Is blackjack a zero sum game?

is an expectation of zero. What you ultimately stand to win (or lose) in such a scenario is zero. You break even.

One example is a fair coin toss, betting for heads or tails. If you bet an x amount for heads or tails, and receive 1:1 payout, you will break even in the long run, because you are expected to win and lose half the time.

Another example of a zero sum scenario is taking the insurance bet when 1/3 of the remaining cards in the shoe or pitch are 10�s. We have a 2:1 payout here. So, we are expected to win twice our bet 1/3rd of the time and lose our bet the remaining 2/3rds of the time, yielding a zero sum, or expectation.

Choosing to double or not on a soft 15 vs 4 off the top of a deck is also close to zero sum.

Another good example, which a gentleman here posted a while back, is the change machine. You put, for example, a dollar into a change machine, and then you are given back 4 quarters. This is a zero sum scenario, and also specifically a zero variance scenario.

Do you believe in "Flow of the cards" too? Cards such as 7's and 8's have no brain and no conscience and therefore they do NOT try to stick together. However, the cards run at random and can be changed from one random to another random.

because no one else did:

"Is blackjack a zero sum game?"

Blackjack is a unique casino game, which, asking whether or not it�s zero sum, is player action and game rules dependent on. So therefore, it is depending on criteria you haven�t specified on.

If you want a generic figure, the answer is no, it�s negative.

7up's question uses the term "zero sum game". This term has specific meaning in the area of game theory. He then provides examples which validate that he is using it within that specific meaning. Strictly from the perspective of game theory, blackjack is a zero sum game and the dealer/house is a player.

What many people are discussing is whether blackjack is an even money game. From that perspective, the house is just the house. The reason for becoming an advantage player is to learn to identify when the edge in blackjack swings away from the house to your favor and to bet and play accordingly to increase your return.

It may not be the best choice mathematically, I'm no expert there. But it seems to me unless the count goes way high in SD that One hand head up or with one to two players ONLY is the best plan. The count going over +7 seems to give too many 20s for both the dealer and head up player; so I play two hands many times if not most when the count is extremely high.

But when the count goes negative I always wish I had a knowlegeble confederate that where we could in sinc spread two to three hands each; forcing the dealer to shuffle that neg count away. The sooner a new shuffle the chance of a positive count 'we hope', providing one of those skillful dealers doesn't know how to manipulate the deck where another negative deal starts out the better it seems to me. I believe I've heard it called 'clumping', dealers dealing techniques to offset the player's win ratio!

But I'm no math expert, I just know what seems to work.

Count Blackjacula

I took an Artificial Intellegence class many years ago and barely got through.

D

That's why I finally realized to distinguish zero sum versus even money. Zero sum is jargon from the fields of economics and applied mathematics. Computer sciences has taken it from applied math and used it on more restricted problem sets (than, say, economists do). To be honest, I have an econ degree and hated game theory ("you know that I know that you know I know, therefore, you will take X action versus Y action".... yeah, right).

The non-jargon concept of zero sum is what might also be called even money games. Games in which the amount you bet, over time, equals the amount you win. This is where your comment about rule variations comes into play. The rules effect the house's edge and determines how high the count must be for the game to swing from negative expected value to positive expected value.

One player on blackjack table plays against the house, outcome=win or lose
One prisoner in police station plays against the police, outcome...
Confess=5 years in jail
Not confess=0 years or 10 years in jail

Is this a non zero sum game?
Is there a rule that there are minimum two prisoners?

Two players on blackjack table play against the house.
Decision of player A would affect the result of both himsefl and player B, although there is no information of what the result will be.
Two prisoners in police station play against the police, as in the classic example.

If the prisoner's dilemma is a non zero sum game, why the two blackjack players case is not?

Criticism accepted. I meant "tic-tac-toe is the simplest zero-sum game that has been tackled with a computer algorithm..." I hope we don't get into an argument about whether tic-tac-toe is simpler/harder than NIM, etc, of course. :)

But somehow zero-sum seems to be confusing to some, because they are factoring in wagers which don't have to be balanced, but wins/losses do...

