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which equals???
(Lazy and stupid, sorry)
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((1 / 6)^7) * ((5 / 6)^143) * (150 choose 7)
= 4.99496505 × 10-6
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Assuming the expression is correct (I didn't check), the bold number is the probability. This is about 1 in 220,202. Or odds of 200,201:1 against.
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Although this is the probability of exactly 7 finishes in the money. If you want no more than 7 finishes the probability of that is slightly higher.
A person running with X => Y (all assuming 150 tourneys and 1/6 chance to cash):
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3 cashes or less => more than 5-sigma bad.
8 cashes or less => more than 4-sigma bad.
11 cashes or less => more than 3-sigma bad.
15 cashes or less => more than 2-sigma bad.
19 cashes or less => more than 1-sigma bad.
24 cashes or less => more than 0-sigma bad.
25 cashes or more => more than 0-sigma good.
30 cashes or more => more than 1-sigma good.
34 cashes or more => more than 2-sigma good.
39 cashes or more => more than 3-sigma good.
45 cashes or more => more than 4-sigma good.
50 cashes or more => more than 5-sigma good.
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So 7 or less cashes is about as likely as 46 or more cashes given the player is a true 1/6 cashing player. And both are very, very unlikely.