SNG Probability Question

[quinn]

What is the probability that a person who has a 10% ROI over 100 SNGs has a real ROI over 0%?
What about the same question, but for..
250 SNGs?
500 SNGs?
1000 SNGs?
Assume that the player and all his opponents always play with the exact same skill level.
We can define "real ROI" to be the ROI that the player would have over an infinite number of SNGs.

[gaming_mouse]

You really need more info than this. That is, the answer to your question depends on the player's variance, and this in turn depends on the how many firsts, seconds, or thirds he gets.

For example, a player who always tries for first, and takes risks when he might instead be able to safely assure a third place (but thereby lessen his chance of a first place) will have much bigger swings.

You really need to assume that the player comes in 3rd x% of the time, 2nd y%, and 3rd z%.

[GrekeHaus]

I thought it had been shown that SD for SNGs was roughly 1.7 buyins/SNG. Slightly higher for winning players, slightly lower for losing players.

link (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=singletable&Number=1479432 &Forum=All_Forums&Words=%2Bstandard%20%2Bdeviation &Searchpage=0&Limit=25&Main=1479432&Search=true&wh ere=bodysub&Name=15228&daterange=1&newerval=1&newe rtype=y&olderval=&oldertype=&bodyprev=#Post1479432 )

[gaming_mouse]

[ QUOTE ]
I thought it had been shown that SD for SNGs was roughly 1.7 buyins/SNG. Slightly higher for winning players, slightly lower for losing players.

link (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=singletable&Number=1479432 &Forum=All_Forums&Words=%2Bstandard%20%2Bdeviation &Searchpage=0&Limit=25&Main=1479432&Search=true&wh ere=bodysub&Name=15228&daterange=1&newerval=1&newe rtype=y&olderval=&oldertype=&bodyprev=#Post1479432 )

[/ QUOTE ]

This doesn't contradict my comments. He just shows that the reasonable range is between 1.5 and 2.

So I'll assume 1.7 and answer the OP's question.

The amount won after 100 games is normal with:

mean = 100*.1 = 10 (the units are buyins)
SD = sqrt(100)*1.7 = 17

The chance of being even or down is therefore about 27%.