Re: *** Official joining every $4/180man until I win one ***
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The probabilities ought to be additive.
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Not correct.
Each tournament is an independent event. Just because you didn't win 179 in a row doesn't mean you're guaranteed to win #180.
As with any other grouping of independent events you have to calculate the risk of not winning one specific tournament:
NW(1) = (180 - 1)/180 = 179/180 = 0.9944444 ....
From there you can calculate the risk of not winning any of X tournaments:
NW(X) = NW(1) raised to the power X = NW(1) * ... * NW(1) (that reads: NW(1) multiplied with itself X times).
This gives us the chance of winning (at least) one out of X tournaments:
CW = 1 - NW(X)
We're looking for the number of (random outcome) 180/$4.40 to play to have exactly 50% chance of winning one:
X = log(0.5) / log(NW(1)) = 124.4
So to have 50% chance of winning (at least) one tournament in a completely random universe (which doesn't seem too far off when it comes to $4.40 buy-ins) you have to play a little more than 124 of them.
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