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# 'variance evens out in long run' partly false?

• Bronze
Joined: 11.08.2012
So let's say you have never played a poker hand before. For the next infinite hands you play EV= actual profit because variance evens out in the long run.

How about this scenario. You played 10000 hands and ran 10bi under ev. By the concept of varianve in the long run, the next infinite hands you play EV= actual profit. But that effectively means you will still be 10bi under EV. Shouldn't you be running at EV if variance evens out?

What I said might not make sense to some of you. But think about it. If someone complains on going on a downswing, you tell them variance evens out in the long run right? As a result, this person might feel he has a higher chance of closing the gap between the green line and the EV line than the chance of widening the gap. But that is not true. Both chances are equal.

Another example, in roulette (ignore the green 0) there's equal chance of hitting black and red. So in the long run EVBlack=50% and EVRed=50%. If the concept of variance is true, wouldn't it be profitable to bet red if 75% of the last 100 results are black? But no. EVBlack for next 100 results=50, not 25.

Hence it seems like the this statement about variance is the likely cause of the gamblers fallacy. Because you expect to run better after you ran bad. There should be a better way to explain variance.
• 76 replies
• Bronze
Joined: 13.07.2011
Yea thats a big misconception, if you are running 25BI below EV for 100k hands, what you have to hope for in the next 100k hands is to run at least at even EV rather than 25BI above EV. You are not entitled to close the gap, you just have to hope it doesnt get bigger.
• Black
Joined: 02.11.2010
you just have % that your winnings = ev winnings more likely the longer you play. If you look at a stretch of hands with assumption that you start with -10BI its obvious in long run you will end up with you ev winnings -10BI you started with.

(not the ones shown in your hud but the actual winrate ev, which is more complex than showdown ev, like running into top of ranges with bluffs, second nuts, hitting boards and creating more/less +ev spots etc)

Each hand starts new stretch and the outcomes of old ones have no influence over any future result...

EV does not care how you've lost the money;d

If you have to hope for something, hope you'll make +ev plays.
• Bronze
Joined: 29.08.2008
i think they want to say,if you have AA and vs 22 with just river coming,and you have 93% chance to win,and opponnent hits 2...so,you lose...and if we count its roughly 13(93%):1(7%) it happens...so,you come again in same situation in next hand...and lose river again...and then next hand you lose AGAIN??so you get 3 suckouts in a row,but you should get ONLY 1 EVERY 14 time,so it would bassiccly means that in next 100 games,it should iron out...or 1000 or 10k hands...

but i hard disagree with that...
• Black
Joined: 02.11.2010
it shouldnt iron out. he got sucked out - tough life. next ~infinite hands he will still get sucked out 1:14 times.

hell, even if he got sucked out bilion times in a row, really "unlucky" guy, he will still get sucked out 1:14 times in next ~infinite hands

but look at the bright side, if you run hot as hell it is not more likely you will "have to" give it back to "variance". There is nothing to give back Each hand, each sessions, thousands of hands - they don't know how much under/above ev you are.
• Bronze
Joined: 29.08.2008
so,you basiclly saying that OUR cards have not real value,as it is opossed to say??so in my example AA with 93% losing is very normal and should happens regulary??so,according to your words,STARS(or any other room)is determining the outcomes as they please,not according to hand strengh???so its possiblle to lose w AA hundred hands in a row and thats OK??

sorry if bit off topic,but i also try to understand VARIANCE according to your words..
• Bronze
Joined: 20.03.2010
your hands have "real value". When you get it in AA vs 22, you have 93% chance to win and thats all about it. Luck has no memory or similar sort of things. Chance of winning AA vs 22 is not affected by outcome of last flip you won/lost. You dont owe luck anything and luck doesnt owe you anything. If you had downswing it has no impact on future run, and so on...

