Math to show betting systems don't work - Page 2 - Gambling and Probability

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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09-14-2020 , 07:37 PM

#27

d2_e4

certifiable moron

Join Date: Sep 2014 Posts: 12,025

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.

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09-14-2020 , 10:41 PM

#28

David Sklansky

Administrator

Join Date: Aug 2002 Posts: 17,075

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.

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09-15-2020 , 03:40 AM

#29

d2_e4

certifiable moron

Join Date: Sep 2014 Posts: 12,025

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.

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09-15-2020 , 06:40 PM

#30

David Sklansky

Administrator

Join Date: Aug 2002 Posts: 17,075

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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09-15-2020 , 08:20 PM

#31

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

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).

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09-15-2020 , 10:25 PM

#32

David Sklansky

Administrator

Join Date: Aug 2002 Posts: 17,075

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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10-01-2020 , 08:15 AM

#33

MaLifeBeLikeooahh

stranger

Join Date: Jun 2020 Posts: 5

Quote:

Originally Posted by d2_e4

I mean, my whole argument was that you can't change EV of a given game/bet through any strategy that involves modifying the amount wagered in a given trial of said game. This is well known in these 'ere parts, but when someone who is fairly well versed in maths turned around and said "prove it", I stumbled a bit.

By the way, if a real-life roulette wheel rolls in a specific quadrant 10 times in a row, it is actually more likely to roll in the same quadrant the 11th time than dictated by pure chance for an idealised wheel.

Could you explain this please?

Last edited by MaLifeBeLikeooahh; 10-01-2020 at 08:15 AM. Reason: The roulette wheel part

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10-01-2020 , 08:17 AM

#34

d2_e4

certifiable moron

Join Date: Sep 2014 Posts: 12,025

Quote:

Originally Posted by MaLifeBeLikeooahh

Could you explain this please?

If there is any bias in the wheel, it's likely to favour the quadrant where the ball has landed 10 times in a row.

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