Risk of Ruin playing blackjack surrender

[wall_st]

I am playing blackjack surrender on bet365.com with 200 bets. Can anyone tell me what my risk of ruin is and how do I calculate it ?

[BruceZ]

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I am playing blackjack surrender on bet365.com with 200 bets. Can anyone tell me what my risk of ruin is and how do I calculate it ?

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This is a negative expectation game, and the risk of ruin for a negative expectation game is always 100%.

[JimDrang]

Is there a site/calc where you can get specific %s for risk of ruin depending on how many bets you make at a certain $ amount with a certain BR?

[AaronBrown]

Figuring out your exact risk of ruin depends on the details of the game. In most cases of real games, the best approach is just to simulate a lot of outcomes.

You can get a pretty good approximation using the expected return and standard deviation of each bet. For example, suppose you pay $1 to flip a fair coin and get $X if you win. Your expected value per flip is $X/2 - 1. Your standard deviation per flip is $X/2.

After N flips, your expected profit is N*(X/2 - 1) and your standard deviation is (N^0.5)*X/2. You can use the Excel NORMDIST function to get the approximate probability of having lost B or more dollars:

=NORMDIST(-B,N*(X/2 - 1),(N^0.5)*X/2,TRUE)

However, if you started with B dollars, your chance of going broke on or before the Nth flip is greater than this. This is the chance that a guy with unlimited credit would be down B or more dollars after N flips. In some cases, he would have lost B dollars, but later had a winning streak to get positive.

If your expected value is zero, that is, if the game is fair, your chance of being broke is exactly twice the formula above (this is due to the "reflection" principle). If your expected value is not zero, there's no simple formula for the answer, but there are ways to compute it.