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# Playing it smart -Splits at blackjack are advantage bets even if they don't yield an edge

23 April 2007

When you start a round at any casino game, you're the underdog. The house has an edge on your action. In blackjack, for instance, say you bet \$10 and follow Basic Strategy at a table with more or less standard rules. At the getgo, your \$10 has an expected value of \$9.95 with that figure reflecting probabilities and payoffs. Your five-cent statistical loss is the house's average profit.

A little luck in the deal will flip the advantage to your side. For example, if you receive a 10-nine versus a dealer's seven-up, your hand is "conditionally advantageous." Assuming you stand on the 19, the expected value of your \$10 bet has grown to \$16.15.

Blackjack also has wagers with absolute rather than conditional advantage. You don't have to hope they'll become favorites; you have an edge when you make the bets. Skipping them betting when the house has "the best of it" then declining to do so when you're in the catbird seat, is generally weak gambling.

The additional money tossed on the table to double down, on hands for which this is prescribed by Basic Strategy, constitutes an advantage bet. Likewise for the chips you slide onto the layout when "the book" decrees that you should split a pair. The effects of advantage in proper doubles and splits differ in an important way. Doubling, you have an edge with the hand as dealt using next best alternative usually hitting but in cases like ace-seven versus six, standing; doubling then gives you a greater edge. When splitting pairs, three situations may occur. 1) The initial hand has an advantage, the split pair more so. 2) The initial hand is at a disadvantage, the split pair is at an advantage. 3) The initial hand is at a disadvantage, the split pair is also unfavorable but less so.

For the first of these split scenarios, pretend you start with nine-nine versus six. The conditional advantage standing on the 18 gives the \$10 up for grabs a \$12.81 expected value. Splitting puts \$20 at risk with an expected value of \$24.39. This means that the extra \$10 for the split has an expected value of \$11.58 (\$24.39 - \$22.81), so the bet has an advantage when you make it.

The second split situation is illustrated by pairs of sixes versus a five. You're at a disadvantage standing on the 12, with the initial \$10 bet having an expected value of \$8.43. Splitting, the \$20 total is worth a theoretical \$20.74. The extra \$10 was an advantage bet with an expected value of \$12.31 (\$20.74 - \$8.43).

The third is the toughie because it's somewhat counterintuitive. Imagine you get a pair of eights. If you don't split them but use the next best move (stand versus two- through six-up, hit on seven-up and above), it's an uphill battle. Hitting against 10, for instance, \$10 has an expected value of only \$4.65. Splitting the pair still leaves you at a disadvantage against 10, with what's then \$20 having an expected value of \$15.17.

However, were the second bet simply a wash face and expected values both \$10 the combined total would theoretically be worth \$14.65. The \$0.52 which brings the \$20 at risk on the split up to \$15.17 results from the expected value of the added \$10 being \$10.52. The supplementary bet therefore has an edge when it's made, despite not yielding an advantage on the total.

Converse reasoning highlights the penalty for improper splits. Consider six-six versus seven-up. Basic Strategy is to hit. The conditional expected value of a \$10 bet if you do is \$7.79. Splitting, the combined \$20 is worth a theoretical \$17.51. The expected value of the auxiliary \$10 is \$9.72 (\$17.51 - \$7.79).

The extra \$10 you bet for this split "costs" you \$0.28. Except under unusual circumstances, it's a poor tactic. Unless you think you can lose money on every bet and recover it on volume. Or believe your hunches are more reliable than the laws of the known universe. Either of which suggests you flout the philosophy in this venerable verse by the punters' poet, Sumner A Ingmark:

Expect the unexpected to avoid surprises tragical,
But know that unexpected will be possible not magical.

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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.