Monday, April 20, 2009

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.

21 comments:

Unknown said...

I saw that time and time again while banking blackjack for a corporation here in California. It really is insane. This was at a tiny $5 minimum table with a huge house edge though... to hear that people to that at high stakes...

Well it explains Vegas now, doesn't it?

Gunslinger said...

I imagine it's no different than the mentality of a poker player who, when they get their money in as a mere 2:1 favorite, believe they are entitled to win EVERY time, and go nuts when they don't. In blackjack, when this type of player sees someone take a card where they're sure 95% of players wouldn't, and they SEE what card they would have gotten that would have given them a winning hand instead of busting, well, someone has to be blamed, and the person playing incorrectly is the easy scapegoat.

Wow, my apologies for that run-on sentence.

Coach Parker said...

You're correct. This is a common complaint, often from people who should really know better. In my book, this line of reasoning is second only to the roulette player betting against or with streaks.

There's a slightly different and equally invalid complaint about crap players at a table when the deck's good. It pisses me off way more when you've got a full table of min betters with a rich deck all get dealt 20s and my big bet picks up a 15. Of course they did nothing to affect this (other than eat up more of the deck by not kindly leaving the table) but it still gets to me.

As for blame or credit for the cards coming out, it can be amusing to see what "would have happened" but as soon as someone tries to apply intent or causation, it becomes very clear what kind of a player you're talking to.

Michael said...

It is entirely selective memory. Blackjack players fail to realize that the player taking or not taking a card they should have not only allegedly changes the outcome of that hand, but also of every other hand dealt from the deck or the show. It used to drive me nuts when I played Blackjack.

I also hear from BBJ whores how you should always post out of position or come into a game out of position rather than wait 1, 2, or several hands to come in after the button because they or their friend waited and a jackpot hit. I look at them and say "ummmm, but if your you or your friend did take a hand then the result of the hand would have been entirely different". They don't get it!

Michael

Pete said...

You have it correct.

In the Book KO Blacjack by Olaf Vancura and Ken Fuchs they provide a mathematical proof of the fact that another players conduct is neutral to your EV on a particular hand.

My copy is packed away somewhere or I would copy the proof.

Grange95 said...

You are overlooking one important detail, I think--a shuffled deck in poker or traditional blackjack is ordered. Unlike dice which are truly random each throw, the deck in fact has "memory" as to which cards have been dealt or removed from play. Also, dice can't be "set" to give a partiular string of outcomes (7, 3, 11, 8, 12, etc.), but the order of a deck is in fact "set" once shuffled.

To use your royal flush example, you are correct that the cards dealt are random, so no player has any particular expectation as to the cards he picks up on any given hand. However, once the dealer has shuffled and cut the cards for a specific hand, each player's hand and the board is "set".

So let's say you pick up AhKh. The flop comes out QhJh6d. There is a premature turn because the dealer acts too quickly. To correct the error, the floor will have the dealer burn and turn the river, then shuffle the premature turn card back into the deck. Now, if the Th was the original river card giving you the straight flush, wouldn't you agree that maintaining the order of the deck to enable you to hit the card you were supposed to hit actually matters a great deal? Alternatively, let's say that the Th is the card inadvertently exposed on the turn; aren't you going to be furious if "your" turn card ends up not being in play? (This happened to me once recently where a dealer error kept me from flopping quad 9s--oh well, errors happen!).

Similarly then, if a player makes a bad (incorrect) play in blackjack, and the dealer ends up not busting when they otherwise would have with proper play, or someone improperly hits and takes the next player's ten on his double down, it is entirely understandable that players get upset. In those cases, the player did not get Random Card B in place of Random Card A; instead, he got Specific Card B instead of Specific Card A. Of course, human nature being what it is, players only remember when the replacement card is bad for them, and forget the many times it was good for them (which is a more valid criticism of this kind of whining).

