interesting math

having played the paradise poker $10tourneys for the last two months and winning, i was wondering what the standard deviation($/tourney) would be for someone who played say 100,200,400,10000...etc tournaments. i wrote a computer program and would like to share my results with you.

let x=probability of winning tourney.

ley y=probability of coming second.

let z=probability of coming third.

i then calulated the standard deviation of $tourney for 100,200,500,..etc tournys using different values for x,y and z.

my results summary:


1.after 100 torneys your calculated $/tourney average has at least a 95% chance of being within $4 of actual $/tourney regardless of what x,y, and z are.

2.after 1000 tourney your calculated $/tourney average has at least a 95% chance of being within $1.20 of actual $/tourney regardless of what x,y and z are.


example of how to use these facts.


lets say a player after 100 tournaments won 20%, came second 10%, and third 10%.

his calculated expectation ($/tourney) would be:

exp=.20X39+.1x19+.1x9-(.6x11)=$3

hence his actual $/tourney value has a 95% of being between -1$ and $7 after 100 tourneys, and a 95% chance of being between $1.80 and $4.20 after 1000 tourneys. any feedback would be welcomed.


tootaloo


sotiris