The “not a zero sum game” canard is tiring. Just because a game is not sero-sum doesn’t mean it suddenly becomes fair, however we choose to define “fair”.
Here’s a non-zero sum game: hold 'em poker, no blinds, yet the value of what the blinds would be magically appears after every hand in the pot. An excellent example of a game with incomplete information. If all players use the same strategy (we don’t even have to assume that an optimal strategy exists), the player with the deepest pockets wins in the long haul, statistically speaking. Every player attempts to minimize losses by folding in proper situations and only rarely bluffing, and every player attempts to maximize wins by sticking out their good hands with favorable pot odds. The total number of chips increases after every game, but you could also make it increase after every transaction by tossing the big blind in after the flop, turn, and river, or after every round of betting, etc.
The game gets interesting when the lead player decides to loan someone some chips who would otherwise be out. It’s a relatively safe loan since some of the chip leader’s earnings are from the “free” blinds, and since no one has to pay blinds, and since everyone is just about as good… but no longer can they all be using the same strategy. The person in debt to the chip leader needs better pot odds:hand odds than others in order to cover his debt. He sees less hands through to completion, increasing everyone else’s chance of winning.
But let’s make game number two. The game almost inspires shadenfreude when the players aren’t equal. The chip leader can make loans to anyone who needs it from his stack of “free” blinds, further decreasing their odds of entering hands (since they’d need better pot:hand odds), further increasing his take of the free blinds, and still having the safety net that when any of his opponents manage to stumble on a good hand that he’ll get some of the earnings anyway. After his initial lead, his chances of weathering randomly bad hands become very good. The more people he has “working” for him, the more likely he is to stay ahead because, as before, he will see more hands through than the others since the necessary odds for them to stay in will go up, and the necessary odds for him to stay in will go down. They fold more often, and he collects more free money.
Who here would volunteer to play the first game, and everyone sits down with the same number of chips? Who would volunteer to enter the first game after there is a clear chip leader? Who would volunteer to enter the second game, knowing that you weren’t the best player, even if everyone started out with the same number of chips? Who would volunteer to enter the second game after a clear chip leader emerged?
Oh, final rule: you can’t quit playing. Remember, your survival is at stake.
Maybe we should try game three, instead. Instead of the free money going just into the pot for anyone to win, the free money is split up between the people who stuck though to the end of the hand. The winner always gets 60% of it, and the rest is shared between the losers (those who didn’t fold but had a worse hand). Feel like playing now?
Game four has a casino dealer that collects 20% of every pot, but otherwise plays like game three.
Game five has a casino dealer that collects a percentage of the pot based on who won and how much they had in chips at the time of winning, but otherwise plays like game three.
Game six has a casino dealer that collects a percentage of the pot based on who won and how much they had in chips at the time of winning, and distributes some of that to the losers. The rake never exceeds 40%. It otherwise plays like game three.
Game seven has a casino dealer that collects a percentage of the pot based on who won and how much they had in chips as a step function where some money means no rake, the next level of money means a 10% rake, the next level means a 20% rake, and so on, up to a maximum of 40% with no ceiling. It otherwise plays like game six.
Game eight is like game seven except that it sometimes uses its rake to replenish the lower quality chips, and definitely replaces cards so that they can’t be marked from hand to hand. Oh, forgot about cheating, didn’t you?
Game nine is like game eight, except now players do have to pay their blinds.
Game ten is now like game nine, except that if a player has to leave the table momentarily the casino can use some of its rake to cover the player’s blinds… but the player automatically folds all hands when this happens.
Game eleven has the chip leader encounter a new player who is better than him but with far, far less chips. He is allowed to hire this new player to play with his bankroll and his cards, and promises he can have 10% of every winning pot added to his own earnings. This player is, of course, playing his own hand still.
Additional rules to be added on to various games: fixing the loan percentage. Allowing players to make outside bets about who will win the hand. Forbidding players to make outside bets on their own hands. Only one hole card is face down. Add as necessary.
Which game do you want to play? Why? What rules get made that would stop you from playing the game? Why?
We forgot to play the non-zero sum part right in all of this and just had a constant influx of free chips that were or were not distributed in some way based on winning. Would it really make a difference WRT which game you’d prefer to play if we said that the free money came from some percentage of bets instead of just being a flat amount?
Just because wealth is increasing doesn’t mean a damn thing to most of the players after a clear chip leader emerges. It does change the dynamics, yes, but in the medium to long term, the chip leader has better odds and deeper pockets. That is what it takes to win poker.
I understand, of course, that poker is not the best model for an economy… but it is a good way to illustrate that spontaneous wealth generation isn’t a recipe for equality, or even floating all ships. Without knowing whether we were excellent players or not in game two before sitting down, we would be a very stupid gambler to sit in on it when better games exist. Game one and game two have their purity in their favor, if that is a measure of “good games”. I don’t believe so, but the question I really intend to address is the non-zero sum aspect. Only in particular circumstances does it actually mean more than squat.