tag:blogger.com,1999:blog-1690550055620514587.post2420730243260759390..comments2016-04-14T06:19:54.939-07:00Comments on Quantitative Poker: How far from Gaussian (normal) are poker results?Unknownnoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-1690550055620514587.post-22612307166141751152011-02-25T11:02:41.244-08:002011-02-25T11:02:41.244-08:00Not jumping the gun at all, these are all things I...Not jumping the gun at all, these are all things I intend to discuss soon.<br /><br />The utility function we've established should make it pretty straightforward to solve problems about moving up and moving down when we make assumptions at our winrates and variance at the two stakes. For each level of bankroll, we can compare the utility of playing the higher stake versus that of the lower stake, and there should be a unique point of indifference. This may take some more subtlety than this, but I'll figure it out soon. Adding uncertainty about winrates (ex. when moving up to a new stake) into this would be interesting and may be reasonable enough to try.<br /><br />The "long run" issues of a unique opportunity might actually be less interesting of a topic than I originally thought, though I still want to say something more about it at some point. You get no normality on a unique event, but if you can approximate its actual distribution, you can just plug in and go with the utility function. The WSOP certainty equivalent analysis basically did this for the case when the unique event is the WSOP ME - you only get one try at it, so you look at the expected utility of (X+Y), where X is all of your other play for the year (approximately Gaussian) and Y is the unique event. A similar approach could be used for any opportunity where you "can't get to the long run". There are more implications of this that could come up that I might discuss later. For example, it might be the case that, for a given player with a given skill level, bankroll, and risk aversion, it is -EV (after tax/util) to play the Main Event, but it would be +EV if he were able to play 2 identically-distributed Main Events in succession. It should be the case that any positive-pure-EV opportunity would be worth taking for *anyone* as long as it could be repeated at least N times for some N.Mike Steinhttps://www.blogger.com/profile/04085932960610615123noreply@blogger.comtag:blogger.com,1999:blog-1690550055620514587.post-1088557984940207622011-02-25T10:26:25.098-08:002011-02-25T10:26:25.098-08:00Nice post Mike. I know you’re still in the ‘buildi...Nice post Mike. I know you’re still in the ‘building assumptions’ mode here (and sorry if this is jumping the gun) but:<br /><br />- I’m curious how, if you are on a bad losing streak, we could use this to find the optimal number of buyins in your bankroll you would drop to before moving to lower stakes, using our utility function. Your risk of ruin probabilities might be more practically modified to ‘risk-of-dropping-a-level’ probabilities.<br /><br />- Conversely, at what point can you justify taking a shot at the next highest level without being accused of recklessness? <br /><br />- You mentioned a while ago that you would talk about choices to be made where you won’t be able to reach the Long Run; what kind of effect does that have here? Saying “I’ll get to that later” is fine.drewhamiltonhttps://www.blogger.com/profile/08326162621571241084noreply@blogger.com