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Statistics: I'm not a student, but...

Statistics:

I'm not a student, but there's no more relevant category to submit this question. I took a few stat classes in college, but just don't know/remember enough to create the proper equations for this, so I'm hoping you can help.

I'm trying to more fully understand some statistics for the game Roulette. There are a couple of scenarios I want to understand the underlying probability for. I've heard that the process I created is actually fraught with fallacy, but it has worked incredibly well for me so far. I've never lost, and in reality, I've gained around 100% ROI across the 4 or so times I've played. I just want to prove it to myself that it works (or doesn't) from a probability standpoint.

Let me outline how I play first, and then I'll add in some of the known probabilities.

1) First, I pick a color and will always play that color, never once varying it.

2) Then, I will determine the consistent bet I want to make. In most cases, this is either $1 or $5 (let's use $5 for our example) depending on the table limit. The table limit seems to be the deciding factor (rather than the actual bet itself) on what a solid bet is.

3) I will then bet that amount. Each round I will either win or lose. If I win, I take the 1:1 winnings ($5) off the table and leave the original $5 bet. I've now gained $5. During the next turn, I will again either win or lose. If I lose this time, I will put another $5 up to match the amount I lost. During the following round, if say I lose again, I will instead put $10 up to match the $10 I've lost so far in total. This will continue exponentially as long as I lose, and as long as I do not hit the table limit. Theoretically it seems given no table limit and an infinite amount of money the probability is definitely on my side that I'd win the money back. It only takes one victory to get all of the lost money back in this way. A win is removed from the game, and a lost is played until one single victory regains the lost money.

That's how I play. The logic being that you can spread the break even point over a number of plays, creating a sort of interdepencence between events that would otherwise be considered independent. I've heard this referred to as "progressive betting" and have been told a number of times that there is an inherent fallacy in the process. Maybe there is, and that's what I want to find out.

Here are my questions, which are all variations on the same scenario:

1) What would be the probability of winning your money back (if we are losing X number of times in a row) given that for every loss, the next bet will exactly match the money lost from all previous bets? How would you set up this equation?

2) What is the optimal number of bets required to achieve a favorable outcome? IE: How much better is 7 turns before you hit the max bet for the table than 5 turns? (Playing $1 on a $30 max bet seems logically to be better (5 chances to recover) than $5 on the same table (3 chances to recover).

3) If it's possible, how could we set up an equation to determine the optimal bet amount ($) given a specific table limit?

Let me know if you would like further clarification on anything, or if this is the wrong place to ask this question!

I'm not a student, but there's no more relevant category to submit this question. I took a few stat classes in college, but just don't know/remember enough to create the proper equations for this, so I'm hoping you can help.

I'm trying to more fully understand some statistics for the game Roulette. There are a couple of scenarios I want to understand the underlying probability for. I've heard that the process I created is actually fraught with fallacy, but it has worked incredibly well for me so far. I've never lost, and in reality, I've gained around 100% ROI across the 4 or so times I've played. I just want to prove it to myself that it works (or doesn't) from a probability standpoint.

Let me outline how I play first, and then I'll add in some of the known probabilities.

1) First, I pick a color and will always play that color, never once varying it.

2) Then, I will determine the consistent bet I want to make. In most cases, this is either $1 or $5 (let's use $5 for our example) depending on the table limit. The table limit seems to be the deciding factor (rather than the actual bet itself) on what a solid bet is.

3) I will then bet that amount. Each round I will either win or lose. If I win, I take the 1:1 winnings ($5) off the table and leave the original $5 bet. I've now gained $5. During the next turn, I will again either win or lose. If I lose this time, I will put another $5 up to match the amount I lost. During the following round, if say I lose again, I will instead put $10 up to match the $10 I've lost so far in total. This will continue exponentially as long as I lose, and as long as I do not hit the table limit. Theoretically it seems given no table limit and an infinite amount of money the probability is definitely on my side that I'd win the money back. It only takes one victory to get all of the lost money back in this way. A win is removed from the game, and a lost is played until one single victory regains the lost money.

That's how I play. The logic being that you can spread the break even point over a number of plays, creating a sort of interdepencence between events that would otherwise be considered independent. I've heard this referred to as "progressive betting" and have been told a number of times that there is an inherent fallacy in the process. Maybe there is, and that's what I want to find out.

Here are my questions, which are all variations on the same scenario:

1) What would be the probability of winning your money back (if we are losing X number of times in a row) given that for every loss, the next bet will exactly match the money lost from all previous bets? How would you set up this equation?

2) What is the optimal number of bets required to achieve a favorable outcome? IE: How much better is 7 turns before you hit the max bet for the table than 5 turns? (Playing $1 on a $30 max bet seems logically to be better (5 chances to recover) than $5 on the same table (3 chances to recover).

3) If it's possible, how could we set up an equation to determine the optimal bet amount ($) given a specific table limit?

Let me know if you would like further clarification on anything, or if this is the wrong place to ask this question!

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