Quote:
Originally Posted by kioetara
How did you come up with those graphs? In particular the HU hyper turbo ones.. What kind of statistical model did you use? I'm rusty with my knowledge on the various distributions... :P
The calculations are done using a
Markov Chain.
In a way you can view your current position in a downswing as a single state and from this state you can move to another state either up or down depending on whether you win or lose (or with bigger fields jump to a few states if you can come 1st,2nd,3rd,4th... or lose).
From any state we know how likely you are to jump into any other as we have the finish distribution of your games. In HU, lets say you win 54% and lose 46% of the time .
If you are in state X you either jump to state X+a or X-b
You can write these states as a matrix and then use matrix maths to calculate what happens in the long run.
I am calculating how often a specific swing occurs and if we hit this state we never get out even if we have more 'throws' or games left to go we have aready hit theis sized swing. Also when we hit a point as high as the downswing size this is the top state and we never move to any higher state - we want to see if we ever hit a run that takes us X below a high water point so the top row of the matrix is this high water mark, the bottom row is the downswing.
Here is an example matrix for a hu with 54% win and for use calculating a 3BI swing (ignoring rake)
Code:
0 -1 -2 -3
state 0 ==>[ 0.54 0.46 0. 0. ]
state -1 ==>[ 0.54 0. 0.46 0. ]
state -2 ==>[ 0. 0.54 0. 0.46]
state -3 ==>[ 0. 0. 0. 1. ]
being in state "0", 54% we 'jump' to state "0" ie, no change we are at the high water mark, and 46% we jump to state -1.
Notice once we get to state "-3" we stay there as 100% of the time we jump from state "-3" to state "-3", ie. no move.
From state "-1" we jump to state "0" 54% of the time and state "-2" 46%.
and here is a decent video about Markov Chains:
http://www.youtube.com/watch?v=afIhgiHVnj0
Last edited by BaseMetal2; 10-22-2014 at 07:10 PM.