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Best of Alan Krigman

Gaming Guru

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How Helpful Are Doubles and Splits in Blackjack?

28 April 1997

House advantage in blackjack comes from settling the dealer's hand after the player's. If both have the same final value, for instance 20, the hands "push" and neither wins. Except when both "break" by exceeding 21. Here, the bettor loses even if the dealer subsequently also goes over the limit.

Under standard multi-deck rules, a dealer must draw to 16 or less and stand on 17 or more. This gives the dealer 28 percent probability of breaking. Solid citizens following identical rules - with no options to split or double - will have the same odds of various final hands, including 28 percent chance of breaking.

Results balance, no advantage either way, except when the player and dealer both break. The likelihood this will occur is 28 percent of 28 percent or 7.8 percent, and would be the house edge in such a game. The 3-to-2 payout on uncontested player blackjacks shaves this to a still-whopping 5.5 percent.

Edge can be cut to half a percent or less with player options. One such alternative is standing below 17 against suitably low dealer up-cards. Another is augmenting bets after initial cards are dealt when circumstances permit and conditions are favorable.

Doubling down is a way to augment a bet that raises the expected return on a hand. A player makes a second bet, up to the value of the first, then draws a single card. Splitting, the other way to augment a bet, sometimes increases expected win but may also be used to trim anticipated loss. A player divides a pair into two starting hands, each with a bet equal to the initial wager.

The import of splitting and doubling is shown in the accompanying table. Entries give chances of winning and losing multiples of the initial bet. Values are for players who follow "basic strategy" in games in which pairs can be resplit into as many as four hands, with doubling is permitted after splitting and on any two cards. Under these rules a one-unit bet can grow eightfold, resplitting pairs into four hands and doubling down on each.

 

betting
units
probability (%) of
winning
losing
0
8.82838
*
1
32.58078
43.35600
1.5
4.50858
0
2
5.86603
4.23710
3
0.24553
0.21257
4
0.07695
0.05238
5
0.01673
0.01086
6
0.00458
0.00225
7
0.00083
0.00034
8
0.00010
0.00003



The table shows that players can expect to lose almost 11 percent more single-unit hands than they win. Part of this will be made up by 1.5-to-1 blackjack payoffs. The rest of the compensating effect occurs because multi-unit bets tend to show net profits.

Consider, for instance, a three-unit net. A player can expect to win three units 0.24 percent of the time and lose this much 0.21 percent. Such a win could occur several ways. Perhaps on a three-way split with no doubles, winning every hand; maybe on a four-way split with two doubles, winning both doubled bets while losing and pushing one each of the singles.

OK, you may be thinking, splits and doubles favor players precisely when they help the most - with extra money on the table. So, why not make these moves more aggressively than basic strategy suggests?

Because the benefits come from acting under propitious conditions. Sure, splitting and doubling by the seat of the pants may turn out well, but the odds are that doing so will cost players their shirts. The minstrel of multiple bets, Sumner A Ingmark, summarized it this way:

Gambling houses' firm foundations,
Rest on those whose speculations,
Aren't investments but donations.

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.