Less you care about these things, more time you have to care about something that matters.
• Bronze
Joined: 28.03.2011
Originally posted by janushr
so,you basiclly saying that OUR cards have not real value,as it is opossed to say??so in my example AA with 93% losing is very normal and should happens regulary??so,according to your words,STARS(or any other room)is determining the outcomes as they please,not according to hand strengh???so its possiblle to lose w AA hundred hands in a row and thats OK??

sorry if bit off topic,but i also try to understand VARIANCE according to your words..
It's possible to lose w AA billion hands in a row. (however slim chances of it hapening are - it's still possible.

Think about this example - (before you proceed, take in mind, that I thought of this while being high). Let's say "place any big number you want" people plays "Rock, paper, scissors" tournament in a Play-Offs style. That means that the guy who wins, has to win all the way to the top and then win the finals.

Can you imagine being that guy? You just win, win, win, and then win again, and some more, and you can't do anything about it, lol.
• Black
Joined: 02.11.2010
no clue how you came to those conclusions after reading my answer.

ev is ev, it doesnt change because you are under or above it. it is expected value... you use it to make decision not to predict future outcomes.
• Bronze
Joined: 25.06.2012
seriously this thread, lol. Why do you guys focus at things you can't change? ev is ev, some people might be luckboxers and run higher than ev in long run and some might run bad, It's like throwing a dice 100 times, some will get 10 sixes and some will get 20. that's just how it is, but fortunately with a big sample like 1000000 it's not that likely a person made 0 sixes is it? what im trying to say is that some people are luckier than ev and some are more unlucky, but MOST people are somewhere in between. So just play good and let variance be variance, thx
• Super Moderator
Super Moderator
Joined: 02.09.2010
Originally posted by tommygecko
So let's say you have never played a poker hand before. For the next infinite hands you play EV= actual profit because variance evens out in the long run.

How about this scenario. You played 10000 hands and ran 10bi under ev. By the concept of varianve in the long run, the next infinite hands you play EV= actual profit. But that effectively means you will still be 10bi under EV. Shouldn't you be running at EV if variance evens out?
Perhaps you are correct in absolute terms, but after playing several hundred thousand hands, that 10 bi is totally insignificant.

The term "expected value" is used many different ways.

I prefer to state the case this way:
"Over a large sample size, everyone will get the same number of each of the 1326 possible starting hands. For each starting hand, each of your opponents can have only 1 of the remaining 1325, 1324 ... hands".

Thus on a 6-handed table, that means that there are 1325x1325x1324x1323x1322x1321.
So at any 6-handed table there are 5 x 10^18 possible combinations of hole cards.
Now we come to the flop.
Let's not. I think that you get the picture.

If you play 12 tables of zoom at 150 hands per hour 10 hours per day 7 days per week all year, you only play 6.5 million hands per year.
At that rate, it would take 100 billion years to play each and every combination of HOLE CARDS ONLY.

There will be long strings of crappy cards, and long strings of good ones, and short strings of each as well.

It is not that it "evens out", but it "is the same for everyone".

So if it is the same for everyone, then the determining factor is your skill level. You must build that up, because it is the only thing at the table you yourself control.

Another example, in roulette (ignore the green 0) there's equal chance of hitting black and red. So in the long run EVBlack=50% and EVRed=50%. If the concept of variance is true, wouldn't it be profitable to bet red if 75% of the last 100 results are black? But no. EVBlack for next 100 results=50, not 25.

Hence it seems like the this statement about variance is the likely cause of the gamblers fallacy. Because you expect to run better after you ran bad. There should be a better way to explain variance.
The idea that "a run of good luck inevitably follows a run of bad luck" is indeed the gambler's fallacy. Especially in poker.
It may be true, but how good and how long matter too.

I am convinced that some "pros" are actually not that good -- just on incredibly long heaters.

The true pros can make money even from garbage hands, by reading the board and knowing their opponents.

Read the quote at the bottom of my sig.

Great post!

Oh -- and if I totally screwed up the math, please somebody post the real numbers.

all the best,
--VS
• Bronze
Joined: 29.08.2008
It is not that it "evens out", but it "is the same for everyone".

