20 Jun 2024, 00:16

How to estimate your poker winrate vs variance



8 Posts

the : 13/12/2012

Recently, I posted a few vids of mine (check some of my vids here : http://www.poker-coach.net/poker-coaching-videos.html) on a poker vids website, and a viewer who probably thought he was clever posted something like "Ahaa another poker loser who claims to be a poker coach : check his PTR stats, he is a loser!".


I am not a PTR fan for many reasons.

1st, I think PTR selling hands is bad for the game. 

2nd, I know how wrong their stats can be, as I have used many many accounts and played many many hands in my poker career, and most of the time, my PTR stats are wrong because PTR miss a tonn of hands, so the winning/losing results are everything but reliable.

But this post is not about PTR, but about poker.


So, when I read this user's comment, I checked the PTR stats of the account I had used for this vid. Here are the key numbers : 

-Hands = 10.000

-Winrate = -5.81 bb/100

-Earnings = -9.800$ (in fact it's not a key parameter)

Most of the hands had been played between NL400$ and NL1K€. Half of the hands were taken from Shorthanded games and the other half came from Heads Up games.


Now, how can we analyse these PTR stats?

You can't take a winrate at face value without taking into account a few parameters :


1. how many hands did you play? 

Imagine you play a HU match, you got dealt Aces for your first hand and your opponent got a good hand too, you go all in and unfortunately you lose all your 100bb stack before the second hand gets dealt... Your winrate will be -10000 bb/100, but if you had won, your winrate would have been +10000 bb/100 (and your winrate EV after this only hand is probably around +8000, depending on your opponent's hand). No need to say that in this case the winrate after your 1st hand is a useless information.

Well after 10.000 hands, the winrate is a more accurate information than in the above example, but 10.000 hands is still a very small sample in the poker area. I have been part of forums where this subject has been discussed a lot : some say that the sample needs to be at least 40K hands, others say that it must be at least 100K hands to be reliable... most of the time, the more experienced the poster, the higher the number!


2. What type of games did you play?

Every poker game has its own variance. For example, I think we can say that : 

PLO HU variance >> PLO SH variance > NLHE HU variance >> NLHE SH variance 

Variance is related to standard deviation, as standard deviation is the square-root of the variance.

Most of the time, we can evaluate NLHE SH standard deviation around 80, depending on a few criteria. NLHE HU std dev is much higher.



Well, once you have analysed the number of hands and the type of games you had played, you can discuss the calculated winrate : is it reliable or not?

Any expert or confirmed poker player would tell at 1st sight that calculating a winrate after 5K hands of NLHE HU and 5K hands of NLHE SH is a nonsense.

But we can't conclude with such an approximative statement. So we are going to ask for the help of mathematical tools. And some great tools exist in this matter!!!


Here is a great tool about today's thematic : 


This tool helps you analyse a winrate depending on the other parameters we have already discussed.

You must fill in the parameters (in our case : the winrate is -5.8 ; let's say 90 for the std dev as the hands were played in HU and SH ; let's keep the 95% confidence ; and number of hands = 10.000).

This tool shows a graph which has been determined thanks to the given parameters. If you place your mouse to the extreme right of the graph, you can read : 

Number of hands : 10.000

Upper Bound : 11.81

Lower Bound : -23.41


What does that mean?

Well that means that if I continue playing in the same conditions (same games, same tables, same opponents, same style, etc...), in the long term, there is 95% chance that my winrate be between +11.81 bb/100 hands and -23.41 bb/100 hands !!!

The mathematical analysis allowed by such tools sheds new light on the understanding of poker results and PTR stats, doesn't it?





PS : by the way, OP, these 10K hands are not even the third of the hands played with this account which I use to experiment new things, and make vids, so please don't take these 10K hands as my one and only achievement in my all poker career ;-)