# Two players with the same skill get very different results?

• Bronze
Joined: 18.01.2008
Hi, I'm recently in a debate with someone, and he says that the results from 2 poker players with the same skill (same expected value) tend to diverge. So this means that player A could get a \$10K BR and player B get only a \$2K BR for the same number of hands played (with many hands played), and this divergence would become larger and larger the more hands they played.

Does it make sense?
• 51 replies
• Bronze
Joined: 07.05.2008
Its called variance.

2 players that's played exactly the same could end up with 2 completely different bankrolls at the end of that period, true.

Different opponents.
Different hands.
Different table dynamics.
Different times of days.

Think you get the point..lol
• Bronze
Joined: 09.02.2009
Ofc it makes sense.

Doesn't makes sense thinking that Player "A" will always have the 5x positive results. One time or another B will be ahead, A will be down...
• Bronze
Joined: 13.03.2009
I'm player B.
• Bronze
Joined: 03.10.2007
if player's skill is fixed and neither players improve, there will be a decrease in divergence as time goes on however (ie difference in bankrolls/net profits will become the same)
• Bronze
Joined: 18.01.2008
So this basically negates the "luck is equal for everybody in the long run" statement, because it's possible to have very different results with the same edge. However poker players with different bankrolls may play the same limit and at that time their bankrolls will converge and higher limits mean lower winrates, but with traders this doesn't happen.
• Bronze
Joined: 18.01.2008
Originally posted by chenny8888
if player's skill is fixed and neither players improve, there will be a decrease in divergence as time goes on however (ie difference in bankrolls/net profits will become the same)
if they play at the same limit yes, but not if they play at different limits (with the same winrate).
• Bronze
Joined: 08.11.2008
Originally posted by Tosh5457
So this basically negates the "luck is equal for everybody in the long run" statement, because it's possible to have very different results with the same edge. However poker players with different bankrolls may play the same limit and at that time their bankrolls will converge and higher limits mean lower winrates, but with traders this doesn't happen.
Yes... But many people do not really know how long the "long run" actually is. Once you have seen a graph of 1,5 million hands and 300 buy-ins below all-in EV, you start asking yourself how long it really is . In theory, they will eventually have the same bankroll in the end, but that might take a few million hands to happen .
• Silver
Joined: 18.03.2008
this is not true. since they are both equally good they will both get the same winnings. this means their bankrolls will only varie by up to 10\$
• Black
Joined: 20.02.2008
they will converge. opposite of diverge.

in the shortterm they will go apart because of variance and BRM, but in the longterm they converge

if 2 equally good players both play an infinite amount of hands, they will win amounts that are only minute fractions different from eachother
• Bronze
Joined: 16.12.2009
I think the real question behind the question asked is:
"Damn I think I am as good as *** but why am I down 100BI when he's up 300?" AKA "Is life fair?"
• Bronze
Joined: 08.11.2008
Originally posted by yeahyoung0312
I think the real question behind the question asked is:
"Damn I think I am as good as *** but why am I down 100BI when he's up 300?" AKA "Is life fair?"
There is something called karma .
• Bronze
Joined: 18.01.2008
they will converge. opposite of diverge.
In theory, they will eventually have the same bankroll in the end, but that might take a few million hands to happen.
But if for example on the case of trading, you win 100% per year on your account. Two traders start with 10K. If by the effect of variance account of trader A goes to 11K and player B's account goes to 10K, since they have the same EV (100% per year) it's most probable in the long run that trader A will have more money than trader B (more 10%), and then they'll tend to diverge (the difference between them gets bigger and bigger, although player A is expected to have 10% more than player B and this percentage is expected to remain constant). It's like trader A started with 11K and trader B started with 10K.

In fact, in the beggining if they have the same edge it's expected that they'll have the same bankroll in the end. But as one of them gets a different bankroll by the effect of variance, that's no longer the most probable scenario, the most probable scenario is that the difference between their bankrolls will rise.
• Bronze
Joined: 29.05.2009
Originally posted by Schnitzelfisch
Originally posted by yeahyoung0312
I think the real question behind the question asked is:
"Damn I think I am as good as *** but why am I down 100BI when he's up 300?" AKA "Is life fair?"
There is something called karma .
might I remind you that you are not unlucky
• Bronze
Joined: 08.11.2008
Originally posted by taavi1337
Originally posted by Schnitzelfisch
Originally posted by yeahyoung0312
I think the real question behind the question asked is:
"Damn I think I am as good as *** but why am I down 100BI when he's up 300?" AKA "Is life fair?"
There is something called karma .
might I remind you that you are not unlucky
thanks . might i remind you that you are lucky (at least currently?) .
• Bronze
Joined: 02.01.2009

diverge in short-term

probably still diverge in medium term

may begin to converge in long term

will converge eventually, but may take longer than the human lifespan to actually happen
• Bronze
Joined: 29.05.2009
Originally posted by Schnitzelfisch
Originally posted by taavi1337
Originally posted by Schnitzelfisch
Originally posted by yeahyoung0312
I think the real question behind the question asked is:
"Damn I think I am as good as *** but why am I down 100BI when he's up 300?" AKA "Is life fair?"
There is something called karma .
might I remind you that you are not unlucky
thanks . might i remind you that you are lucky (at least currently?) .
Hahahaha, thanks. True
• Bronze
Joined: 18.03.2008
I doubt however, that the 2 players are exactly equially skilled. Even if they are, I really really doubt the two players would always make the same moves in the same pots, I would say that's close to impossible.

All players are different, even if they are somewhat equal in skills. I would in fact get scared if I found someone that would make the exact same moves as me, with the exact betsizing etc in more then 90% of the cases
• Bronze
Joined: 03.10.2007
Originally posted by vonki
I doubt however, that the 2 players are exactly equially skilled. Even if they are, I really really doubt the two players would always make the same moves in the same pots, I would say that's close to impossible.

All players are different, even if they are somewhat equal in skills. I would in fact get scared if I found someone that would make the exact same moves as me, with the exact betsizing etc in more then 90% of the cases
obviously it's a hypothetical situation. there is variance in the scenarios they will encounter as players, and as a result equal numbers of tough and easy games will come up
• Bronze
Joined: 21.07.2009
I always thought that if you run under EV then there is no reason you should run above EV in the future, or to put it simply: "The dice has no memory".

So if you run 10BI under EV for 20k hands, you EV will then be expected to stay 10BI under EV, not for you to run 10BI above EV for the next 20k hands so you will meet up with you long term EV. That wouldn't make sense at all, that's basically saying "I was unlucky before so i've got to be lucky in the future".

So no, they should not diverge or converge if they have ran at different levels of EV.