It can be attacked by a particular type of game strategy called minimax tree searching... The main point is that it is a "two-player" game. There are lots of games that are not zero-sum, and minimax can't be used to solve them. That's the only reason the term "zero-sum game" is of interest to a computer scientist. It simply defines the solution algorithm for the game. Much like NP-completeness defines how hard computationally the solution will be.

You seem to be describing "expected value". Which is a different thing from a "zero-sum game". If you and I play chess, and you have a FIDE rating that is 200 points larger than mine, if we play a game, it will be a zero-sum game as only one of us can win. But your EV will be that you should win 3 of every 4 games we play because you are that much better than me.

EV and zero-sum are not talking about the same thing. EV is about expected win/loss rate against a given player. zero-sum simply says that only one of the two participants can win a single trial, and it defines the computer science strategy required to play the game (minimax).

In the general sense, either the prisoner wins or he loses. If he wins the police lose and vice versa. The sentence you mentioned is like a wager and odds given at any one game. Think about it like this: In 3cp you will win or lose a specific number of hands and the dealer will win/lose inversely to you. But even though the number of wins/losses match since this is a two-player game, the amount of money you will win or lose is based not on the number of hands you won, but how you won 'em (pairs, tres, etc.)

So again, you have to separate the outcome of the actual game (win or lose or draw) from the money that changes hands. "double or nothing" doesn't change a thing about the fact that if I win, you must lose. But it says a lot about the money that will change hands based on that outcome...

"break even" is not part of a zero-sum game. Two chess players can play and if one is much better, he will win more games than he loses. But for each game played, there is one winner and one loser. Contrast that with trading some sort of goods where both sides win (each has too much of something and by trading away the excess (which would be wasted) he gains something he didn't have enough of.) So both sides win. That's not zero-sum. It isn't about the number of wins or losses. It is about the two-player case in a contest where when one wins, the other loses. We could use a 6-sided die, and define the game where a "1" wins for the roller, anything else loses. The roller will lose 5 of every 6 rolls, but then his opponent will win 5 of every 6 and it is still zero-sum because of that balance of one side wins and the other side loses.

I tried to say that the casino should not be considered as a participant, because the police was not considered as a participant in the classic example.
"Whether the casino is a participant in the game?"...that is the arguing point.

EV is a precise quantity, the average return. The issue of zero sum has no relevance what so ever in regards to advantage play when defined as the computer people do. The number of wins and losses always balance. What is there to talk about?

BTW: chess may cease to be zero sum when you bring ratings into it as I believe they are inflationary.

Non-zero sum is only possible when two sides give up something different and do not place the same value on what is at stake. I pay somebody $5 to wash my car. A clean car is worth more to me than $5. The car washer values $5 more than the time he gave up to wash it. We both win.

The number of wins and losses doesn't match in _all_ games. In two-player games, generally they do, but not always as in the example of trading stuff...

Perhaps some form of Poker would be better here where now there is a fixed pool of money and everyone wins/loses from that pool. No additional buy-ins, no side-bets, or anything to upset the cart. One could, I suppose, call that a "zero sum game" but in computing, it won't work because the two-player algorithm won't work. There is a theorem that says that any N-player zero-sum game can be reduced to individual 2-player games where minimax will work. But not in this case.

I see nothing wrong with your definition for APs, except for the confusion when you try to talk to people like myself. :) For example, if someone offers you a "free lobotomy" would you accept? You turn it down. The later on, you discover that Lexus just came out with a 2007 lobotomy and that was what you had turned down, rather than having part of your brain excised. :)

Common terminology makes communication work...

The dealer hands out money and takes money in. Where does it come from on the sessions where that table loses badly to the players? When I lose my 19 to a dealer 20, who rakes in that money? And who pays me when my 20 beats the dealer's 19? So clearly, in its most elementary form, blackjack is a game between me and the dealer. The game may not be even, or fair, but it is a game between the two of us and when one wins, the other loses. In other words, our goals are the exact opposite of each other's...

The police was not considered as a participant.