The ideal strategy for playing with the most ammount of money.

[KalleHammar]

Say a casino is giving out bonuses depending on how much you have played for. They do not care about your wins and losses.

On this casino there is an option of choosing your odds and getting a multiplier depending on the odds you choose with the catch that they hold a 1% edge over the player.
The player has 10000 units of whatever currency, is the maximum ammount he could play for consistently without losing 100 times his balance or can he extend it with exponential increases on losses (like a martingale except it is not trying to win back every loss, but only a small enough portion to make up for the house edge)? Lets pretend there is no minimum bet and you can bet into the 0.000..-s

 

[Deleted member 4993]

Say a casino is giving out bonuses depending on how much you have played for. They do not care about your wins and losses.

On this casino there is an option of choosing your odds and getting a multiplier depending on the odds you choose with the catch that they hold a 1% edge over the player.
The player has 10000 units of whatever currency, is the maximum ammount he could play for consistently without losing 100 times his balance or can he extend it with exponential increases on losses (like a martingale except it is not trying to win back every loss, but only a small enough portion to make up for the house edge)? Lets pretend there is no minimum bet and you can bet into the 0.000..-s

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[KalleHammar]

Well, I did calculate that for every 100 units played for the player would lose one. On a 0.01 times multiplier and one unit bets (98%) the player would lose 0.5 units for every cykle of 50 bets after you take the normal loss minus what they lose to the house edge meaning the player would have to win an aditional 0.5 every 50 bets.
In order to win 0.5 units on a 0.01 times multiplier the player would have to bet 0.5/0.01 = 50 units every loss (or a 4900% increase on loss) to get a plus minus zero average expected return. If that is the case the initial bet of 1 would be way beyond the 10000 balance in just 2 losses in a row.

The risk of 2 losses in a row at a 98% win chance is 0.02^2 = 0.0004

1/0.0004 = 2500

So according to this math the player would only place on average 2500 bets of one before going bust which is worse than if he had just bet units of one with no increase until he was out of money (which would give him a "played for" ammount of 1000000).

Surely there is something wrong with my math?
If so could you point it out, maybe give me some suggestions and tell me if there actually is a way to get the played for ammount past 1000000 from a balance of 10000 with a loss on average of 1% of every bet.