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 06-08-2012, 01:48 PM #1 stranger   Join Date: Jun 2012 Posts: 6 Question regarding EV on a martingale variant Hello. Suppose we are offered 2-to-1 odds for a game. These odds correspond to a (fake) probability of 33% of our bet happening. Since the house should have an edge, let's suppose that this edge corresponds to an (actual) probability of 23%, or something along the lines of 10-to-3. Our bankroll is \$150, we start with \$10 and double up on every loss. This means we can take up to 3 losses. EV is calculated by the formula EV = Total Profit * (1 - q) - Total Loss * q, where q == the actual probability of losing every bet up to and including this. In simpler terms, q = (1 - 0.23)^(bet No#) Bet #1: Bet: \$10, (possible) Total Profit: \$20, (possible) Total Loss: \$10, EV = -3 Bet #2: Bet: \$20, (possible) Total Profit: \$30, (possible) Total Loss: \$30, EV = -5.27 Bet #3: Bet: \$40, (possible) Total Profit: \$50, (possible) Total Loss: \$70, EV = -4.08 Bet #4: Bet: \$80, (possible) Total Profit: \$90, (possible) Total Loss: \$150, EV = +7.08 Now, this shows that every sequence of 4 bets produces a positive EV. My question is this: Given that my calculations are correct (if not, please point out the errors), is this strategy sound? And if not, why is this?
 06-08-2012, 02:23 PM #2 veteran     Join Date: Nov 2008 Posts: 3,256 Re: Question regarding EV on a martingale variant It seems you found the holy grail. Please delete this thread! This is how the whole forum makes their living and we do not want to have it out in the open. Good luck.
 06-08-2012, 02:47 PM #3 veteran   Join Date: Sep 2002 Location: Cookie Monster Singing Posts: 3,343 Re: Question regarding EV on a martingale variant You can't combine -EV bets to make a +EV series, no matter what. Even if its 2-1 or 100-1.
06-08-2012, 02:56 PM   #4
stranger

Join Date: Jun 2012
Posts: 6
Re: Question regarding EV on a martingale variant

Quote:
 Originally Posted by acesover8s You can't combine -EV bets to make a +EV series, no matter what. Even if its 2-1 or 100-1.

How come this does not show up in the calculations? Could you please point out where the mistake is in the math?

06-08-2012, 03:16 PM   #5
grinder

Join Date: Aug 2010
Posts: 518
Re: Question regarding EV on a martingale variant

Quote:
 Originally Posted by panos In simpler terms, q = (1 - 0.23)^(bet No#)
So when you lose the first round karma then transfers over to the next I N D E P E N D E N T event adding %s to your hit probability
It would make a nice video game tho

06-08-2012, 03:27 PM   #6
stranger

Join Date: Jun 2012
Posts: 6
Re: Question regarding EV on a martingale variant

Quote:
 Originally Posted by tukkk So when you lose the first round karma then transfers over to the next I N D E P E N D E N T event adding %s to your hit probability It would make a nice video game tho
Isn't a prerequisite of the total loss (let's say in bet #3), that bet #3 and both bet #1 and bet #2 are unsuccessful?

Since they are independent events, isn't the probability of losing all 3 bets q=(1 - 0.23) ^ 3 ?

06-08-2012, 08:22 PM   #7
old hand

Join Date: Sep 2008
Location: VA
Posts: 1,913
Re: Question regarding EV on a martingale variant

Quote:
 Originally Posted by panos Isn't a prerequisite of the total loss (let's say in bet #3), that bet #3 and both bet #1 and bet #2 are unsuccessful? Since they are independent events, isn't the probability of losing all 3 bets q=(1 - 0.23) ^ 3 ?
that is the probability of losing all 3 bets in sum. but when you're placing bet 3, you've already lost the first two bets.

 06-09-2012, 02:32 AM #8 adept     Join Date: Jul 2009 Posts: 1,185 Re: Question regarding EV on a martingale variant brb printing money.
06-09-2012, 04:10 PM   #9
stranger

Join Date: Jun 2012
Posts: 6
Re: Question regarding EV on a martingale variant

Quote:
 Originally Posted by wahoo3 that is the probability of losing all 3 bets in sum. but when you're placing bet 3, you've already lost the first two bets.
I finally got it. Thanks a lot!

 06-12-2012, 07:53 PM #10 Carpal \'Tunnel     Join Date: Feb 2003 Location: Looking forward to AA Posts: 15,280 Re: Question regarding EV on a martingale variant Glad the forum could do your homework for you.

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