I believe that ICM is a great way to model $ev but I also did not believe that it was completely accurate compared to actual $ outcomes in some situations and I wanted to find these differences and see if there are practical applications for this.
So, I wrote software that analyzes ICM and real outcomes for every player in every hand of an SNG and stores the results in SQL database for processing. My first run through this incorporated results from about 1700 SNG's and my intention is to continue to increase the sample size. Any contributions are appreciated.
So far the results have been extremely interesting at least to me. In this first go around I have categorized stack sizes into 5 groupings:
Very Small = bottom 10% of samples
Small = 10th to 30th percentile
Average = 30th to 70th percentile
Large = 70th to 90th percentile
Very Large = top 10th percentile
So these grouping are done per level or per number of players remaining so obviously relate to different stack sizes for each level.
At EVERY level, a subtle but distinct thing happens between ICM $ and Real $. There is an S curve... I think this is pretty huge. At every level very low stacks are highly overvalued, low stacks are overvalues, average stacks are pretty close but vary by level, large stacks are highly undervalued and very large stacks are somewhat undervalued.
I then looked at it by number of players remaining (instead of by level) and found similar trends. For example, here are the results when there are 4 players remaining (note: all results here are based on 800 chip games. I do expect similar trends albeit with different nuances for 1000 chip games but have not looked at those results yet):
and here is the data:
Thses differences are not small... Obviously this will change the results of ICM $EV calculations used to determine optimal push / fold scenarios. Lower stacks will find that hands that were previously easy folds now become easy pushes and conversely larger stacks have even more value than ICM gives them credit for and therefor many of the marginal and not so marginal pushes need to becomes folds.
I plan on charting this for every blind level and # players remaining and then moving on to things like determining where you are in relation to the blind and blind size and how that affects real $ results.
Comments?
rvg