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Martingale system
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savrababa
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Location: Greece

PostPosted: Thu Jul 14, 2011 2:38 pm    Post subject: Martingale system Reply with quote

Here is an idea..

Let's say that any given player has at least a 40% winrate in HUSNG's.
Suppose we have someone staking that guy with unlimited $$$.

If we put this player to play a $5 game and he wins we have a profit of $5 obviously.
If he looses we put him to play a $10 game.
If he wins we go back at $5.
If he looses we put him in a $20 game and so on.
Eventually he will win.
The profit we have every time he wins is $5.

I'm not going to try this obviously, but I thought it was a funny way to exploit the game Very Happy
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hjbear
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PostPosted: Thu Jul 14, 2011 2:57 pm    Post subject: Reply with quote

rake would be the negative factor i think
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savrababa
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PostPosted: Thu Jul 14, 2011 3:26 pm    Post subject: Reply with quote

True I forgot about rake.
That would screw the plan pretty badly.. Smile
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chesslw
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PostPosted: Thu Jul 14, 2011 4:13 pm    Post subject: Reply with quote

The fun things you can do with infinity...

If you like money, don't ever try this-  not only for poker.

Also with "infinite" money it doesn't matter what strategy you use, you can't ever win or lose and will always end up with the same as you started with.
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Simba
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PostPosted: Sat Jul 16, 2011 10:00 pm    Post subject: Reply with quote

It actually doesn't matter what the winrate is if your money is infinite.

To prove this, suppose that we win a proportion x of our games (0 < x < 1), and also assume (as is reasonable considering that we have infinite money), that we can play as high as we want. We can use this to circumvent rake by simply jumping up more than one step (or for simplicity, we can just assume that there is no rake, to avoid having to factor in the superficial above consideration).

Now, assume we play n games. We can consider the random variable Y ~ Bin(n, x) to model our situation. Now, we win money with probability P(Y > 0) = 1 - P(Y = 0) = 1 - (1 - x)^n.

Since we have infinite money, we consider lim(n -> inf) in the above.

lim(n -> inf) [1 - (1 - x)^n] = 1, since |1 - x| < 1, due to 0 < x < 1.

So no matter what the probability of winning a game is (as long as it's not 0), we make money in the long term.

By a very similar argument, you can actually prove that even a player winning 99.9% of his games will eventually go bust, if he plays an infinite number of games.

Of course from the above analysis we conclude... infinity is weird. Wink
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chesslw
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PostPosted: Sun Jul 17, 2011 5:01 pm    Post subject: Reply with quote

Simba wrote:
It actually doesn't matter what the winrate is if your money is infinite.

To prove this, suppose that we win a proportion x of our games (0 < x < 1), and also assume (as is reasonable considering that we have infinite money), that we can play as high as we want. We can use this to circumvent rake by simply jumping up more than one step (or for simplicity, we can just assume that there is no rake, to avoid having to factor in the superficial above consideration).

Now, assume we play n games. We can consider the random variable Y ~ Bin(n, x) to model our situation. Now, we win money with probability P(Y > 0) = 1 - P(Y = 0) = 1 - (1 - x)^n.

Since we have infinite money, we consider lim(n -> inf) in the above.

lim(n -> inf) [1 - (1 - x)^n] = 1, since |1 - x| < 1, due to 0 < x < 1.

So no matter what the probability of winning a game is (as long as it's not 0), we make money in the long term.

By a very similar argument, you can actually prove that even a player winning 99.9% of his games will eventually go bust, if he plays an infinite number of games.

Of course from the above analysis we conclude... infinity is weird. Wink


Yes- though even the notion of "we make money in the long term" isn't even well defined...

Even if we win with prob 1 or 0, we still end up with the same amount as we started (or more, or less- depending on your definition). This whole idea bares a similarity to pyramid schemes which will only work if there were infinitely many people.

The important thing to know is that even if you have a very large sum of money, trying a martingale betting system (the house has an edge on each bet) is always a bad idea (even though the chance that you lose is very small).

You could then go on to talk about utility functions, and why people choose to play the lottery knowing that it is -EV. Now that is an interesting topic for discussion. Very Happy
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Simba
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PostPosted: Sun Jul 17, 2011 9:37 pm    Post subject: Reply with quote

chesslw wrote:
You could then go on to talk about utility functions, and why people choose to play the lottery knowing that it is -EV. Now that is an interesting topic for discussion. Very Happy


Haha, mmm, and the issue is complicated even more if you consider crazy convex utility functions...

Can't say I'm an expert on that though - there was only one (optional) module on financial mathematics in my degree, and I only read up on it for fun, rather than being examined on it. I didn't do any measure theory so some of the probability and Lebesgue integrals were a bit "Hmm...". Working in finance might be interesting at some point, but I'm not into the whole suit-and-tie shenanigan; I would much rather be relaxed and comfortable where I work than feel 'proper'/'businessy'...
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savrababa
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PostPosted: Sun Jul 17, 2011 10:02 pm    Post subject: Reply with quote

I guarantee you working in finance is nowhere near fun.
Also finance is not science. It is a way of complicating otherwise simple concepts, so that most people don't understand how money creates dept.

Regarding people playing the lottery or any other form of gambling, it has to do with various emotional decisions.
There is nothing rational about it.

From my experience working in the casino I would say that most degenerate gamblers kind of do this to justify their incompetence in various other tasks.
It gives them a good reason to say "I am cursed. I can't succeed because I am so unlucky" or something similar.
These people subconsciously want to loose money.
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chesslw
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PostPosted: Mon Jul 18, 2011 12:25 am    Post subject: Reply with quote

Haha. Lotteries can be +EV though- in the UK it can be +EV when there is a rollover, and it is very +EV with a double rollover (though variance is humongous). Even if you buy out all the tickets (I'm not sure if this is legal), there is a big chance that there are multiple jackpot winners (i.e. still big variance)...

You'd be surprised how many people are ignorant of basic maths.

My uncle once asked me to help him win a raffle by working out patterns in sequences...
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savrababa
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PostPosted: Mon Jul 18, 2011 1:24 am    Post subject: Reply with quote

They put those notepads next to the roulettes  in the casino.
They are for players to keep the sequence of numbers that came up so that they can break the roulette algorithm I guess  Razz
You won't imagine how many people fall for this and sit and write down number after number to get some kind of edge... Very Happy
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