Oh another thing I wanted to bring up that I get wrong sometimes and wanted to get better at understanding.
TBJ and I were going over this hand (any Bayesian experts that want to crunch the numbers on this would be appreciated).
Here is the link:
https://forumserver.twoplustwo.com/6...y-nit-1837154/
So we know this guy is 11/11 (VPIP/PFR) over 35 hands.
Most people will assume this is a nit even though we don't know for certain, correct?
But this is where statistics gets counter intuitive (at least to me).
It's actually WAY more likely that he is not a nit and is just a regular running bad.
I'm hoping someone can crunch the math here but I'll post TBJ's data analysis and conclusion.
Out of a DB of 97.5 million hands from players with VPIP/PFR <30. Only 42,000 hands were from people with a VPIP of 13 or less.
42000/97,500,000 = .0000043 of all hands
Let's say the average VPIP for a NIT is 18 VPIP, now what are the odds he has an 18 VPIP over 35 hands when the data show's 11 VPIP?
Okay well we can use Tombo's calculator (shoutout to tombo from GTO Wizard).
Okay so there is around an ~82% chance that this unknown is a nit with an 18 VPIP or less after showing 11/11 over 35 hands. But then we realize only .0000043 of all hands were from players with 13 VPIP or less.
So now instead of it being likely he is a real nit--------->it becomes extremely likely he is just a reg that is running bad (yes other people can run bad not just you! lol).
I'll try to calculate this:
Probability of being a nit P(A): 82%
Probability of being a reg P(reg): 18%
Posterior Probability = Likelihood * Prior Probability / Evidence
Prior Probability = Random player with 11/11 stats over 35 hands being a nit (18 VPIP or less ) = 82%
Likelihood = .0000043%
.82 * .0000043
Probability of evidence = Probability of likelihood (.0000043%) * Probability of being a nit (82%) + Probability of likelihood (.9999957) Probability of reg (18%)
Only two possibilities for purposes of this discussion. He is either a nit or a reg.
Probability of evidence = .1800034486
Posterior Probability = .000003526 / .1800034486 = .00001956 = About .0002% = This player is actually a nit and not a regular just running bad.
I won't lie I probably butchered some of this math so feel free to correct me. I won't it take it personally.
The main thing to take away is that even very good players will incorrectly identify a player as a nit when it is with very high certainty that they aren't a nit and instead a regular that is running bad.
P.S
Check my math
Last edited by DooDooPoker; 05-04-2024 at 01:17 PM.