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10-01-2005, 02:15 AM
I answered this question a few times this week; I think people are curious enough about it to justify putting it in.

Odds of m OOTM in a row

OOTM = 1 - ITM
Odds of OOTM all of one specific set of m SnGs = OOTM^m

Now, in a set of N games where N > m, the number of sets of m is N + 1 - m (verify this for yourself with numbers). Thus, the odds of having at least one streak of m OOTM in a row in a set of N games is just:

1 - (1-OOTM^m)^(N+1-m).

So, with 40% ROI for 1000 SnGs, the odds of one streak of 15 OOTMs is 37%. For 2k, it's 99.99%.

A rough approximation for eyeballing this is:

N * OOTM^m. This (much) rougher formula gives 47% for the odds of a streak of 15 OOTM in 1k SnGs and 94% for 2k. (Note that it gives 141% on 3k. That's why the other formula's better.)
lorinda
10-01-2005, 02:16 AM
I've always loved (and posted about) this (http://faculty.vassar.edu/lowry/binomialX.html) little gem.

Lori
10-01-2005, 02:19 AM
It's a great idea. I found it very useful. But you should fix up that small mistake first.
SlackerMcFly
10-01-2005, 02:22 AM
Lori - Ouch! There are numbers and equations on your link. I am very distressed about it all now.

NoMathMcSlack
10-01-2005, 02:22 AM
[ QUOTE ]
It's a great idea. I found it very useful. But you should fix up that small mistake first.

[/ QUOTE ]

Clarify please?
lorinda
10-01-2005, 02:25 AM
Ignore those and scroll down to the calculator /images/graemlins/blush.gif


Lori
10-01-2005, 02:28 AM
[ QUOTE ]
I've always loved (and posted about) this (http://faculty.vassar.edu/lowry/binomialX.html) little gem.

Lori

[/ QUOTE ]

Nice link. Real math on the internet is rare.
10-01-2005, 03:00 AM
[ QUOTE ]
Clarify please?

[/ QUOTE ]

A set of 2k gives a 60% or so OOTM 15 in a row, 20k would give 99.99% chance of OOTM 15 in a row.
10-01-2005, 04:50 AM
Also the 40% ROI part is meant to say ITM, right?
10-01-2005, 05:03 AM
[ QUOTE ]
[ QUOTE ]
Clarify please?

[/ QUOTE ]

A set of 2k gives a 60% or so OOTM 15 in a row, 20k would give 99.99% chance of OOTM 15 in a row.

[/ QUOTE ]

Jeeze. Dumb and fixed.

I'm such a math geek that I don't even stop to think about what numbers mean any more--I just crunch them.
10-01-2005, 05:04 AM
Oops. Not fixed because it's too late.