- #1

bernd

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- TL;DR Summary
- For given roulette gambling system decide wether betting on shorter series or betting more per series is more profitable on average?

Hey, gotta do some explanation first:

I assume you know how roulette works. (if you dont: ball is thrown into a pit and it can either land on red, black or zero, each having a certain likeliness to land there. you can bet on where the ball will land)

let's assume unrealistically you have the ultimate knowledge where you know that a ball will only land on a certain color in a row a max of like 15 times.

so if for example the ball this round lands on red, you could go ahead and repeatedly bet on black until you win (cause as assumed there will come at max 15 times red in a row, so you will win sooner or later.)

obviously the amount you bet on black has to increase with eahc round or you will get a negative total in the end.

so you like bet 1 buck on black.

won? great, series over.

lost? bet 2*1 on black next round.

rinse and repeat, betting double on black what you bet before.

martingale.

now if the first bet in such a series is 1 bucks, you would need a sh it ton of money to be able to bet 16 times or so. (we always assume worst case)

so we play smart and for example say:

we "empty bet" 5 times first, meaning we wait until we have 5 times red in a row.

And only THEN start betting 1 buck, 2 bucks, etc.

so the balance needed so you can pay up till the certain win is much bigger (it namely is like 1+2*1+2^2*1+...+2^11, which is less than 1+2*1+...+2^16*1).

anyways, say we got the needed balance and all so we can empty bet 5 times and bet the remaining 11 times on opposite color.

now, due to repeatedly winning, lets assume our balance has doubled in comparison to what we started with.

this gives us 2 possible choices:

now we either initally bet 2 bucks isntead of 1 bucks, basically doubling our profit for each series we do.

or we go ahead and emptybet only 4 times instead of 5 times. this also improves the profit because obviously in a given time span it is more likely to have a color appear 4 times in a row than it is for a color to appear 5 times.

now that I hopefully have gotten the gist of the whole thing over, my big question would be:

is it better to increase the bet amount? or emptybet less? what on average should yield better returns, what is the better choice when "one upping" our system?

I know that this whole thing is likely unrealistic as f but please go along with it.

say someone does play rouletter for like 1 hour and, randomly assumed, a total of like 60 rolls are done, so we get 60 symbols in that time ( something like (RZBZRRRZBZRRRRRRRRBBBZBRRBBRZBRBR or such, 60 roll results, R= red, Z=zero, B=black). (obviously if we are in the middle of a betting series we will play it till the win)

I feel like we should be able to ind the answer with probabilities.

cause you can calculate how likely it is for like 5 times red in a row to occur and 4 times red to occur, so it should be comparable via probabilities.

but I cant get m head around the details yet.

someone any idea on this hypothetical roulette gambling scenario?

I know, one could go ahead and just do 2 trillion simulations where you do 60 rolls, look how mony rows of same color appear, how long the are, etc. and built the average about it all.

but I would assume there should also be a more proper mathematical way to solve this than jsut... trying it out.

Edit:

Attached is a picture which hopefully better shows what I mean:

Let's assume you currently wait till you see 5 times red in a row and then martingale bet (base bet amount 1 buck) until you win in the 16th round.

now you suddenly got enough money to make this more profitable.

shpould you still wait for 5 times red and have a base bet of 2 bucks isntead of 1?

or keep the base bet the same but wait for 4 times red isntead of 5 (which obviously should appear more often than the other)?

whats more profitable on average, how to mathematically calculate that?

I assume you know how roulette works. (if you dont: ball is thrown into a pit and it can either land on red, black or zero, each having a certain likeliness to land there. you can bet on where the ball will land)

let's assume unrealistically you have the ultimate knowledge where you know that a ball will only land on a certain color in a row a max of like 15 times.

so if for example the ball this round lands on red, you could go ahead and repeatedly bet on black until you win (cause as assumed there will come at max 15 times red in a row, so you will win sooner or later.)

obviously the amount you bet on black has to increase with eahc round or you will get a negative total in the end.

so you like bet 1 buck on black.

won? great, series over.

lost? bet 2*1 on black next round.

rinse and repeat, betting double on black what you bet before.

martingale.

now if the first bet in such a series is 1 bucks, you would need a sh it ton of money to be able to bet 16 times or so. (we always assume worst case)

so we play smart and for example say:

we "empty bet" 5 times first, meaning we wait until we have 5 times red in a row.

And only THEN start betting 1 buck, 2 bucks, etc.

so the balance needed so you can pay up till the certain win is much bigger (it namely is like 1+2*1+2^2*1+...+2^11, which is less than 1+2*1+...+2^16*1).

anyways, say we got the needed balance and all so we can empty bet 5 times and bet the remaining 11 times on opposite color.

now, due to repeatedly winning, lets assume our balance has doubled in comparison to what we started with.

this gives us 2 possible choices:

now we either initally bet 2 bucks isntead of 1 bucks, basically doubling our profit for each series we do.

or we go ahead and emptybet only 4 times instead of 5 times. this also improves the profit because obviously in a given time span it is more likely to have a color appear 4 times in a row than it is for a color to appear 5 times.

now that I hopefully have gotten the gist of the whole thing over, my big question would be:

is it better to increase the bet amount? or emptybet less? what on average should yield better returns, what is the better choice when "one upping" our system?

I know that this whole thing is likely unrealistic as f but please go along with it.

say someone does play rouletter for like 1 hour and, randomly assumed, a total of like 60 rolls are done, so we get 60 symbols in that time ( something like (RZBZRRRZBZRRRRRRRRBBBZBRRBBRZBRBR or such, 60 roll results, R= red, Z=zero, B=black). (obviously if we are in the middle of a betting series we will play it till the win)

I feel like we should be able to ind the answer with probabilities.

cause you can calculate how likely it is for like 5 times red in a row to occur and 4 times red to occur, so it should be comparable via probabilities.

but I cant get m head around the details yet.

someone any idea on this hypothetical roulette gambling scenario?

I know, one could go ahead and just do 2 trillion simulations where you do 60 rolls, look how mony rows of same color appear, how long the are, etc. and built the average about it all.

but I would assume there should also be a more proper mathematical way to solve this than jsut... trying it out.

Edit:

Attached is a picture which hopefully better shows what I mean:

Let's assume you currently wait till you see 5 times red in a row and then martingale bet (base bet amount 1 buck) until you win in the 16th round.

now you suddenly got enough money to make this more profitable.

shpould you still wait for 5 times red and have a base bet of 2 bucks isntead of 1?

or keep the base bet the same but wait for 4 times red isntead of 5 (which obviously should appear more often than the other)?

whats more profitable on average, how to mathematically calculate that?

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