# Math Help - Martingale Betting System- expected value

1. ## Martingale Betting System- expected value

Hi, I have been learning/experimenting with the Martingale betting system recently. I have read a lot about how no "system" works for betting in casinos. However, I want to either prove or disprove the validity of the system by looking at its expected value/payout. I will be using the game of roulette as an example, assuming I have a 50% of getting black or red. Here is how the payout will work-

If the ball lands on black, I win $5 If the ball lands on red 7 times in a row, I lose$155

What is the expected payout of me playing roulette with this system?

winning payout = $5 * (1/2) ;have a 50% chance of getting black losing payout = -$155 * (1/2)^7 ;have a 50% chance of getting red, 7 times

net payout = winning payout - losing payout
=$1.29 So according to this, if I use this system then there will be a positive payout. What do you guys think? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~ If you want to how i got the winning/losing payouts then here is the explanation for that- The way the system works is that you first bet your initial, let's say it's$5. If you lose, you double your previous bet, and if you lose again you double up again, etc. So if I start at $5 and keep losing, my bets will go like this -$5,$10,$20,$40,$80....
Using this system, you will earn $5 every time you win. To see this, assume I lose$5,$10,$20 but on the $40 bet I win. I will have lost$35 from before but gained $40, i.e.$5 profit.

***Now, according to this if I have enough money I can eventually earn $5 as long as I have a crap load of money. This is why tables have maximum bets, but many cheap casinos don't. Moving on, if i lose 5 times in a row, I will lose 5+10+20+40+80 =$155. Let's say I "restart" after I lose 5 times. Also, because I am so clever, I will bet only until I see two reds. Therefore, I can technically "lose" 7 times in a row and still lose only $155. All in all, one can see that this ^ is where the losing payout comes from, and that the winning payout is me simply winning$5 on black.

2. ## Re: Martingale Betting System- expected value

My first reply here will be a story of how you should proceed with caution when actually using this system... I used this system at an online poker site before online gambling became illegal in almost all of the United States. I invested only 50 dollars of my money initially and my first investment was doubled to one hundred dollars. I took a timid approach at first and started my first 5 dollar bet after 4 blacks in a row and was betting red. Not much time had passed and I broke 500 dollars. I then started betting my initial 5 dollars after a win, after two losing blacks like you mention in your example. My original 100 dollar bank roll eventually turned in to over 1800...... then I was astonished when I lost over 9 bets in a row. Proceed with caution. I will reply again in a while about some overlooked math. And go into some theory behind why this doesn't work. Unless as you say you have a crap ton of money.

3. ## Re: Martingale Betting System- expected value

I see that i have a few mistakes in my calculations that basically destroys the system. I was too deep inside the Gambler's Falacy. First the winning probability should be 1-.5^5. This is because I need to get one black in 5 rolls to win $5. Second, the probability of me losing should still be based on losing 5 times in a row, not 7. This is because even if you wait for 2 of the opposite color to come up, the next 5 are independent of the previous 2; it took me a long ass time to completely understand it. After you do both things one can see that the net payout is$0. However, most casinos have a 0 and 00 so the probability of winning decreases and the probability of losing increasing, leading to a negative payout. So in the long run, you lose. =(

4. ## Re: Martingale Betting System- expected value

Exactly I was going to mention the green 0 and 00 on american tables. Also each independant roll would yield a probability of winning equal to 18/38=.4736842 so the probability that you will lose is always higher. I was going to mention some other things but based on your latest reply I can tell that you get it. It is a really fascinating thing to think about. Another mothod of casino money making I looked into and did for a while was the same betting concept applied to games of blackjack, where I adhered to the same rules for hitting and staying as the house do. This has seemed to work better in many ways for making my 5 dollar wins come sooner therefore fruitioning into some degree of profit over time.