So if it is the same for everyone, then the determining factor is your skill level. You must build that up, because it is the only thing at the table you yourself control.

i personnally dont agree that its SAME for everyone....

ok,vorpal,so if i come back to my example w AA vs 22,where we know we have 93% chances,and we suckout..and again and again...so,i show my SKILL by getting into that 93% situation...and i suckout...and again and again...so,where is my SKILL when poker room decide it isnt me who will win the hand at the end???or their RNG who shuffls and deals,what ever....and make it again and again...when will my SKILL come to pay dividends???

and i am sorry.according to my understanding,what you bassiclly say is that outcome is determined by poker room,not our SKILL or hand strenght...and they will decide when you will win or lose...and according to you,its possiblle,but unlikely to happens,some weird example like mine and thats OK??and we all just should trust poker rooms that all is correct,right??
• Bronze
Joined: 18.08.2012
I went to a lecture open day at Oxford Uni's math department and they actually talked about a closely linked concept.

There's actually not much math to it.

So you're playing perfect poker and so is your opponent(s). Over a large enough sample, I don't care what anyone says, you will both be dealt the same hands with very small error margins. Assumption 1.

You get AA in 10 times in a row, pre, (perfect poker), against KK or whatever and lose. Therefore you lose 10 bi's. Assumption 2.

Now here is where people shout and scream 'Probability has no memory', 'All results are mutually exclusive', 'Losing 10 times in a row does not guarantee you'll win the next one'. Well, you're wrong. You're looking at theoretical straight line probability. As in, you suggest that as poker is a 0 sum game, ev starts a fresh every hand. But this is a completely wrong assumption. EV starts FROM the START. From the very first hand. Not from the last hand you played. Otherwise you would be 0 ev +-.

So essentially what I'm saying is, in the long run it does 'Iron out' because probability dictates that it will be off skew on both sides of the equilibrium. Therefore in the short run he receives negative expectations, but in the long run it will be +EV to get those Rockets in
• Bronze
Joined: 18.10.2011
Originally posted by ShadDoneWin
I went to a lecture open day at Oxford Uni's math department and they actually talked about a closely linked concept.

There's actually not much math to it.

So you're playing perfect poker and so is your opponent(s). Over a large enough sample, I don't care what anyone says, you will both be dealt the same hands with very small error margins. Assumption 1.

You get AA in 10 times in a row, pre, (perfect poker), against KK or whatever and lose. Therefore you lose 10 bi's. Assumption 2.

Now here is where people shout and scream 'Probability has no memory', 'All results are mutually exclusive', 'Losing 10 times in a row does not guarantee you'll win the next one'. Well, you're wrong. You're looking at theoretical straight line probability. As in, you suggest that as poker is a 0 sum game, ev starts a fresh every hand. But this is a completely wrong assumption. EV starts FROM the START. From the very first hand. Not from the last hand you played. Otherwise you would be 0 ev +-.

So essentially what I'm saying is, in the long run it does 'Iron out' because probability dictates that it will be off skew on both sides of the equilibrium. Therefore in the short run he receives negative expectations, but in the long run it will be +EV to get those Rockets in
Hey I was able to understand what you typed here but I am a little confused by what you mean here (I bolded it). Can you elaborate?
• Bronze
Joined: 29.08.2008
hey,ShadDoneWin nice to attend oxford,wish you best with it...

what can you say about my thinking,lets not involve rigged theory.just about outcomes that occure and tend to deviate from "what should be standard"???how we can be sure that their RNG or what ever it is,that its dealing properly???we all hear storys about diffrences about LIVE and ONLINE poker,and that its not the same;IE:too many suckouts happening in very short time??lets also leave theory about much more hands and so you remeber only the bad ones,i am more interested into fair and correct enviroment and how to determine thats its fair and correct dealing???

as in my example w AA vs 22,or some others said,we can have "billions" suckouts in a row,and that should be fair??all conclusion that i am drawing from that is that my AA isnt 82% preflop vs 22,rather that number tends to shrink,i even recived some answer from poker room support how every hand have equal chances to win postflop,so,what happens if our both hand have ;IE;50%:50%..or 70%:30%??so,where there SKILL come to equasion??if i push w AA and you call w 22,i also expect to crush your soul,am i wrong??

