Quote from: actmyname on March 22, 2018, 02:27:29 PM

Quote from: LuanX3 on March 22, 2018, 09:07:00 AM

Theoretically, it is possible for a gambling site to profit from a 0% house edge gambling game. There are two reasons why, first is bet size limits and the house having more money than the player.

False. The rest of your post with the scenario does not matter.

It doesn't matter whether there are bet limits or if the house has more money than any given player (or heck, even all the players). If they bet some amount, they have an equal chance of winning and losing. That's it.

Greed doesn't matter. They could still very well win all their bets or lose all their bets. Once you get past this, it's easy to understand that with variance, martingale can end up with a player busting but when you consider the entire space of players (we'll call this S), it's different.

The expected value of the amount that S is returned is going to be 1. And this value is equivalent to the amount that the house gets: 1.

If statistically the house makes no money on each bet, how can you expect to profit regularly?
Hoping that individual players get greedy doesn't help because of the very question: what if they win? There isn't a house edge to make the chance of them losing more likely.

But the fact is that they cannot go over the bet limit. So in cases of martin gale they cannot perfectly use it.

It is correct that we cannot assume that every player will be greedy and they will gamble every penny they have until they lose, but the fact is that there will be players that will get greedy and try and chase their losses.

Assuming we get 1:1 losses and wins for the casinos and the players. With an expected value of 0, as you say. But let's assume 10% of the players do get greedy and try to win back everything and fail, then that means the casino will be in profits from those 10%. Of course we can assume as well that there would be players the profit from the casino, but theoretically it would still be hard to defeat the casino with the limits in place.