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05-20-2013, 12:56 AM   #6
MUD

Join Date: May 2005
Posts: 817
Re: Simulated risk of ruin in \$1500 WSOP events

Quote:
 Originally Posted by NeverScaredB Thanks for doing all this work, really fascinating stuff. Can you elaborate on the difference between these please? Trad. Ruin % 72.70979 Iter. Ruin % 26.21671 Sim. Ruin % 26.83000
Quote:
 Originally Posted by Sherman The traditional risk of ruin formula is given as e-2 * WR * BR / Var where e is the constant 2.78128, WR is your expected win-rate (ROI), BR is your starting bankroll, and Var is the mathematical variance of results around your expected win-rate.
It seems to me that the script might be calculating this wrong but it doesn't matter because the whole point of the program is to not calculate it this way. This is because our finish distributions as winning players are not normally distributed, which the Traditional formula assumes. For example our 66% ROI player would have to finish in each position 1.84 times (not 1.66 due to rake) more likely than a breakeven-minus-rake "normal" player. While we can agree ROIs of 66% are possible in large field MTTs, nobody has ever cashed 1.84 times the payout ratio (would correspond to 26% ITM on Stars longterm). And since we have an edge for the entirety of thee tourney it stands we "should" finish it each spot a little more often than the previous spot. which takes us to

Iter. Ruin= Iterative Risk of Ruin %

I don't fully understand this one so I'll just quote
Quote:
 Originally Posted by Sherman The key here is finding the value R because Rnumber of BIs in bankroll is the Risk of Ruin. Finding the value of R is complicated and iterative methods are used to find it (i.e. "try a value and see if it works, if not adjust and find a better fitting value, stop when the fit is good."). Iterative methods are great unless there is more than one solution. For most of the problems we are talking about there is only one best solution though. The advantage of the RoR.iter() is that it never goes over 100% (like the traditional RoR sometimes does). It is well behaved.

Sim Ruin%= Simulated Risk of Ruin%

This just takes the distribution of finishes % we put in and picks randomly a finish position according to those %s. It continues to do this until your bankroll hits 0 or hits your "winning" number. Which I just arbitrarily set to \$1.5 million. Sim Ruin % equals the % times it hits 0 first.