In any event, with the advent of continuous shuffle machines at many blackjack tables, this "you took the bust card" or "you took my card" complaint no longer has any validity.

Cranky said...

I used to play blackjack before poker bit me. I think the frustration I have is with people who are ignorant of the best way to play (so you lose the least) for whom the game is a big guessing game on every card. The reality of the situation is that, once you know basic strategy, if you're not a card counter, you're really just an educated monkey taking the same actions every time. I used to have the kind of reaction you spoke of in your post, but then I began noting when someone "taking the wrong card" won me money. That got me over my frustration.

Anonymous said...

How about this example: third base has fifteen, dealer has a six up. The entire table stands and third base hits a ten and busts. The dealer then turns a four and everyone busts.

Anonymous said...

What about the following situation?

If you count cards, and the count favors 10 (i.e., there are a lot of 10's left) then the following is -EV to you:

There are two players. You have 15, the other player has 16. The dealer has a 6 showing.

The correct play is to stand, and see if the dealer busts. This is basic strategy as you know.

But combined with the count, it's even more in favor of the other player standing. But does it change your overall EV? I think it does....

Hmmm.... It would take me too long to write a program, but a simple test using a real deck should work.....

(Thanks for getting me to waste 30 minutes of my life for this, lol)

The Vegas Flea said...

This is why I stopped playing recreational blackjack.

Most of the time you'll get criticism from the players AND the dealer. No thanks.

timpramas said...

I agree with your observations. Still, it was frustrating at times to know the outcome would have been favorable for me had another player at the table played his/her hand "correctly." But I always knew another player's decisions were neutral in their effect on my results and do remember the "incorrect" play of others benefitting me as often as it hurt. The most frustrating part of blackjack would be players who would ask others for advice, I would give polite advice, and have players ignore the good advice to their detriment. I was always thinking it too bad there wasn't a game in the casino where I could play against other players rather than against the house in a game with a built in edge. Then I saw a sign for a casino's "poker room" and my black jack days were mostly over.

RedXBranch said...

I only ever play blackjack at the low limit $5 table. It is recreational at this limit.....for everyone at the table whether they admit it or not. It is very aggravating when someone tells you how to play YOUR money. Blackjack is not a team sport, but trying to get that through the thick skull of some nit wit is like.....like...trying to WIN at a $5 blackjack table. And BTW....if you want to play $50 a hand, do us all a favor and go to the higher limit table.

Great blog

MMMed said...

Just arguing with grange95. Of Course the deck is "set." But unless you have marked deck, or some other way that you know the order of the cards, it is still random card A and random card b. If I was allowed to put the deck in a certain order that I wanted, then it would be specific card a and specific card b. Since I can't find a casino which will let me do that, it is still random card a and b.

Anonymous said...

You are wrong.

If the serious player were in the habit card counting and then the anger becomes rational. Any window of opportunity is only ever going to be for a limited number of cards, some idiot hitting where they should never do so is costing the serious player significant fractions of opportunity that they will have waited hours for. To reduce the chances of this happening it is important to get stupid players to not hit when the dealer is showing a 3 or 4 or 5 or 6. The continual stream of acerbic commentary on stupid play is rational, because even if it makes you seem like a jerk it is not going to get you banned from the casino whilst providing the guy to your right with a rational explanation on how their bad play will ultimiately impact on the profitability of your card counting will.

Anonymous said...

Great post...

You are absolutely right and any of the other posters who claim otherwise are simply perpetuating bad math. Grange in particular.

Certainly the deck is set, but the point is you don't know HOW it is set. Will the poor-playing BJ player have an affect on the card you receive? Of course he will, but the point is you don't know what that affect is. Grump's point is that sometimes it will benefit you and sometimes it won't. And the fact of the matter is, it will be 50/50 either way.

One thing I like to do when I see abuse levied on a novice player is, when the abuser wins the next hand, I tell him, "You would have busted if Joe here hadn't made that mistake earlier." Whether it is true or not is immaterial - the abuser doesn't know.

