Stay informed with the
NEW Casino City Times newsletter!
Best of Alan Krigman
How Pushes Affect House Advantage in Casino Games6 July 2005
Some casino bets either win or lose. Others have a third possibility, they can "push," neither winning nor losing. In games where pushes can occur, they may play a more significant role than most folks realize. Always, although superficially, because the action is slower with fewer exchanges of money in any given number of rounds or time period. Occasionally, yet more substantively, when pushes change the house advantage by shaving the probabilities of losing and winning by different amounts.
To illustrate this phenomenon, envision a hypothetical game with outcomes dependent on players' decisions. Assume a particular even-money proposition can be handled in two ways. One offers 46 percent chance of winning and 54 percent of losing. The other has 45 percent chance of winning, 5 percent of pushing, and 50 percent of losing. Which is preferable?
The enigmatic blackjack decision hit or stand on a 12 against a dealer's two-up shows the potential pertinence of pushes in the casino simulacrum of reality. And, for solid citizens whose quest for enlightenment goes past assuming "the unseen card is a 10," helps explain why "you're supposed to" hit this hand.
Blackjack buffs who stand on 12 win only if the dealer busts and can't push. The chance of the dealer busting and therefore of players winning when they stand is 35.36 percent. The probability of the dealer finishing from 17 through 21 and beating players who stand at 12 is the complementary 64.64 percent. The joint's juice is accordingly (64.64 - 35.36) = 29.28 percent.
Theoretical outcomes for hitting and standing on 12 versus two-up are summarized in the accompanying table. The figures show this particular hand to be an underdog regardless of how executed.
Theoretical outcomes of alternate ways to
Under some circumstances, an argument can be made for picking the option predicted
to win most often. Standing might get the nod in this instance, but the improvement
over hitting is a scant 0.56 percent. The decrease in the chance of losing when
players hit rather than stand is much greater, at 4.43 percent. And, the edge
represents 3.89 percent less penalty hitting than standing. All because of pushes
you might not have thought important. Since basic strategy in blackjack comprises
the moves giving the bosses the least edge on adverse hands or the players the
most under favorable conditions, "the book" says to hit. Recalling
the rhyming rejoinder of the Punter's Poet, Sumner A Ingmark:
In settling on the tactical technique you're gonna use,
Best of Alan Krigman