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

Spaded · #1 06-28-2005, 03:03 AM

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 · #2 06-28-2005, 03:18 AM

I think you'd find some of the old martingale thread (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 · #3 06-28-2005, 03:22 AM

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 · #4 06-28-2005, 03:33 AM

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I think you'd find some of the old martingale thread (s) very interesting.

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

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 [img]/images/graemlins/wink.gif[/img]

PairTheBoard · #5 06-28-2005, 07:58 AM

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 · #6 06-28-2005, 05:43 PM

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 [img]/images/graemlins/smile.gif[/img])

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 · #7 06-28-2005, 07:09 PM

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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

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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 · #8 06-28-2005, 07:38 PM

[ 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.

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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.

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Is this basically a question of bankroll?

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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.

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

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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 · #9 06-28-2005, 10:46 PM

[ 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 · #10 06-30-2005, 06:22 PM

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.