The only caveat I will provide is that, although I don't believe it to be true, I suppose counting cards may change things. (It should be noted that Grump explicitly excluded the case of card-counters in his complaint of abusers like this.) I believe the simulations that determined the player advantage associated with tens in the deck all assume that other players at the table are playing basic strategy. I can't say for sure that it matters. Intuitively, I think it does not.

I'm not a mathematician but these arguments always come down to "conditional probability." That is, a probabilistic statment that starts with "Given that..."

For example, in the case of roulette...The probability of 15 Reds coming up in a row is astronomically low. However, GIVEN THAT 14 Reds have come up, the probability of 15 Reds coming up is the same as the probability of 1 Red coming up.

If you have a 12 and the dealer has a 10, the probability that the 1st card on top of the deck is a 10 is equal to the probability that the second card on top of the deck is a 10. So your probability of winning/losing is the same regardless of how the guy in front of you plays. However, the example everybody seems to be describing is, GIVEN THAT the bad player has refused to hit his 16 and GIVEN THAT I get the 10 he would have gotten, my probability of losing is higher. Well, of course it is - the probability of losing is exactly 1 - you've just removed all the probability out of it. But you've only described one scenario - not the general one.

For every scenario like this you describe, I can describe one that works the other way. For example, the bad player refuses to hit his 16 and the next card is a 9. I win.

Irwin15 said...

I think it's a lot like when a donkey gets the money in bad in poker, we never get upset about it unless they pull the miracle card to beat us.

Yes, we should be happy they put their money in so bad, but some of us exclaim, "how could you call that" and "didn't you know I had a set". However, if we would have won the pot we wouldn't have said anything at all, we would have been happy about our win and wouldn't have thought but for maybe one second on how stupid that guy was for making the call.

Anonymous said...

Anon 3.23pm here again.

The strategy the other players take is irrelevent to how any other players hand will play, but that is not the point.

Having a lot of tens remaining is the desired state that rarely happens. It only occurs for the last few cards played in a shoe. A serious player will identify this and increase bet size to extract maximum value.

If there are only 2 players at the table and both are competent. They do not take uncalled for draws. Each of them get more chances to win when the going is good.

If 1 of the players was a donk they would take the draws. That reduces the number of hands the serious player gets to play when the going is good.

I imagine the closest analogy for a poker pro is a player a skilled as yourself who plays slow. The impact on your profitability is neutral on a hand by hand basis, but you play less hands and therefore make less money.

Pete said...

Yes a counter may in fact have a situation where it is better that the other player not draw another card as he is depleting a beneficial deck . . . which is what the poster above is saying.... but in this case it is true that the counter doesn't want the other player to draw another card regardless of whether correct basic strategy calls for a hit or not. In fact the counter wants the other player to get up and leave so that the counter can maximize his hands with the beneficial deck.

Anonymous said...

Pete,

Yeah, but counters also do not want to have a dealer's full attention.

Anon 3.23pm

Anonymous said...

Anon 3.23 is not addressing the general case. He is assuming that the mistake the novice player makes is drawing when he shouldn't. He is not accounting for the times the novice player doesn't draw when he should (in which case the advantageous deck is perpetuated longer).

So, unless you can show that the more common mistake is to hit when you shouldn't, in the long run, again, the effects cancel each other out.

Anon 8:49

Anonymous said...

8.49,

A Thats how PG wrote out the complaint and is my experience of how it happens.

B Its harder to call someone an idiot for not taking a hit. For example you are both on 13 and he stands, but you hit. If a 10 comes you bust, but it is really hard to tell him he is an idiot for not busting. If a 7 comes you aren't going to be feeling pissed off about it.

C I've seen people complain about hitting on a 12 when the dealer has a 2, these were serious players who I couldn't figure to be ignorant of the game - that bothered me for the longest time until I came up with the above theory. Don't go shooting it down with your logic.

3.23