all this cause i ask this(sorry OP,i really dont troll,i would like to hear his opinion,after all,man is from oxford )is cause this outcomes define VARIANCE...as that guy said,we can lose billion hands in a row and we are simply "UNLUCKY"',or we can win billion in a row and dont care...WHERE SKILL COME TO EQUASION?'how to determine that??

and pls,dont answer if i play million tournies,i will know
• Bronze
Joined: 11.08.2012
Originally posted by ShadDoneWin
I went to a lecture open day at Oxford Uni's math department and they actually talked about a closely linked concept.

There's actually not much math to it.

So you're playing perfect poker and so is your opponent(s). Over a large enough sample, I don't care what anyone says, you will both be dealt the same hands with very small error margins. Assumption 1.

You get AA in 10 times in a row, pre, (perfect poker), against KK or whatever and lose. Therefore you lose 10 bi's. Assumption 2.

Now here is where people shout and scream 'Probability has no memory', 'All results are mutually exclusive', 'Losing 10 times in a row does not guarantee you'll win the next one'. Well, you're wrong. You're looking at theoretical straight line probability. As in, you suggest that as poker is a 0 sum game, ev starts a fresh every hand. But this is a completely wrong assumption. EV starts FROM the START. From the very first hand. Not from the last hand you played. Otherwise you would be 0 ev +-.

So essentially what I'm saying is, in the long run it does 'Iron out' because probability dictates that it will be off skew on both sides of the equilibrium. Therefore in the short run he receives negative expectations, but in the long run it will be +EV to get those Rockets in
I used to think so too, but it can't be true. Otherwise roulette would be profitable.
• Bronze
Joined: 28.01.2012
Originally posted by tommygecko
Originally posted by ShadDoneWin
I went to a lecture open day at Oxford Uni's math department and they actually talked about a closely linked concept.

There's actually not much math to it.

So you're playing perfect poker and so is your opponent(s). Over a large enough sample, I don't care what anyone says, you will both be dealt the same hands with very small error margins. Assumption 1.

You get AA in 10 times in a row, pre, (perfect poker), against KK or whatever and lose. Therefore you lose 10 bi's. Assumption 2.

Now here is where people shout and scream 'Probability has no memory', 'All results are mutually exclusive', 'Losing 10 times in a row does not guarantee you'll win the next one'. Well, you're wrong. You're looking at theoretical straight line probability. As in, you suggest that as poker is a 0 sum game, ev starts a fresh every hand. But this is a completely wrong assumption. EV starts FROM the START. From the very first hand. Not from the last hand you played. Otherwise you would be 0 ev +-.

So essentially what I'm saying is, in the long run it does 'Iron out' because probability dictates that it will be off skew on both sides of the equilibrium. Therefore in the short run he receives negative expectations, but in the long run it will be +EV to get those Rockets in
I used to think so too, but it can't be true. Otherwise roulette would be profitable.
No, because say you put \$5 on red and lose 10x in a row. You are now \$50 below EV as your expected value is 0. (Actually this isn't true because there is a chance it lands on the green number, that's how casinos make profit since the payout odds and the actual odds are different.) but lets say we had a fair roulette wheel from a non profit casino.

In the long run if you kept putting \$5 on red, you would expect things to even out from when you first started playing.

I don't see how this being the case could even make roulette profitable though...
• Coach
Coach
Joined: 09.07.2010
It didn't take that long before rigged theories were drawn to this discussion.

I think most of the problems in thinking comes from the assumption that poker is a 100% skill based game where the better player always wins. Most of us understand that it's not. The skill ensures that we get to those 93% equity situations a lot more than we get to those 17% equities. While bad players tend to find themselves in those 17% equities a lot more.

That's it. The rest is up to variance, luck, rigged rng's, unknown gods, rabbit foots and everything else that is related to randomness.

