3 Doors game min and max bet question

Hey Math Guys

Let's say I offer the 3 doors game as an online game as it was done, but the payout goes like this.
We know that after the player chooses a door, he gets to see a door with a goat behind it and is asked if he wants to switch or stay.
Let's say he placed a bet of $100 and the payout looks like this

The player who switches gets $150 for his $100 bet = $50 profit.
the player who stays gets $300 for his $100 bet = $200 profit

This should be a game with no house edge, if I am not mistaken.

My question is:
What should be the minimum and maximum bet for such a game with no house edge? e.g. min $5 and max $50?

What would be a healthy min and max for the house?

As always, thank you for your help and please feel free to ask any questions.

Seven

If there is no house edge, then the "healthy min and max for the house" as far as the house is concerned is, min = max = zero. You might as well open up a door with a goat and then let the player choose a door, with an even-money payout. There's a reason for the green number(s) on a roulette wheel.

Setting minimum and maximum bets is not really a "math problem."

Maybe you could argue that a very high min and max bet would be best if you provided the bet in person rather than online. The house would need a big bankroll but the "dealer" might make something on tips. After all you have to feed those goats.

Seriously though, I do like they idea of "fair" gambling, especially when there is some skill involved, but the business model would be very challenging. The data sale of player information based their gullibility, math skills, and adaptability, for example might be valuable even if the gambling was a wash.

Quote: ThatDonGuy

If there is no house edge, then the "healthy min and max for the house" as far as the house is concerned is, min = max = zero. You might as well open up a door with a goat and then let the player choose a door, with an even-money payout. There's a reason for the green number(s) on a roulette wheel.

Setting minimum and maximum bets is not really a "math problem."
link to original post

Thanks for the answer.
not sure if i understood you correctly. do you mean that min and max should be same amount? for example everyone can bet $100 per bet not more and not less?

Quote: seven

Quote: ThatDonGuy

If there is no house edge, then the "healthy min and max for the house" as far as the house is concerned is, min = max = zero. You might as well open up a door with a goat and then let the player choose a door, with an even-money payout. There's a reason for the green number(s) on a roulette wheel.

Setting minimum and maximum bets is not really a "math problem."
link to original post

Thanks for the answer.
not sure if i understood you correctly. do you mean that min and max should be same amount? for example everyone can bet $100 per bet not more and not less?
link to original post

No. I am saying that the casino should not be offering the game at all.

Quote: ThatDonGuy

Quote: seven

Quote: ThatDonGuy

If there is no house edge, then the "healthy min and max for the house" as far as the house is concerned is, min = max = zero. You might as well open up a door with a goat and then let the player choose a door, with an even-money payout. There's a reason for the green number(s) on a roulette wheel.

Setting minimum and maximum bets is not really a "math problem."
link to original post

Thanks for the answer.
not sure if i understood you correctly. do you mean that min and max should be same amount? for example everyone can bet $100 per bet not more and not less?
link to original post

No. I am saying that the casino should not be offering the game at all.
link to original post

Sorry but I did not ask the question if a casino should offer this game or not. I asked what min or max would be healthy for a game like the 3 doors with a zero HE as described in my first post

Quote: seven

Quote: ThatDonGuy

Quote: seven

Quote: ThatDonGuy

If there is no house edge, then the "healthy min and max for the house" as far as the house is concerned is, min = max = zero. You might as well open up a door with a goat and then let the player choose a door, with an even-money payout. There's a reason for the green number(s) on a roulette wheel.

Setting minimum and maximum bets is not really a "math problem."
link to original post

Thanks for the answer.
not sure if i understood you correctly. do you mean that min and max should be same amount? for example everyone can bet $100 per bet not more and not less?
link to original post

No. I am saying that the casino should not be offering the game at all.
link to original post

Sorry but I did not ask the question if a casino should offer this game or not. I asked what min or max would be healthy for a game like the 3 doors with a zero HE as described in my first post
link to original post

And I gave what I consider to be the correct answer: max = zero. Nothing else is "healthy" for the casino. If the house edge is zero, the actual house profit is negative, as the casino still has to pay the dealer for their time dealing the game.

Maybe if you could define "healthy" a little better, we could come up with what you might consider to be a better answer.

Quote: ThatDonGuy

Quote: seven

Quote: ThatDonGuy

Quote: seven

Quote: ThatDonGuy

If there is no house edge, then the "healthy min and max for the house" as far as the house is concerned is, min = max = zero. You might as well open up a door with a goat and then let the player choose a door, with an even-money payout. There's a reason for the green number(s) on a roulette wheel.

Setting minimum and maximum bets is not really a "math problem."
link to original post

Thanks for the answer.
not sure if i understood you correctly. do you mean that min and max should be same amount? for example everyone can bet $100 per bet not more and not less?
link to original post

No. I am saying that the casino should not be offering the game at all.
link to original post

Sorry but I did not ask the question if a casino should offer this game or not. I asked what min or max would be healthy for a game like the 3 doors with a zero HE as described in my first post
link to original post

And I gave what I consider to be the correct answer: max = zero. Nothing else is "healthy" for the casino. If the house edge is zero, the actual house profit is negative, as the casino still has to pay the dealer for their time dealing the game.

Maybe if you could define "healthy" a little better, we could come up with what you might consider to be a better answer.
link to original post

again sorry as I never talked about a land casino I wrote very clearly that I was thinking of offering the game in an online casino. so no dealers there but there are other expenses that I can easily cover.

