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What are the chances of various wins and losses per hand at blackjack?

30 April 2012

To unsophisticated casino patrons, gambling is gambling. They pay their money and take their shots. Usually, although not always, they know the payoffs they hope to obtain. This, because the amounts are posted in some way, in plain sight, on all machines and many tables.

More enlightened solid citizens not only know the payoffs, but – by reading or word of mouth – have ascertained the house advantage or edge on games or bets they make, as well. The most erudite gamblers are also familiar with the chances of winning, losing, or pushing individual wagers – other, at least, than on the slots where chances are assigned arbitrarily and specific values regarded as proprietary data. Dedicated dice devotees, for instance, are or ought to be aware that the odds overcome to win Place bets are 2-to-1 on fours or 10s, 3-to-2 on fives or nines, and 6-to-5 on sixes or eights; likewise, roulette regulars are or should be conversant with chances such as 26-to-12 on columns, 35-to-3 on rows, and 37-to-1 on spots.

At blackjack, proficient players can generally approximate the edge following Basic Strategy at tables having alternate sets of parameters, although few can state the chance of various results. As an illustration, ask an experienced blackjack buff the likelihood that a hand about to be dealt will conclude up or down. You’re apt to get a guess of slightly under and over 50 percent. In actuality, for a six-deck game with resplitting and other liberal rules, Basic Strategy prospects are 42.4, 49.1, and 8.5 percent for net wins, losses, and pushes, respectively.

The considerably greater chance of losing than winning on a hand-by-hand basis surprises the majority of players, who think of blackjack as an even-money game with a low inherent edge and therefore close to 50-50. The poor success rate arises mainly on the 87.8 percent of all hands which Basic Strategy says to hit, stand, or surrender. Of these, just 41.0 percent are projected to win 1-to-1 or 3-to-2, an average of 50.5 percent to lose all or half of the starting wager, and 8.5 percent to push. These results are 36.0, 44.4, and 7.5 percent, respectively, of all hands.

The large difference between percentages of wins and losses are offset by properly managed splits and doubles. The consequences of getting then winning or losing a lot of these hands is usually obvious. But receiving and having them work out at close to the theoretical rates is essential to keeping the house advantage at bay. And not many blackjack players have the faintest idea what frequencies are considered in the normal range.

Opportunities for Basic Strategy doubles in six-deck games theoretically occur in 9.6 percent of all hands. All such doubles have positive expectation and are projected to win far more often than lose – the rates being 55.0 percent to succeed, 38.1 percent to fail, and 6.9 percent to push.

Situations calling for Basic Strategy splits occur in only in 2.5 percent of all hands. Further, not all splits have positive expectation. Some are anticipated to lose more often than they win, but to cost bettors less than it would to stand or hit on the original total. An example is the widely reviled 8-8 vs 10. Standing on 16, the expectation is to lose 53.68 cents per dollar of initial bet; hitting, the projected deficit is slightly less at 53.54 cents per dollar; and splitting, the penalty is lower yet, at 47.48 cents on the dollar. The split is adverse, but it’s the least of the evils.

Of hands calling for splits, 69.4 percent have positive and 30.6 percent negative expectations. In six-deck games allowing resplits of all pairs including aces to four hands and doubling after splitting, chances of various net wins or losses are as shown in the accompanying table.

Projected outcomes of splitting pairs up to a total of four hands

Win or loss     fraction     fraction
   per unit       of all       of all
initial bet       splits        hands

win 4 or more	   3.86%        0.10%
win 3             10.50%        0.27%
win 2             24.19%        0.61%
win 1              6.68%        0.17%
push              13.30%        0.34%
lose 1             8.33%        0.21%
lose 2            22.31%        0.56%
lose 3             8.42%        0.21%
lose 4 or more     2.40%        0.06%

Oh yes. A thought for blackjack buffs who “double for less” or hesitate to split pairs when “the book” so ordains. The butterflies in your stomach are keeping you from laying down the extra dough, right? Well, the real message they’re trying to send is that you’re overbetting your budget and should be putting less at risk from the get-go. If you’re gonna be in the game, be there to win and do it right. The celebrated songster of success, Sumner A Ingmark, put it like this:

Commit to gamble all the way,
Or stay at home and do not play.

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.