346 - 0.3913) or $2.86.

The table also lets you explore what happens if you cut exposure by "doubling for less." Against two through six, chances of winning and losing are the same for hitting and doubling, so this ploy merely reduces profit. For the previous case of 10 vs six, doubling with an additional $5 rather than $10 cuts theoretical earnings to $15 x (0.6100 - 0.3222) or $4.32.

Against seven through nine, gains and margins of triumph over tragedy are both reduced. At some point, with these upcards, doubling for less has a lower statistical expectation than just hitting. Imagine you bet $10 and have 10 vs eight-up. Hitting anticipates average earnings of $1.98 as above. You'd also average $1.98 if you double with $3.82 instead of $10. Doubling with less than $3.82 puts you below $1.98.

Proper doubling across the board cuts what would otherwise be the edge in blackjack from about 2.0 to under 0.5 percent. There may be valid reasons to forego a double under certain circumstances. But if you do it as a routinely, because you're hesitant to go for the extra dough, you're probably overbetting your fanny pack from the getgo. For, as the poet, Sumner A Ingmark, said:

If you're in for a penny but not for a pound,
You're in trouble before both your feet hit the ground.

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.