Is blackjack a zero sum game?

On the net...
Zero sum games:
Chess, for example, is a zero-sum game: it is impossible for both players to win (or to lose).
Monopoly (if it is not played with the intention of having just one winner) on the other hand, is a non-zero-sum game: all participants can win property from the "bank". In principle, in monopoly, two players could reach an agreement and help each other in gathering a maximum amount from the bank. That is not really the intention of the game, but I hope I have made the distinction clear: in non-zero-sum games the total amount gained is variable, and so both players may win (or lose). When they can both win by cooperating in some way, we might say that their cooperation creates a synergy.

The casino is the "bank" as above? Or it is just another player in the game?

or all can lose. Or some players can win. The luck of one player has nothing to do with the luck of other players at the same table. Obviously an incredibly lucky dealer will translate to mostly unlucky players.

Suppose 100 people put up $10 entry fee for a chess tournament. All $1000 is returned as prize money. But suppose a sponsor matches the entries so that the prize pool is now $2000. Now it is no longer zero sum, it is positive. If no money were put up by sponsers, and the organizers deducted expenses from the entry fees before determining the prize pool, then it would be negative.

A game is zero sum when the amount returned is equal to the amount wagered by the participants. It is positive when the amount returned is greater. It is negative when the amount returned is less.

The question of zero sum is better applied to a fixed pool of money that is to be distributed. Paramutual betting is negative. The house pays the winners out of the money wagered by the losers and keeps a cut. Blackjack is not like this when played for money at live tables. The house pays all winners.

after searching on the net, some examples tell the different stories:

"Options and future contracts are examples of zero-sum games (excluding costs). For every person who gains on a contract, there is a counter-party who loses. Gambling is also an example of a zero-sum game."

"Situations where participants can all gain or suffer together, such as a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, are referred to as non-zero-sum."

"played in a casino is a zero-sum game"

"All sports and gambling games are zero-sum."

In blackjack, can we say the house is one of the participants?

Normally, in the world of computer science, the term "zero sum" is a two-player game where if one wins, the other loses. It doesn't really factor in prizes or anything else. With exactly two players, one player can't win more games than the other player loses, the wins and losses sum to zero, which is where the name comes from. The entire game of chess revolves around that idea, as does checkers, connect four, Go, and any other type of game between two players. The game of 21 is zero-sum when you only consider the dealer and player, since they are really just playing one of several games that are being played. At a full table, the dealer is playing 4-5-6-7 zero-sum games simultaneously...

Poker is a better counter-example since everyone is playing against everyone. Just two people and it turns into zero-sum again...

In blackjack, the house is one of _two_ participants. If there are multiple players at the same table, there are multiple "games" being played simultaneously, but either the dealer or a player wins, which is what a zero-sum game is all about...

You should not believe everything that's written on the net.
Chess is clearly an unfortunate example because it's not necessarily played for money.However,when their is a prize fund, it's only partly financed by entry fees, so Chess is certainly not a zero sum game.
A typical zero sum game is poker (when played privatly) because players play against each other.Poker played in a casino is even a negative sum game.
Typical casino games like roulette or blackjack are definitely not zero sum games, because the bank is not considered as a participant.
All the players can win in roulette or blackjack but not in poker.

Francis Salmon

The luck of one player has nothing to do with the luck of other players at the same table.

There is a mild effect associated with card-eating. Players who wong in or out, or spread to multiple hands, slightly deflate the expectation of other players at the same table.

In the example, what the two prisoners gain should be considered as what the police lost. But the police is not counted as a participant, only the two prisoners do.

If the police is counted as a participant, then it is a zero sum game.

For blackjack, the casino acts the same as the police, (although the casino is involved in the win/loss, as the police), still should not be counted as a participant, so blackjack is a non zero sum game.

...just an idea.

Your definition is wrong. You can find a definition of "zero-sum game" in any good computer science book that discusses artificial intelligence. Chess is zero-sum because if one side wins, the other side must lose. It has nothing to do with chess tournaments or chess matches, just simply chess games. The simplest zero-sum game is tic-tac-toe, but there are many others. Their most notable characteristic is that they can be attacked by a computer program based on minimax search, and minimax is purely a zero-sum game algorithm.

That blackjack is a game between the dealer and the player. It doesn't matter that the dealer plays several games simultaneously. I've done that several times (I have played multiple players at the same time, something that you might find any good chess player doing at a local club. But each game is, by itself, zero-sum. Because you have one winner, and one loser or the game ends in a draw. What happens to me in the game of 21 doesn't affect any other player's bankroll... So they are not involved in "my game" and I am not involved in "their game" other than we sit at the same player and make playing decisions with the same dealer (in succession).

I'm not sure how one could draw any other conclusion with the computer science / game theory literature so full of this same explanation and examples, repeated over and over...

