A Less Obvious Martingale Fallacy

[Dov]

I followed you pretty well.

I was just trying to see if you can prove that since Martin's advantage per spin seems to change and we know that it can't that you can't say that his EV +1/n where n is the number of trials in the series.

Just taking a shot at my first ever proof.

LOL

[superleeds]

[ QUOTE ]
The house's advantage is fixed on every spin of the roulette wheel. So too is the Martingaler's disadvantage.

[/ QUOTE ]

The Martingaler's changes every spin given that with an infinate number of rolls he will win. His expected win every time he starts a series is at least 1/infinity per roll

[MMMMMM]

[ QUOTE ]
[ QUOTE ]
The house's advantage is fixed on every spin of the roulette wheel. So too is the Martingaler's disadvantage.

[/ QUOTE ]

The Martingaler's changes every spin given that with an infinate number of rolls he will win. His expected win every time he starts a series is at least 1/infinity per roll

[/ QUOTE ]

His mathematical disadvantage does NOT change every spin...or on any spin.

This is the most basic and incontrovertible part of the whole scenario.

[SheetWise]

In this hypothetical, I think you are wrong to look at the EV. One of the things you have to remember is that the casino realizes its expectation when you win.

Consider a roulette wheel that pays 35:1 for a win, while the true payoff should be 37:1. Thet make no money when you lose. They could have been paying you 40:1 -- it doesn't matter -- you lost. It's when you win, and they pay you at less than true odds that they realize their advantage.

If the player wins every time, they will never realize their advantage, because they are taking it out of your winnings.

How's that for a twist?

[superleeds]

[ QUOTE ]
His mathematical disadvantage does NOT change every spin...or on any spin

[/ QUOTE ]

Agreed. But he compansates for this.

[MMMMMM]

[ QUOTE ]
[ QUOTE ]
His mathematical disadvantage does NOT change every spin...or on any spin

[/ QUOTE ]



Agreed. But he compansates for this.

[/ QUOTE ]

So if what you believe is true, we have a paradox.

If he truly compensates for it, he is essentially causing a series of negative values to sum to a positive value.

But...even an infinite number of negative values cannot sum to a positive value.

So, which is wrong? For reasons outlined elsewhere, I believe he actually doesn't "compensate for this."

[superleeds]

[ QUOTE ]
So if what you believe is true, we have a paradox

[/ QUOTE ]

I don't believe so. Whilst each individual roll has a negative expected value, if at some point a win will be acheived (which infinity allows) and a compenasating factor (the martingale system) has been employed
each roll now has a positive expected value.

[Dov]

[ QUOTE ]
If he truly compensates for it, he is essentially causing a series of negative values to sum to a positive value.

[/ QUOTE ]

You can multiply by -1 to change the negative to a positive.

Maybe that's what happens when he wins. Maybe a win = (Loss incurred so far(-1)) + 1

Nah, that doesn't make any sense.

Oh shoot, I just got sucked out on in my game. That decides it then, Martin is definitely -EV. [img]/images/graemlins/ooo.gif[/img]

[Dov]

[ QUOTE ]
Agreed. But he compansates for this.

[/ QUOTE ]

He doesn't really compensate for it.

The logic would be that he is not getting paid enough when he wins, therefore he is losing. Instead of being up 1 unit, he should be up much more than that.

[superleeds]

[ QUOTE ]
He doesn't really compensate for it

[/ QUOTE ]

Yes he does. He knows that eventually he will win 1 unit if he doubles his bet everytime he loses. He has an infinate amount of money so that is no problem, he has an infinate amount of times he is able to make this bet, therefore he is compensating for the times he loses.