Poker Gods or Fallacy?

[Nichomacheo]

X-Post from Probability Forum.

Say I lose five hands AA vs QQ. My equity on each hand is, say, 0.18. I should have won, on average, $90 after five times, if the pot is $100 each time, right?

Say, instead, I lose all five times. Now, the Poker Gods "owe" me 0.90 equity.

On the sixth hand, I get it all in, but this time I only have 0.10 equity (I'm heavily dominated). Is it fair to say that if I win, its just the odds swinging back in my direction, since I was "owed" 0.90 equity?

I can't wrap my head around whether this is accurate or not. I appreciate any comments you guys have to offer.

Nichomacheo

[PantsOnFire]

Well that's an interesting take on things. I suppose in a way if you lose five times in a row with AA over QQ, then you have some "luck credits" in the bank for the future. However, there is no timeline for them to be paid back so it could happen on the next hand or next month or next year.

In other words, the Poker Gods will eventually pay you back what they "owe" you but it will be on their own terms. They may even take a bit more from you before they start their payback plan, just to see if you lose your cool and make bad plays which negate some of the "owed" credits.

[Nichomacheo]

Yes. Someone in the other forum thought I was saying that I was more likely to get it on the next hand, but thats not what I was saying.

But, this still seems wrong to me. WTF is a "luck credit"? Luck has no memory, right? I seem to be contradicting myself, but thats the problem...

[PantsOnFire]

[ QUOTE ]
Yes. Someone in the other forum thought I was saying that I was more likely to get it on the next hand, but thats not what I was saying.

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Well you are definitely not more likely to get it in the next hand. If the next hand you again get AA vs. QQ you will win %80 of the time, regardless of your last hand or your last one thousand hands. This is standard statistical knowledge and not up for debate so that guy on the other forum is out to lunch.


[ QUOTE ]
But, this still seems wrong to me. WTF is a "luck credit"? Luck has no memory, right? I seem to be contradicting myself, but thats the problem...

[/ QUOTE ]
Let's take a break even player. He makes exactly the same number and kinds of mistakes as his opponents. We will give him a bankroll and send him out playing. Now, we will graph his bankroll at the top of every hour for say a year. We will assume his bankroll compared to the limits he plays is very large so he never dips to zero. Now, after a year, we will conintue to plot his bankroll every hour until he lands on exactly what his starting bankroll was. That might happen in a month a year or 20 years.

But when it does happen, you stop graphing and look at the chart. It will likely resemble something like the stock market except the start amount and end amount are the same. In that rollercoaster, there are snapshots you can pick where some very "bad luck" occured and the bankroll dipped fast and some other parts of very "good luck" where it increased rapidly. Since this guy played the same break even style over the life of this graph, the peaks and valleys can only be explained by "luck". In mathematical terms, "luck" here means statisical variance. You started at the same point as you ended with various fluctuations in between.

I don't what the hell I just said here so I expect some questions back.

[Nichomacheo]

The problem is this...

Pick 10,000 coin flips.

Say the first 20 I flip heads. Over the 10,000 flips I should break even. I cant say that I'm more likely to flip more tails now so that it averages out. Over the next 9980 flips, I'm still expected to break even, which means that at the end of 10,000 flips, I'm expected to be down 20.

This is a contradiction to what I said before, but I think its correct. Meaning, there is no "luck credit". At any given point, thats what you are expected to be at at N hands from now.

[Nichomacheo]

[ QUOTE ]
There is a sense in which short term statistical anomalies tend to cancel each other out over the long term, but it doesn't involve the current trial being influenced in any way by previous trials. For example the more times you flip a fairly weighted coin, the closer the percentage of heads will tend to approach 50%. But each individual flip is still equally likely to come up heads or tails, regardless of whether heads or tails is currently leading the tally. In a sequence of 10 coinflips the percentage of heads may or may not be between 40% - 60%, it wouldn't be very surprising if it was outside that interval. Its less likely that heads percentage would be outside the 40% - 60% interval after 100 coinflips. And its highly unlikely that heads percentage would be outside that interval after 1000 coinflips (a table of standard deviation statistics would turn those vague phrases into actual probabilities). So that's the sense in which the percentages tend to converge. You can't use that fact in any way to predict the result of an individual coinflip though. Do a search on "law of large numbers" and also do a search on "gambler's fallacy".

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You wouldnt know it from this post, but I'm actually very good with statistics.

It's just mindboggling to me that, if you have 10,000 coin flips, you know the result should be about even. But, if you pick a starting point within that 10,000, say, like 4328 which has the talley at +32 heads or whatever, that you cant say that it will balance out.

Thats my problem. I'm still wrestling with it.

[DWarrior]

[ QUOTE ]
The problem is this...

Pick 10,000 coin flips.

Say the first 20 I flip heads. Over the 10,000 flips I should break even. I cant say that I'm more likely to flip more tails now so that it averages out. Over the next 9980 flips, I'm still expected to break even, which means that at the end of 10,000 flips, I'm expected to be down 20.

This is a contradiction to what I said before, but I think its correct. Meaning, there is no "luck credit". At any given point, thats what you are expected to be at at N hands from now.

[/ QUOTE ]

It's pretty simple to compute a confidence interval of the normal # of wins after 10k flips. I'm too lazy to do it, but I'm pretty sure the actual probability of you winning exactly 5k flips is pretty low. You'll most likely end up either over or under.

[SplawnDarts]

[ QUOTE ]
Yes. Someone in the other forum thought I was saying that I was more likely to get it on the next hand, but thats not what I was saying.

But, this still seems wrong to me. WTF is a "luck credit"? Luck has no memory, right? I seem to be contradicting myself, but thats the problem...

[/ QUOTE ]

You're correct - luck has no memory. Let's say you're flipping a fair coin for $1 each flip. This is obviously 0EV.

Now, let's say on the first 10 flips, you're unlucky loose $10. Now, all future flips are still 0EV, so if you do an additional 1000 flips, your expectation is that you will still be down $10. Same if you do 1 million flips. No number of flips will catch you up expectation-wise.

The basic fact is that luck does NOT even out. If your luck has been bad, there is no mechanism that makes up for it in the future - what's lost is lost, and you're just as likely to have even more bad luck in the future as you are to have good luck.

That may sound depressing, but it's also true the other drirection. IF you get lucky, there's no corresponding bad luck spell coming to get you in the future. If you were up $10 after the first 10 flips, and then flipped 1 million more, you would still expect to be up an average of $10 at the end.

[phish]

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But, this still seems wrong to me. WTF is a "luck credit"? Luck has no memory, right? I seem to be contradicting myself, but thats the problem...

[/ QUOTE ]

Actually, there's a website you can go to to see what your current luck credit is. I'll try to dig up the link and post it.

Last time I checked mine, I was overdrawn on the poker luck, but had tons remaining in my chicks account.

[mvdgaag]

Lol [img]/images/graemlins/smile.gif[/img]

I've used up the chicks, but traded some luck for some more.