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 09-14-2020, 07:33 PM #26 David Sklansky Administrator     Join Date: Aug 2002 Posts: 15,587 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%.
09-14-2020, 07:37 PM   #27
d2_e4
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Join Date: Sep 2014
Posts: 4,315
Re: Math to show betting systems don't work

Quote:
 Originally Posted by David Sklansky 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.

09-14-2020, 10:41 PM   #28
David Sklansky

Join Date: Aug 2002
Posts: 15,587
Re: Math to show betting systems don't work

Quote:
 Originally Posted by d2_e4 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.

09-15-2020, 03:40 AM   #29
d2_e4
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Join Date: Sep 2014
Posts: 4,315
Re: Math to show betting systems don't work

Quote:
 Originally Posted by David Sklansky 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.

 09-15-2020, 06:40 PM #30 David Sklansky Administrator     Join Date: Aug 2002 Posts: 15,587 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.
09-15-2020, 08:20 PM   #31
heehaww
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Join Date: Aug 2011
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Posts: 4,850
Re: Math to show betting systems don't work

Quote:
 Originally Posted by David Sklansky 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.

Quote:
 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).

 09-15-2020, 10:25 PM #32 David Sklansky Administrator     Join Date: Aug 2002 Posts: 15,587 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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