How do you explain Martingale to someone who doesn't understand EV?

[Komodo]

Take a look at this thread:

http://forumserver.twoplustwo.com/sh...t=all&vc=1

[flatline]

I did read that thread. I can't believe they went on so long with such nonsense.

Look. Give me, the Infinite Martingaler, any goal for winnings. Say $500. What are my chances of winning $500 with this system? My chances are 100%.

Halfway through that thread they started saying that infinite losing streaks are possible. They aren't. Here is a simple proof (credit to WhiteWolf). Please find the flaw in it.

[ QUOTE ]

Assign x the value of 0.99999...:
x = 0.9999...

Multiply each side of the equation by 10:
10x = 9.9999...

Factor out 9.9999... as 9 + 0.9999...
10x = 9 + 0.9999...

Since x= 0.9999..., replace 0.9999... in the right hand side of the equation:
10x = 9 + x

Subtract x from each side:
9x = 9

Divide each side by 9:
x = 1

Since x equals both 1 and 0.9999..., 1 does indeed equal 0.9999....


[/ QUOTE ]

[The Goober]

Think about it this way...

Suppose you take your infinite bankroll and decide to play for a set period of time. You'll play strict martingale and stop at the predecided time regardless of what happens. What are the chances that you'll finish a winner? Well, it'll work out that there will be a largish chance that you will be a small winner, and a smallish chance that you will be a big loser (because you stopped during a string of loses). Do the math, and your estimated EV at the stop time will be exactly your EV for the game (given you average bet size).

Of course, that's not really playing with an infinite bankroll - if you have a hard time limit, you have a hard bankroll limit too (how much it would cost you to lose every roll for the whole length of time). If we take it as a given that martingale doesn't work for a finite bankroll, but claim that it does work with an infinite one, then we must concede that we might need an infinite amount of time to get to our goal. So now it reduces to: "you can make a profit martingaling with an infinite bankroll, but you have to gamble for an infinite amount of time, and if we stop and check your progress at any point, more likely than not, you will be losing." That doesn't really sound like you are making a profit at all.

Another thing to think about. Suppose we took our infinite bankroll and simply doubled our bet every time. This strategy is just as good as a martingale one: At any one time we are more likely to be behind than ahead, but more likely that not will we be ahead again as some point (although it might take an infinite amount of time). Any betting system works this way as long as you increase your bet size consistently so that the std. deviation will overwhelm your expectation.

[junkmail3]

Take him to play money roulette online. Have him start with $1. See how long it takes him to lose whatever play money they give him.

[Rev. Good Will]

just say "the green numbers"

then say: "even if the green numbers didn't exist, it wouldn't work; its like saying a coin lands more on heads than tails."

[punter11235]

Hello,

I hope to give some insight into this problem.
Suppose you can make a bet in roulette every 1 minute. Suppose that you are able to make a bet of any size.
If you plan to use martingale system it can be easily shown that for every minute in the future your expected amount of money is negative (if sb dont understand this I can elaborate but this is really basic). It is true for 50 minutes from the start as it is for 1 000 000 from the start etc.

The problem is that EV alone is not good enough reason to make decisions in life, so our intuition isnt really working based on EV. In fact there even exist games with infinite +EV for a player but no sane human would give even 50$ to play in a such a game (for reference and very good article see this article ).


The problem is that if probability of being slightly ahead is almost 1 but eventual lose is enormous our intuition dont understand it and just assumes that we will for sure be ahead one day (the same is true other way around). Try to answer following questions to better understand the problem :
-If martingale system can make money once it shuould be able to make money twice etc. right ?
-If martingale system can make money how much $$ per hour it is?
-If for every minute in the future in abovementioned example it is true that a player have negative expected amount of money how it can be true that he will make money ?

I think its some good food for thought.

Best wishes