Missing card at blackjack

8 November 2015

By John Grochowski

QUESTION: I was playing at a charity event against the dealer who had a five deck shoe. I won huge.

At the end of the night he counted his cards and realized that 11 of the "bust cards" (4, 5 and 6s) were missing from the deck. The total number of cards he had was only 249, by 260.

He asked for all of his money back because he said the odds were way in the player's favor. Is that true?

ANSWER: The elimination of 11 low cards does favor players, and if you know basic strategy, you probably had an edge on the game, depending on what rules were in play.

You didn’t tell me what rules the dealer was following, so I’m going to assume a five-deck game in which the dealer hit soft 17, you were allowed to double down on any first two cards, split any pairs except aces up to three times but split aces only once, and blackjacks paid 3-2.

That game gives the house an edge of 0.59% against a basic strategy player.

Now let’s look at the 11 missing low cards, from a card-counter’s perspective. In the Hi-Lo count, each ace or 10-value card is counted as minus-1 as it’s played, and each 2, 3, 4, 5 or 6 is counted as plus-1. The five missing low cards are equivalent to starting the game with a running count of plus-11.

Counters divide that by the number of decks remaining to be played to get a “true count,” or the balance of high cards vs. low cards per deck. Divide the plus-11 running count by five decks and you get a true count of plus-2.2, which you’d round to the whole number, plus-2.

Each increment of plus-1 shifts the edge by about 0.5% in favor of the player. If you start with a house edge of 0.59%, it becomes a house edge of 0.09% at plus-1 and a player edge of 0.41% at plus-2.

So if my assumptions on rules are correct, basic strategy players had an edge of about 0.4%. Average players, on the other hand, still would have been at a disadvantage, spotting about 1%.

If the rules were tougher, then the dealer may still have had an edge. If blackjacks paid 6-5, for example, the normal house edge would be 1.95%, and the short deck would have narrowed that only to 0.95% against basic strategy players.


QUESTION: I have a good one for you. I’ve never hit two jackpots in a row, like some of the players you’ve written about. But I was playing a progressive video poker machine [in September] and drew a royal in spades. I was excited. I’ve had royals before, but always for $1,000. This one was up to $1,153.63, and they rounded up to $1,154 when they paid me.

What was really unusual about mine though, is that right after I’d hit it, before I’d even been paid, the meter reset to $1,000, and a guy across the bank drew a royal. He hadn’t noticed the reset, and he called over an attendant and told her, “This was over $1,150. How come I’m getting only $1,000?”

She had to tell him that I’d beaten him to the punch. He sounded a little miffed.

ANSWER: Congrats on your royal, and I’d offer congrats to the other player, too, if he wrote in. A royal is always reason to celebrate, even if the payoff wasn’t quite as large as he’d hoped.