The effect of card removal in blackjack

Every now and then, I get an inquiry from a blackjack player who suspects one casino or another isn't playing with a full deck. I've never been able to confirm any shenanigans — I've watched as new decks are prepared for shuffles, counted down shoes and never been able to detect any funny business.

I won't go so far as to say no casino anywhere finagles game conditions, but it's rare. It's in the casino's best interest to offer an honest game. The normal odds assure a profit, and a licensed casino that deals a dishonest game risks heavy fines, temporary shutdowns and even loss of license.

Nevertheless, I was intrigued when a reader told he he'd been in a casino that was having trouble with a shuffling machine. He heard a floor supervisor say, "It's missing some kings."

There was no hint that anything was wrong with the game by intent. Casino employees were working to fix the problem.

Still, it leads to the question of just how big an effect a few missing cards can have in blackjack.

Make no mistake. When high cards are missing, it hurts the players. Fewer 10-value cards or aces mean fewer blackjacks are dealt, and it's the players, not the house, who collect 3-2 payoffs on blackjacks. With fewer 10s, players complete fewer 21s when doubling down on 11, and get fewer 20s when doubling on 10.

Removing all the kings would have the same effect as removing all the 10-spots in Spanish 21, and if you're familiar with that game, you know the lengths they had to go to counter-balance taking a whole 10-denomination out of the deck. Double down on any number of cards, surrender even after doubling down, player blackjacks always win, bonuses on 6-7-8 and 7-7-7, bonus payoffs on five-, six- or seven-card 21s — a whole slew of positive rules were added.

On Michael Shackleford's wizardofodds.com, there's a handy-dandy chart of the effect of card removal in blackjack. Removing a 10-value card per deck from play increases the house edge by nearly half a percent, 0.4932%. That would be the effect of removing a single king from a single-deck game, or two kings from double-deck, six kings from six decks, and so on. Remove all four kings from a single-deck game, or all 24 from a six-decker, and that's nearly a 2% swing.

That's almost half again as bad as the 1.4% increase in house edge that comes with paying only 6-5 on blackjacks, and we know how tough that is on players.

All blackjack games have a built-in question of balance. A rule that helps players, such as the dealer standing on all 17s, is usually going to be offset by a rule that helps the house, such as multiple decks being used. If I think hard enough and go back long enough, I've seen single-deck games in which the dealer stands on all 17s, but they're rare.

That's normal enough, and there are many rules combinations that yield a reasonable house edge. A two-deck game in which the dealer hits soft 17, the player may double down on any first two cards, including after splitting pairs, and may split and resplit pairs for a total of three hands has a nearly identical house edge to an eight-deck game in which the dealer stands on all 17s, players may double on any first two cards including after splits, players may split pairs only once with no resplits, but late surrender is offered.

That first combination has a house edge of 0.39% against a basic strategy player, while the second has a house edge of 0.41%. There are many, many ways to build comparable blackjack games using different rules combinations. Single-deck games are not automatically good games, and eight-deck games are not automatically bad games. Every optional rule a casino chooses to use makes a difference.

But a few rules or game conditions are weighted so heavily in favor of the house that the player's best option is to find another game. The house paying only 6-5 on blackjacks is one of those — look for a game that pays 3-2.

Removing 10-value cards from play, whether by design of the game or by malfunction, requires some powerful, positive rules to make up for the impact it has on the odds of the game. That's the lesson we learn from Spanish 21. If there really are 10-value cards missing from a deck in a regular blackjack game, you don't want to play.