Using these twisted definitions, flipping a coin would not be a zero-sum game because I could bet two buck on heads, you could bet 1 buck on tails, so I would win or lose more than you. But the game is not about the "bet", it is about the "outcome". And the outcome of these games (chess, go, connect-4, tic-tac-toe, and 21) is strictly defined in that there can only be one winner or loser (the player or dealer) except when there are none (a push)...

... there are lots of games simpler than tic-tac-toe.

ETF

"The simplest zero-sum game is tic-tac-toe"

You seem to know what you're talking about but you have to admit that the notion of zero sum game existed long before computers were even conceived. Computer science has obviously redefined the term (yet in the context of gambling, I don't see what purpose would serve the earthshaking discovery that in a contest between two persons, if one wins the other one loses).
The traditional notion of zero sum game was designed to answer the question whether a certain activity of a group of people would enrich the group as a whole or not.
In the case of Poker the answer is clearly no, in Blackjack it's a resounding yes!

Francis Salmon

> The traditional notion of zero sum game was designed to answer the question whether a certain activity of a group of people would enrich the group as a whole or not.
>In the case of Poker the answer is clearly no, in Blackjack it's a resounding yes!

Sorry, but Blackjack does not enrich the group. You are confusing the difference between zero sum and advantage play (which is based on fluctuations in the edge between the house and player).

Blackjack is a zero sum game composed (as SSR said) of multiple games between individual players and the house. You put up a bet, the house matches it, and the winner gets the money. In no case do both dealer and player win; if it's a tie, then the bet pushes. And in no case does either side win more than the other lost; you never won $5 where the house only lost $4.

You might go down a few threads to "what you need to know about vegas", which says the casino hold from blackjack in nevada in 2006 was 12.3%. The house lets you walk in, pick a bet (within table limits) which they implicity match, and pay you based on the results because they know that roughly 12% of money played will go in their pocket. Just because it's zero sum, doesn't make it even money.

This boils down to semantics, so there is no right and wrong. There is convention, however.

Blackjack is a decision problem. Only one player makes decisions in the interaction. OTOH "games" (in the game theoretic sense) involve multiple players making decisions that influence payoffs.

Others have mentioned dealing with Wongers, etc., which complicates matters, but in most realistic scenarios, blackjack is not a game. We can turn it into one (in convoluted ways) e.g. by adding players to the table who vary their strategy based on the way you play. But this kind of point is merely academic. Therefore it is an optional homework exercise to come up with examples of this.

Lefty

It has been repeatedly said that the house should not be considered part of the group.Otherwise all games are zero sum and the notion makes no sense. Furthermore, it was quite obvious I was talking about proficient players but for Mike I will rephrase:
In Poker, the players at the table cannot win as a whole, no matter how strong they are,in Blackjack they can.
Anticipating further objections: Im not talking about Caribbean Poker!

Francis Salmon

BP, I understand what you mean here. However, you, myself and most other veterans understand there is no such thing as luck. I wish there was a better word to express what you mean by "luck", "lucky" and "unlucky". I just don't know if there really is a proper word within the English language that would be best used in this sense.

The problem with these words noted above, is that the uninformed person can take it in the unintended superstitious form.

Maybe I'm wrong, as others have posted via this forum, that spreading more hands when the count is high is to their advanantage on SD and DD games, but I find this contrary in experence.

Like yesterday, SD count is +5, one other player, he spreads to three hands.

In my oppinion, which may not have the mathematical soundness as some on this forum, why would I want to split up the hands? It reasons to me, the chances of catching a 20, BJ, or great double-downs are greater. It appears to me, that adding more hands on a positive count can not only waste good potentials for 20s etc,,,, but put one in danger of stiffs and mediocre 17s and 18s.

I can totally agree when the count is plus 7 or greater, head-up, that two hands may be best.

But multiple hands seem to eat up great expectations in one round.

Is this your experince Green Baize Vampire? Or is my understanding of the math too random in my observation?

Count Blackjacula

The subject should not have even been brought up. A game cannot be anything other than zero sum unless the participants do not wager the same thing (like money). Only an exchange where one values what he gets more than what he gives up could it be anything other than zero sum.

Perhaps if I played poker with a plumber. I would wager $100 cash and he would put up $150 of his services. Then it could be a positive game if I indeed valued his services more than dollar for dollar and he came out ahead providing his services for .667 on the dollar. No game where like commodities are exchanged can be anything other than zero sum.

So in the sense that the computer people are talking, all gambling games and contests are zero sum. But that is not how advantage players use the concept when talking about positive and negative games. The casino is not seen as a participant. When the total amount given away exceeds the total amount put up by the participants (not the casino) it is positive. When it is equal, it is zero sum. When the house takes a cut and distributes the rest, it is negative.

Along the same line, I have wondered what is the best situation for a player as in the following scenario:

10 total hands to share with the dealer in a pack of cards

Dealer gets five hands, player gets five hands

Dealer gets three hands, player gets seven hands

What is best for the player?