The push

20 May 2018

By John Grochowski

Several weeks ago, I answered a reader who questioned whether high pair payoffs are really wins since they get you your money back, but no more.

They're the equivalent of pushes in blackjack and other games, I told him. Changing the pay table so every payoff was bigger than the wager would create a much more volatile game, and players often would find themselves running out of credits fast.

A different reader responded via e-mail, asking about the importance of pushes in other games.

"I gather that those high pairs are included in the payback percentage on video poker," he wrote. "What about blackjack? Are pushes included in the house edge? What about other games with? How big a difference do the pushes make?"

Yes, the pays you receive on high pairs in video poker are included in the payback percentage in video poker, and the return of your wager is included in calculations of the house edge in blackjack.

In craps and baccarat, you can find listings for the house edge with or without including pushes.

The don't pass bet in craps has possible pushes. If the shooter comes out with a 12, pass bettors lose, but don't pass bettors don't win. They just get their money back.

When you see the don't pass house edge listed at 1.36%, that includes money returned to you for pushes. If you see the edge listed at 1.40%, that assumes the wager will be left in play until it wins or loses, and the money you get back from pushes is not included.

In baccarat, house edges usually are listed as 1.06% on banker and 1.24% on player. Those figures include pushes. If you see house edges of 1.17% on banker and 1.36% on player, those are house edges excluding pushes and weighing only bets played to a win/lose decision.

What about blackjack?

The house edges you see are all include pushes as legitimate outcomes, but we can walk through how much difference it makes.

Let's assume a game with a 1% house edge, just to make the arithmetic easy. Blackjack edges are variable because of differences in table rules, In games where blackjacks pay 3:2, house edges almost always will be lower than 1 percent for a basic strategy player, but higher than 1% for an average player.

If you wager $1 a hand for 1,000 hands, your risk is $1,000, not including double downs and pair splits. In those 1,000 hands, normal expectation would for you to wind up with $990, and the house to keep $10 as its 1% edge and profit.

The $990 you keep includes blackjack payoffs, splits and doubles — the house wins about 491 hands per 1,000 while players win about 424.

The other 85 hands are pushes, so $85 of the $990 on the player side of the table at the end of the trial comes from pushes.

If we were to calculate a house edge including only hands played to a win/loss decision, the house would still have its $10 profit, but it would come from the $915 wagered on non-pushes.

The house edge would be the house's $10 divided by the $915 in wagers, multiplied by 100 to convert to percent. That comes to 1.09%, instead of the 1% when pushes are included.

Which calculations do I prefer? The ones that include pushes. I'd rather not ignore hands that occur fairly often, and which do play a role of keeping us in action until the winner come.

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