According to the rules I described, it is a zero HE game. I thought that if I let players bet with a big min and max difference it could hurt the house, but with for example a min bet of $10 and a max bet of $30 nothing bad should happen. But I am sure a smart math guy could tell me a healthy min and max for a zero HE game.

cheers

Quote: seven

again sorry as I never talked about a land casino I wrote very clearly that I was thinking of offering the game in an online casino. so no dealers there but there are other expenses that I can easily cover.

According to the rules I described, it is a zero HE game. I thought that if I let players bet with a big min and max difference it could hurt the house, but with for example a min bet of $10 and a max bet of $30 nothing bad should happen. But I am sure a smart math guy could tell me a healthy min and max for a zero HE game.

cheers
link to original post

ThatDonGuy has told you this is not a math problem. I agree. It is a business problem related the promotional value of a loss leader.

If you want a math-based answer, then there has to be some way of mathematically stating the problem. What value are you solving for or what parameters are you trying to optimize? You have not provided any goal to be optimized. What is the business purpose for offering this wager in the first place? Even online casinos have expenses for offering a game. Staffing help desk, handling deposits and withdrawals, regulatory overhead, all cost money.

Any time your players are playing a promotional game or zero HE game is time they are not playing games where you are banking the house edge. Online casinos do offer many +EV promos. However, they are all limited. I was playing roulette this morning with a 4.6% edge, but the promo was limited to 10 spins at $10 per spin. Barely worth logging in for, but the site often has more valuable promos so I log in every day and check.

If you were to offer a coin-flip type game to incentivize people to log in, then this is a less attractive promo than casinos offer every day. But if you let your patrons gamble $100 per game all day long, what incentive do they have to bet $100 on red on your roulette tables? Your question could be answered by someone with a deep knowledge of effective promotional offers. This depends on the psychology that drives players. It isn't a question of math. The answer will be different depending on whether your customers are only able to deposit $25 a week or if they have a $100,000 balance.

Quote: Mental

Quote: seven

again sorry as I never talked about a land casino I wrote very clearly that I was thinking of offering the game in an online casino. so no dealers there but there are other expenses that I can easily cover.

According to the rules I described, it is a zero HE game. I thought that if I let players bet with a big min and max difference it could hurt the house, but with for example a min bet of $10 and a max bet of $30 nothing bad should happen. But I am sure a smart math guy could tell me a healthy min and max for a zero HE game.

cheers
link to original post

ThatDonGuy has told you this is not a math problem. I agree. It is a business problem related the promotional value of a loss leader.

If you want a math-based answer, then there has to be some way of mathematically stating the problem. What value are you solving for or what parameters are you trying to optimize? You have not provided any goal to be optimized. What is the business purpose for offering this wager in the first place? Even online casinos have expenses for offering a game. Staffing help desk, handling deposits and withdrawals, regulatory overhead, all cost money.

Any time your players are playing a promotional game or zero HE game is time they are not playing games where you are banking the house edge. Online casinos do offer many +EV promos. However, they are all limited. I was playing roulette this morning with a 4.6% edge, but the promo was limited to 10 spins at $10 per spin. Barely worth logging in for, but the site often has more valuable promos so I log in every day and check.

If you were to offer a coin-flip type game to incentivize people to log in, then this is a less attractive promo than casinos offer every day. But if you let your patrons gamble $100 per game all day long, what incentive do they have to bet $100 on red on your roulette tables? Your question could be answered by someone with a deep knowledge of effective promotional offers. This depends on the psychology that drives players. It isn't a question of math. The answer will be different depending on whether your customers are only able to deposit $25 a week or if they have a $100,000 balance.
link to original post

I asked my question because I am not as smart as some guys here in the math section and I still think it is a math problem.
If an admin thinks that my question is not for the math forum section, please be so kind and move it to the right one so I will have a chance to get the right answer instead of telling me that it is not a math problem.

BTW, this is not a promotional gimmick for a day or 2, but yes, the idea is to attract players who are looking for a zero HE game.

IMO in a zero HE game like I described my idea for an online casino game, the min and max bet amount is important to the house because the house does not want to have a high variance. At least I am not looking for high variance.
So my question is and was, should I offer a min/max of $50 or what kind of spread is best? Min $10 and max $30 or min $10 and max $100?

Sure you can tell me again this is not a math problem, but frankly IMO it is.

I hope an admin can solve the problem and move it to the right forum section

Cheers

Quote: seven

IMO in a zero HE game like I described my idea for an online casino game, the min and max bet amount is important to the house because the house does not want to have a high variance. At least I am not looking for high variance.
So my question is and was, should I offer a min/max of $50 or what kind of spread is best? Min $10 and max $30 or min $10 and max $100?

Make the spread as small as possible, at least in terms of the max/min ratio - otherwise you open the door to Martingaling, which could be very popular (and very damaging to the house) on a zero-HE game.

Quote: ThatDonGuy

Quote: seven

IMO in a zero HE game like I described my idea for an online casino game, the min and max bet amount is important to the house because the house does not want to have a high variance. At least I am not looking for high variance.
So my question is and was, should I offer a min/max of $50 or what kind of spread is best? Min $10 and max $30 or min $10 and max $100?

Make the spread as small as possible, at least in terms of the max/min ratio - otherwise you open the door to Martingaling, which could be very popular (and very damaging to the house) on a zero-HE game.
link to original post

Thank you so much for giving me this answer. The min/max ratio spread was exactly what I was not sure about, but I also thought it must still be attractive to a player as a min/max of say $20 or any other amount would not be attractive IMO.

Cheers