Can a casino make money on a 0% house advantage?

[Spaded]

I would think so, as long as the minimum bets are high enough.

Lets say a guy has $100 and sits down at a fair 50/50 betting device. No basic strategy needed. The machine requires him to put in a $25 token each play. If he loses his money, he goes home. If he doubles his money, he keeps playing (he loves making money!) until the day is over or he goes broke.

Now here is why I think the casinos ARE able to make money on a 0% advantage device. The casino ALWAYS quits while it is ahead (the man loses his $100 and walks away), but if the man is ahead he keeps playing until he has to go home.

Is this basically a question of bankroll? The casino has a seemingly infinite BR while the guy has a BR of $100. If the betting was at $10, then he would have to lose more bets to lose his money, and the variance in a 50/50 game would not be high enough for the man to go broke in a short amount of time. If the bets were at a minimum of $50, variance would take his money very quickly, and he would go home a good percentage of the time a loser.

The law of large numbers makes the casino advantage 0%, but the players will leave when they are tapped out, meaning the players do not take advantage of that law.

[ThinkQuick]

I think you'd find some of the old martingale thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=probability&Number=1717442 &fpart=1&PHPSESSID=) (s) very interesting.

One thing I am sure of is that if the casino had a game where the house edge was 0% only when the player employed perfect strategy, they would clearly make a killing.

[Spaded]

Of course if you add in a basic strategy to a game, then yes the casino would make a killing, considering most people are just there to gamble for fun. That's why blackjack is so profitable with its extremely low house advantage.

I guess I should edit my above post to say no strategy!

[Spaded]

[ QUOTE ]
I think you'd find some of the old martingale thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=probability&Number=1717442 &fpart=1&PHPSESSID=) (s) very interesting.

[/ QUOTE ]

Interesting, yes, if I didn't hate late night math /images/graemlins/smile.gif

I'm good at math but I hate having to use symbols, letters and numbers to visualize things. I just like to use intuition, and my intuition tells me that NO betting strategy will help you win money in the long term at any casino game!... except card counting /images/graemlins/wink.gif

[PairTheBoard]

Not everyone plays until they lose all their money. People do go home winners. The Casino would not make money on such a game.

PairTheBoard

[elitegimp]

Any interesting computer simulation:

Give each of X players a bankroll of Y and let them play until either
(a) They are broke
(b) They have played Z hands

Fiddle with X, Y, and Z, and see what happens! (And then report back /images/graemlins/smile.gif)

Example: 5 people play, each starting with 4 bets (i.e. $100 when the game costs $25 to play). Let them play till they're broke or until they've played 20 games, then see if they've lost money (collectively... so sum up all the losses).

I'll try to remember to do this tonight when I get home, but I'm going to a bar beforehand so it may not happen...

edit: although, with specific numbers (i.e. 4 bet bankroll, 20 game limit) you could set up a Markov chain and see if it has a non-zero expected value. Intuitively, I'm not sure...

[Spaded]

[ QUOTE ]
Not everyone plays until they lose all their money. People do go home winners. The Casino would not make money on such a game.

PairTheBoard

[/ QUOTE ]

Of course people go home winners, otherwise the game wouldn't be popular. People go home winners at blackjack, slots, and even the dreaded wheel of fortune with the >20% house advantage.

If you played an infinite number of the 0% advantage game, variance itself would eventually knock you out.

[pzhon]

[ QUOTE ]
Now here is why I think the casinos ARE able to make money on a 0% advantage device. The casino ALWAYS quits while it is ahead (the man loses his $100 and walks away), but if the man is ahead he keeps playing until he has to go home.

[/ QUOTE ]
You are wrong. The casino does not always quit while it is ahead. There will be many winners. They balance out the losers exactly.

E(X+Y)=E(X)+E(Y). The expected value of a series of 0-EV bets is 0. The casino does not expect to be ahead.

[ QUOTE ]

Is this basically a question of bankroll?


[/ QUOTE ]
No.

For some reason there is a common misconception that it gives you an advantage to have a larger bankroll, but you can't win on average without making +EV bets. You can win more than half of the time only if you are risking more money than you stand to gain.

[ QUOTE ]
The casino has a seemingly infinite BR while the guy has a BR of $100.

[/ QUOTE ]
Seemingly infinite is not infinite. There is a positive probability that the casino would lose everything. Much more commonly, the gambler would quit while ahead a small amount.

[PairTheBoard]

[ QUOTE ]
[ QUOTE ]
Not everyone plays until they lose all their money. People do go home winners. The Casino would not make money on such a game.

PairTheBoard

[/ QUOTE ]

Of course people go home winners, otherwise the game wouldn't be popular. People go home winners at blackjack, slots, and even the dreaded wheel of fortune with the >20% house advantage.

If you played an infinite number of the 0% advantage game, variance itself would eventually knock you out.

[/ QUOTE ]

If your argument is that the bigger bankroll wins then the Casino is at a disadvantage because the sum total of bankrolls for all the people who gamble at the casino exceeds the casino's bankroll. It makes no difference whether there are 50 million joe publics gambling $1000 each or one giant JOE PUBLIC gambling with a $50 billion bankroll. If variance is going to kill anybody it's going to be the casino not Joe Public.

