Can someone run the numbers for me...quick calculation

[DVO]

What are the chances of a tourney player in the top 30% in terms of skill level, finishing in the top 12% ( i.e. making the money) only 5% of the time in the course of playing 150 tourneys?

Much appreciated. Hopefully this is easy for someone out there. I just don't know how to calculate this.

[FoxwoodsFiend]

Your answer depends on factors that you don't give, so instead (and hopefully more helpfully) I'll walk through an estimation.

Suppose that a top-30% player will hit the top 12% something like 1/6 of the time. This is probably generous to the top-30% player but is probably not too far off. The probability that this happens 5% of the time through 150 tournaments, or in 7 or 8 tournaments (let's call it 7), is:

(1/6)^7 * (5/6)^143 * (150 choose 7)

The first term represents the cashing probability compounded over the 7 times it happens, the analogous second term is for non-cashing, and the third term multiplies the first two by the number of ways in which it can happen.

I don't have a calculator handy, but it should be easy enough to plug in somewhere.

Please note how dependent the answer is on the probability of cashing. Also note that the probability of cashing is not perfectly correlated with player quality -- some great players don't cash much more than average, and some of the highest cashing percentages probably belong to players who are far from the very top.

[uDevil]

[ QUOTE ]

I don't have a calculator handy, but it should be easy enough to plug in somewhere.


[/ QUOTE ]

Handy tip: Google has a calculator function. Plugging in the expression you give results in

((1 / 6)^7) * ((5 / 6)^143) * (150 choose 7) = 4.99496505 × 10-6

[DVO]

which equals???

(Lazy and stupid, sorry)

[uDevil]

[ QUOTE ]
which equals???

(Lazy and stupid, sorry)

[/ QUOTE ]

[ QUOTE ]

((1 / 6)^7) * ((5 / 6)^143) * (150 choose 7) = 4.99496505 × 10-6

[/ QUOTE ]

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.

[SumZero]

[ QUOTE ]
[ QUOTE ]
which equals???

(Lazy and stupid, sorry)

[/ QUOTE ]

[ QUOTE ]

((1 / 6)^7) * ((5 / 6)^143) * (150 choose 7) = 4.99496505 × 10-6

[/ QUOTE ]

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.

[/ QUOTE ]

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):

<font class="small">Code:</font><hr /><pre>
3 cashes or less =&gt; more than 5-sigma bad.
8 cashes or less =&gt; more than 4-sigma bad.
11 cashes or less =&gt; more than 3-sigma bad.
15 cashes or less =&gt; more than 2-sigma bad.
19 cashes or less =&gt; more than 1-sigma bad.
24 cashes or less =&gt; more than 0-sigma bad.
25 cashes or more =&gt; more than 0-sigma good.
30 cashes or more =&gt; more than 1-sigma good.
34 cashes or more =&gt; more than 2-sigma good.
39 cashes or more =&gt; more than 3-sigma good.
45 cashes or more =&gt; more than 4-sigma good.
50 cashes or more =&gt; more than 5-sigma good.
</pre><hr />

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.