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Old 09-14-2020, 07:33 PM   #26
David Sklansky
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Re: Math to show betting systems don't work

If you martingale a fair coin bet starting with a dollar bet and an infinite bankroll, there is a 99.999999999......% chance that you will, at some point, be up a trillion dollars. But if the coin will come up your side only 49.99% of the time, the chance you will EVER (even in an infinite number of years) be up a trillion dollars, is less than .000001%.
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Old 09-14-2020, 07:37 PM   #27
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Re: Math to show betting systems don't work

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Originally Posted by David Sklansky View Post
If you martingale a fair coin bet starting with a dollar bet and an infinite bankroll, there is a 99.999999999......% chance that you will, at some point, be up a trillion dollars. But if the coin will come up your side only 49.99% of the time, the chance you will EVER (even in an infinite number of years) be up a trillion dollars, is less than .000001%.
The bolded number is equal to 100.
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Old 09-14-2020, 10:41 PM   #28
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Re: Math to show betting systems don't work

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The bolded number is equal to 100.
I wrote it that way because you never get to certainty (to be up a trillion) no matter how many times you flip it. It was a shortcut way to acknowledge that.
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Old 09-15-2020, 03:40 AM   #29
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Re: Math to show betting systems don't work

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Originally Posted by David Sklansky View Post
I wrote it that way because you never get to certainty (to be up a trillion) no matter how many times you flip it. It was a shortcut way to acknowledge that.
I think you are trying to demonstrate the concept of "almost surely" (https://en.wikipedia.org/wiki/Almost_surely), but writing the probability as 99.9 repeating is not really helpful to do this. The probability is in fact 100, which is the same thing as 99.9 repeating, but writing it like that just adds a layer of "does 0.9999.... really equal 1" confusion, without actually illustrating what "almost surely" means.
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Old 09-15-2020, 06:40 PM   #30
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Re: Math to show betting systems don't work

Actually I was tying to avoid that whole technical subject and merely give your dad ammunition even though he is wrong.
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Old 09-15-2020, 08:20 PM   #31
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Re: Math to show betting systems don't work

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Originally Posted by David Sklansky View Post
If you martingale a fair coin bet starting with a dollar bet and an infinite bankroll, there is a 99.999999999......% chance that you will, at some point, be up a trillion dollars.
As you know, the same is true if you don't martingale, for example if you simply bet $1 per flip. That is, pretending there's a such thing as "being up a trillion dollars" when you already started with infinity.

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But if the coin will come up your side only 49.99% of the time, the chance you will EVER (even in an infinite number of years) be up a trillion dollars, is less than .000001%.
Nope, 100% if you martingale. You're 100% to win each dollar because there's a 0% chance of an infinite streak of losses. Repeat the process a trillion times and the combined chance of a trillion 100% outcomes is still 100%. Unlike when betting on a fair coin, martingaling makes a big difference when betting on an unfair coin (if one can't run out of bets to make).
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Old 09-15-2020, 10:25 PM   #32
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Re: Math to show betting systems don't work

Right. I was thinking about typical propositions where the player with the edge will NOT eventually lose to an infinite bankroll.
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