PairTheBoard

[AaronBrown]

This would only be true if the casino could force people to keep playing. For example, suppose I bet you even money that I can draw the Ace of Spades from a well-shuffled deck. That sounds great for you. But I add the stipulation that we have to keep playing for any stakes I name until I want to stop.

I do the first hand for $1,000, then keep doubling the bet until I draw the Ace of Spades. It may take a short time or a long time, but sooner or later I'll get your $1,000. You might as well save the effort and pay me immediately.

But this "casino" is one that refuses to buy back its chips. That makes money only until people figure it out and refuse to buy chips.

[PairTheBoard]

[ QUOTE ]
This would only be true if the casino could force people to keep playing. For example, suppose I bet you even money that I can draw the Ace of Spades from a well-shuffled deck. That sounds great for you. But I add the stipulation that we have to keep playing for any stakes I name until I want to stop.

I do the first hand for $1,000, then keep doubling the bet until I draw the Ace of Spades. It may take a short time or a long time, but sooner or later I'll get your $1,000. You might as well save the effort and pay me immediately.

But this "casino" is one that refuses to buy back its chips. That makes money only until people figure it out and refuse to buy chips.

[/ QUOTE ]

Even then it wouldn't work as long as the Casino was required to at least have the money to back up it's chips. If the big Joe Public has a bigger cumulative bankroll than the casino then Joe Public will be more likely to take the last "good" Casino chip before Joe Public goes broke. From the perspective of the big Joe Public it is JP who is the Casino and the casino is the player. If JP's bankroll is large enough the casino is actually a "small" player. Eventually there will be a player who starts out ahead and stays ahead until he has all the Casino Chips. At that point the casino cannot keep it's end of the agreement to continue play until the player is broke.

PairTheBoard

[Peter666]

Even with a 0% house advantage, the casino will always make money because of the human nature factor. People are subject to fatigue, stress, error and just plain stupidity, while the casino is not.

We've had basic strategy and card counting for decades, yet the casinos still make a killing off of Black Jack. There are a lot more degenerates out there than geniuses.

I think the only way to beat the casino in this situation would be to have a robot play the game with a larger bankroll and bust it out on a favourable variance swing.

[oneeye13]

this is intended as a theoretical question, right? i don't see where the casino is making money (although i do see that the chance of any individual player making money goes to zero). seems like, at 25 units per hand, the amount the casino makes will be 25 units * the number of hands played * zero (regardless of what players played what hands).

[GTSamIAm]

[ QUOTE ]
this is intended as a theoretical question, right? i don't see where the casino is making money (although i do see that the chance of any individual player making money goes to zero). seems like, at 25 units per hand, the amount the casino makes will be 25 units * the number of hands played * zero (regardless of what players played what hands).

[/ QUOTE ]

Exactly. If the house edge is always 0%, over time the casino will break exactly even. The question of people quitting while they are ahead or behind and basically doing progressions changes nothing. Over the long run, the casino will always break even no matter what progression players use. Progressions cannot change edge, they just create different sets of possible outcomes after x hands. That is why people say progressions do not work, they do not change edge.

Example: If my progression is that I always bet 1, after 2 hands I have four outcomes(paying 1 to 1):

+2, 0, 0, -2

If my progression is that after I win I bet my original money plus my winnings, and when I lose I bet the minimum of 1, my outcomes are:

+3, -1, 0, -2

You will notice these two progressions both add up to zero, the spread is just different. Make a tree diagram and add the results at the end, they always equal the edge.

[PairTheBoard]

Suppose the Casino could actually force players to continue playing until they go broke. Also suppose the game is played for cash only - no chips - and the Casino has a finite bankroll. Also suppose this game becomes very popular and a lot of people want to play. There is practicaly no end to the stream of customers who want to play.

So the casino opens up tens of thousands of these games to accomodate all the customers who want to play it. What would you see happen?

Well, you would see a lot of players going broke, quiting, and replaced by other players. The casino would clearly be making money from these players. But you would also see a population of players develop who have not gone broke and who are playing on the Casino's money. In fact, at any point in time the Casino will On Average be behind to these players the same amount as it has won from the players that have gone broke. Furthermore, with the game so popular the cumulative bankroll of all the customers waiting to play will be much greater than the Casino's bankroll and if luck swings enough against the Casino it will someday find all it's cash in the hands of the population of currently winning players. This is far more likely to happen than for the Casino to bust out all the customers who want to play, If the customers are numerous enough and have a very very large cumulative bankroll.

This is easy to see if the Casino opens tens of thousands of these games. However, the same thing will happen if the casino only has one game available. "On average", the casino will be behind to the current player the same amount that it has won from the previous players. Even though that player keeps playing, the winnings he is playing with are not available to the Casino for other uses. Just because the Casino expects to "get even" with that player doesn't mean the Casino is not losing to him at the momement. And it makes no difference whether that player keeps playing or takes his winnings home and is replaced by another player with the same bankroll. The casino is "out" that money at the moment. With just one game the same thing will happen as with the ten thousand games. It will just take longer.

PairTheBoard

[SheetWise]

The game makes no distinction between players coming and going, and could care less whether they win or lose. In the end, it will deliver the expectation (in this case, zero).

I see what you're thinking though. On an individual basis, if you approach me as an infinitely rich adversary with your $100, and are trying to break me -- I'll bet against you. I don't care which side of the roulette wheel you choose, play or deal, it aint going to happen.

But if you could control the wagering limits -- then all bets are off.