If you think that "I have lost \$1000 now in this month, so I should/deserve to win \$1000 next month" you are a degenerate gambler. Or at least pretty close to it. That's the thinking of a gambler, not a thinking of a good poker player.

And if it's hard to understand, here is a nice example that helps me to understand it (let's assume that the coin isn't rigged):

If you flip a coin 99 times and they all are heads, what is the propability of heads for the next roll?

Now if you decide to flip a coin 100 times, what is the propablity of them all being heads?

For the 100th flip the chance is 50/50. But for the whole 100 flip series it's pretty low. It shows that luck has no memory, but we can think beforehand what is the propability of those unlikely streaks.

Now lets use the coin to include poker skill.

We play a little game with a coin flip. Every time it's heads, you pay me \$2. Every time it's tails, I pay you \$1.

For a single flip, what is the chance of it being heads (so I win)? If we make 99 flips and you win them all (again the coin is fair), what is the chance for 100th roll to be heads?

But if we calculate before any flips what are my odds of being a winner after 100 flips, we can see that my expected value is positive. But still, I can't be sure that will be a winner after those 100 flips.

Poker isn't chess. It's all about flipping and gambling, where good player can swing the odds to his favor. And hope he isn't an unlucky bastard.
• Bronze
Joined: 11.08.2012
Originally posted by metza
Originally posted by tommygecko
Originally posted by ShadDoneWin
I went to a lecture open day at Oxford Uni's math department and they actually talked about a closely linked concept.

There's actually not much math to it.

So you're playing perfect poker and so is your opponent(s). Over a large enough sample, I don't care what anyone says, you will both be dealt the same hands with very small error margins. Assumption 1.

You get AA in 10 times in a row, pre, (perfect poker), against KK or whatever and lose. Therefore you lose 10 bi's. Assumption 2.

Now here is where people shout and scream 'Probability has no memory', 'All results are mutually exclusive', 'Losing 10 times in a row does not guarantee you'll win the next one'. Well, you're wrong. You're looking at theoretical straight line probability. As in, you suggest that as poker is a 0 sum game, ev starts a fresh every hand. But this is a completely wrong assumption. EV starts FROM the START. From the very first hand. Not from the last hand you played. Otherwise you would be 0 ev +-.

So essentially what I'm saying is, in the long run it does 'Iron out' because probability dictates that it will be off skew on both sides of the equilibrium. Therefore in the short run he receives negative expectations, but in the long run it will be +EV to get those Rockets in
I used to think so too, but it can't be true. Otherwise roulette would be profitable.
No, because say you put \$5 on red and lose 10x in a row. You are now \$50 below EV as your expected value is 0. (Actually this isn't true because there is a chance it lands on the green number, that's how casinos make profit since the payout odds and the actual odds are different.) but lets say we had a fair roulette wheel from a non profit casino.

In the long run if you kept putting \$5 on red, you would expect things to even out from when you first started playing.

I don't see how this being the case could even make roulette profitable though...
No. Of course if there are no previous sample stats on the roulette wheel EV=0 if you bet red. But what if you watched your friend bet 100 times on red and lost 70 times. If EV starts FROM the START as he said, it would be profitable for YOU to bet on red the next 100 times because based on the EV at the START, EV(red next 100)= 70. Which is obviously not true in reality.
• Bronze
Joined: 28.01.2012
Yeah it isn't gonna be like that in reality, but only because the sample sizes you gave are far too small.

I don't actually know enough in depth stuff about EV so I am not 100% sold that EV starts from the start, but I am leaning towards it does.

If your friend lost 70 times out of 100 and we assume EV started from the start, if you then played 99,999,930 times, to get 100,000,000 between you, then you'd expect there to be 50,000,000 reds and 50,000,000 blacks as outcomes. So I guess it would be very very very slightly more profitable to play red (50,000,000:49,999,930 odds on red), but not in a utilizable way, given limitations of human lifespan nobody can, or would want to, play millions of games of roulette.

While cards have no memory, probabilities inevitably even out over larger samples.