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

[Double Down]

Thank you, very insightful. Especially about how we need Hebrew for the higher order numbers. It always comes back to the chosen peeps.

It still doesn't quite jive with me, I guess I'm getting hung up on the fact that the 3D lines through the point has more than lines through the plane because it contains the lines through the plane. Basically, A=infinity but B= A plus more infinity. Goofy.

[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."

[MCS]

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Please explain how the concept of countably and uncountable infinite applies to the lines through the point example.

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As was already explained, it actually doesn't. They're both uncountable. [img]/images/graemlins/crazy.gif[/img] I was just adding in some extra-sweet stuff.

SamIAm's post is good. He knows more about math than I do. But don't tell him that.

[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