A Less Obvious Martingale Fallacy - Page 16

drudman · #**151** 07-19-2005, 09:52 PM

The average of all of the non-quitting Martingaler's wins and losses is in the black.

His time spent down is unimportant. Like I have said, he is betting with funny money, because he can never run out of it, and because he will eventually win. Funny. Money.

MMMMMM · #**152** 07-19-2005, 11:04 PM

[ QUOTE ]
The average of all of the non-quitting Martingaler's wins and losses is in the black.

[/ QUOTE ]

This is most definitely wrong.

PairTheBoard · #**153** 07-19-2005, 11:58 PM

[ QUOTE ]
The average of all of the non-quitting Martingaler's wins and losses is in the black.

His time spent down is unimportant. Like I have said, he is betting with funny money, because he can never run out of it, and because he will eventually win. Funny. Money.

[/ QUOTE ]

We're now talking about the non-quiting Martingalers playing against the Casino's Roullette edge. The Casino also has unlimited funds.

Funny Money? If the money the Martingaler goes behind when on a losing streak is Funny Money, then the money he goes ahead after a win is Funny Money too, since he keeps on gambling and will eventually go behind once again.

Your viewpoint is Martingaler-Centric. The Casino's viewpoint is just as valid. When the Martingaler goes ahead the Casino doesn't care because it knows it will eventually go back ahead of the Martingaler again - and it will do so more often in #dollars than the Martingaler.

The key measure is (Time Spent Ahead)*(Dollars Ahead).

Run a simulation of 1,000,000 Martingalers playing the Casino and see what happens. You will see a net flow of funds from the combined bankrolls of the Martingalers into the Casino's coffers over time at a rate about equal to the House edge times the action. Do it one roullette spin per player at a time and check the flow of funds after each set of 1,000,000 spins.

PairTheBoard

drudman · #**154** 07-20-2005, 01:22 AM

Why? Every one win he has wipes out every n losses he has sustained, and then some. Every single win puts him back in the black, and the black gets bigger by one every time. He may have terrifically large funny money losses, but he will have one win even larger than all of the previous losses combined in every series. Every series has an average win/loss > 0. The longer the series, the closer the average of that series approaches zero. But all of those positive values adds up. The average of them is positive and non-zero.

drudman · #**155** 07-20-2005, 01:34 AM

The casino's viewpoint is negative. They don't want the Martingaler to play. They know that no matter how bad they beat up on the Martingaler, they will always have to pay back every dime, plus 1 unit bet. They cannot avoid always having to pay up.

Look at it this way. The casino stacks up all of the money they take from the Martingaler on the left of the table. The Martingaler stacks up all of his unit bets won on the right. The stack on the right side of the table never ever decreases. It always increases. The stack on the left does decrease... in fact it decreases to zero frequently! The casino slides all of the cash back to the Martingaler's bankroll every time.

It works even if the casino doesn't pay off the wins using their stack of winnings, so long as you let the Martingaler stack up his huge payouts along with his unit bets.

Maybe you'd like to be the casino, Pairtheboard? I'll give you $10,000 at 9AM every day, and you can stack it up on your kitchen table. Then at 5PM every night, you give it back, plus a dollar. Would you want this deal? (don't try to say "well I can invest it and make more than $1 with it" because the casino does not invest money)

PairTheBoard · #**156** 07-20-2005, 02:11 AM

drudman --
"Look at it this way. The casino stacks up all of the money they take from the Martingaler on the left of the table. The Martingaler stacks up all of his unit bets won on the right. The stack on the right side of the table never ever decreases."

The stack on the right decreases every time the Martingaler loses a bet. If he loses a long streak of bets the stack goes into the red.

Run the simulation and see what happens.

PairTheBoard

SheetWise · #**157** 07-20-2005, 02:23 AM

So, 842 views and 155 posts later -- we have a starting point?

MMMMMM · #**158** 07-20-2005, 07:51 AM

If the house edge is zero (fair coin) then their joint expected loss or win is zero. If the house edge is 5.26% then they are losing more and more the longer they play. If you want to find the avcerage loss per gambler, multiply the total volume bet times the house edge and divide by the number of gamblers.

drudman · #**159** 07-20-2005, 02:24 PM

[ QUOTE ]
drudman --
"Look at it this way. The casino stacks up all of the money they take from the Martingaler on the left of the table. The Martingaler stacks up all of his unit bets won on the right. The stack on the right side of the table never ever decreases."

The stack on the right decreases every time the Martingaler loses a bet. If he loses a long streak of bets the stack goes into the red.

Run the simulation and see what happens.

PairTheBoard

[/ QUOTE ]

The Martingaler doesn't use the stack on the right to make his bets.

drudman · #**160** 07-20-2005, 02:36 PM

I'm all done here. You enjoy looking at those piles of chips you've won from the Martingaler's bankroll pile while they last... you will always push them all back, +1. I'll stack my +1s all the way to the ceiling and on into space.