Blackjack question #1

I never play blackjack. Well, that's not quite true. I think I have played video blackjack machines three times in my almost three years here, all while waiting for a show to begin or my name to be called to a restaurant. I think I lost $5 once, $2 once, and made about $1 once. That's me, Mr. Big-Time Professional Gambler.

Oh, and I played it live once, too. That was when I was here on my honeymoon--we're talking 1984 here, so long ago that I literally can't even remember which casino it was.

But being immersed in the world of casinos, one hears things about games one doesn't play. Something I keep hearing about blackjack that has me perplexed is the complaint by better players that they hate sharing a table with people who don't know what they're doing. As far as I can tell, the gripe is simply this: A player taking a hit when he shouldn't means that the next player gets a different card than he otherwise would have. If that card is a 10 and he busts, it is apparently common to get upset at the player who took what "should" have been his card. The complaint seems to be lodged even by people who are making no attempt at card counting, so that is apparently not part of the issue. As I hear it, many "serious" players will even get up and leave the table because of their fury at the guy who is playing "incorrectly."

If I'm right that this is what the complaint boils down to, it is madness.

Of course it is the case that a player's decision to hit or stand affects what cards will be given to subsequent players. But it does not do so in any systematic way. If Player 1 takes a card, it means that Player 2 gets Random Card B instead of Random Card A. But Random Card B is just as random as Random Card A, which means that it is just as likely to be good or bad for Player 2's situation as Random Card A would have been.

It seems that this is purely a case of selective attention and memory. Player 2 notices when, e.g., Player 1 hits on 17 and catches a 4, which would have proved to be a winning card for Player 2, who instead now busts when a queen comes his way. But he does not mentally attend equally to the situation in which the reverse happens, and Player 1 takes the bust card when he "should" have stood, and Player 2 instead now gets the baby card that gives him the winner.

If the game were played with the dealer (or even the player) selecting a card randomly from somewhere in the deck, instead of always the top card, then this complaint would presumably vanish, because one would no longer be able to determine what would have happened if the offending player had stood instead of hit, or vice-versa. The same would be true if the rules specified that the deck be reshuffled after each player. But there is no mathematical difference between these hypothetical changes and the way the game really is. A random card is a random card. No player can systematically cause either benefit or harm to subsequent players' situations. The effect a player's decision will have on the other players will be unbiased--sometimes favorable, sometimes unfavorable, but with a long-term net effect of exactly zero, with the good precisely balancing out the bad.

Consider a poker analogy. Last night at the Imperial Palace a player recounted how the heart royal flush jackpot had been hit at his table at about 3:00 a.m. that day. He said that it only came because he got up and went to the restroom, thus shifting what cards every player left at the table received. The player who got the royal would have received either one or two different cards than he actually did (depending on their relative table positions) had my storyteller not been absent on the crucial hand. This is the case every time a player leaves the table, joins the table, changes seats, sits out for a few hands, etc.--it changes the cards for everybody else. But nobody complains about it, for three reasons. First, you only rarely figure out what would have happened had the last player/position change not happened. Second, there is nothing "wrong" with any of the actions that result in the alterations, so there is little temptation to lodge any sort of accusation. Third, everybody is still getting two random cards; whatever change is made is just as likely to be helpful as harmful to any given player.

As far as I can tell, the blackjack complaint, though frequently enough voiced that I have heard it from multiple sources despite paying essentially zero attention to the world of blackjack, is utterly irrational. It is based on a combination of superstition, lack of understanding of the nature of randomness, and selective attention to unfavorable versus favorable outcomes.

The purpose of this post is to query my readers and see if I'm missing something. Do I have it right? Is there something actually rational about this complaint that I'm not grasping? It would hardly be the first time I'm confronted with evidence of human irrationality on a large scale, but it would make me happier to hear that there is something genuinely sensible about the situation that I have overlooked, and it is not just another example of masses of people being stupid. Please use the comments to enlighten me.

I have another blackjack question about rationality and irrationality. I'll post it here in the next day or two.