Basically I've been trying to justify to friends why I'm moving up in limits after so few games (97). Edit: I've added the graph for the 97 $5.25 games above. I'm going to summarise my reasons for moving up in this post. There will be maths, and if I've screwed up - likely - then please correct in the comments and I'll go back over the workings. I'm currently playing the $5.25 HU SNGs on Absolute poker. These games are well within my bankroll (50 buy-ins). If you talk to anyone who plays HUSNGs they'll tell you that this is ludicrously nitty in terms of bankrolling for micro stakes HU matches, especially since I have disposable income from my day job that I can top up with every month. So why am I playing them and not the $10.50s or higher? Because I wanted to prove to myself that I can beat the limits from the base up before testing myself at higher stakes. Can I prove after so few games that I'm beating the $5.25s then? I can't prove it, but I can provide a compelling argument. Let's assume we're a break even player (ROI = EV = $0) then we should win on average 53% of the time.

**First let's calculate variance of a single trial (and I'll include the sums so I can quickly spot errors - hopefully):**

0.53*(4.75^2) + 0.47*(-5.25^2) = 24.9125

=> standard deviation = 4.99

The standard deviation of 97 trials is 4.99*(square root(97)) = approx 49

The mean $ won over 97 games is obv 0 and so using a confidence interval of two standard deviations from the mean our upper and lower profit bounds are -$98 < mean < $98 (For those who don't know probability this is the range within which our profit should fall 95% of the time, given a normal distribution)

My current profit is $101 in these games, which would happen no more that 5% of the time if I was only a break even player. This is therefore strong evidence that I'm actually a winner.

0.53*(4.75^2) + 0.47*(-5.25^2) = 24.9125

=> standard deviation = 4.99

The standard deviation of 97 trials is 4.99*(square root(97)) = approx 49

The mean $ won over 97 games is obv 0 and so using a confidence interval of two standard deviations from the mean our upper and lower profit bounds are -$98 < mean < $98 (For those who don't know probability this is the range within which our profit should fall 95% of the time, given a normal distribution)

My current profit is $101 in these games, which would happen no more that 5% of the time if I was only a break even player. This is therefore strong evidence that I'm actually a winner.

The fact that I currently have an ROI of 20% suggests I may be doing better than just beating the games too. But without a bigger sample I just won't know. Also, because I'm so overrolled for the $5.25 games and might be harming my long term winnings by playing at those stakes, I think there's a compelling case to move up now - which I'm going to do. Once the stakes start to become a little more tasty I'm going to start using stricter confidence intervals before moving up limits since there is more risk involved. GL

P.S. All the probability maths and much more can be found in Bill Chen and Jerrod Ankenman's 'The Mathematics of Poker' book.

I can just tell from your graph and having read all of your posts that you r are HU player who is going places . the depth of your knowledge at this level puts me to shame . i am watching with bated breath go go go ftw . regards, adam

ReplyDeleteThanks Adam, I hope so or it's a wasted investment of time and money. Time will tell :) Hope tables are treating you well

ReplyDeleteSi, this was just a bragpost about having over $250 online! Jokes. Good stuff man that's some good volume and a nice graph to look at. Keep up the work ethic and thirst for poker knowledge!

ReplyDeleteThanks Dan, less brag posts in future then haha.

ReplyDeleteYou lost me at First.....

ReplyDeleteI do know you'd need a sample size of 1500-2000 games to get a true idea of your ROI

Thanks United and I'm not very good at explaining things but you're right I think; to get my true ROI I'd need that sort of sample size. But I wasn't trying to guesstimate my likely ROI, I was just trying to show that it's very likely I'm beating the $5 games (for any positive ROI) - even after only 97 matches. I think my argument makes sense given that it's so unlikely that a breakeven player would have such a good run of results over 97 games. Please don't hesitate to question the maths or logic in my argument. I'm a learner, not a teacher and welcome all input. The truth is my maths is poor, and despite the fact I've looked over the equations several times I could easily have made a mistake. I appreciate your post, thanks

ReplyDelete