Do you believe in Luck?

[Beth]

I dug through my notes and tallied up post all in results:

total all ins :241
total expected wins :178
total wins:189

I think that my above info is still too small a sample size and also a result of my being very very careful of the types of hands I go all in with.

Thanks. That's very helpful information. Do you know how the expected wins were computed?

 

[Beth]

I get the same result.

Jay

Many thanks. That gives me more confidence in my result.

 

[BravesFan]

Thanks. That's very helpful information. Do you know how the expected wins were computed?

i didn't use your fancy math stuff really. I just know the odds. Like if I had a TT with a flop of KT5 rainbow, and my opponent had JJ at the all in, I know he has 2 cards to take the lead plus plus the backdoor straight draw which gives me the edge.

Conversely If I call an all in with AhAc against a JT diamonds and face a flop of JKQ also 2 diamonds I know that though I'm leading at the moment my opponent actually has 9 flush outs 6 straight outs , one 3 of a kind out... he has me in the odds by over 68%.... so even though I'm ahead at the moment of all in as far as if the hand ended that moment I win, with 2 cards to come, I am a dog.

 

[Beth]

i didn't use your fancy math stuff really. I just know the odds. Like if I had a TT with a flop of KT5 rainbow, and my opponent had JJ at the all in, I know he has 2 cards to take the lead plus plus the backdoor straight draw which gives me the edge.

Conversely If I call an all in with AhAc against a JT diamonds and face a flop of JKQ also 2 diamonds I know that though I'm leading at the moment my opponent actually has 9 flush outs 6 straight outs , one 3 of a kind out... he has me in the odds by over 68%.... so even though I'm ahead at the moment of all in as far as if the hand ended that moment I win, with 2 cards to come, I am a dog.

Okay, you're estimating the probability of each hand. That's reasonable. How did you compute the expectation of 178 out of the 241 all-ins? That equates to a roughly 3 out 4 prob. of winning on average (74%). You actually won 78% of them. That's not too far from what would be expected.

 

[BravesFan]

I just wrote down what happened everytime i saw a flop and wasnt in the blind) or had activity to the turn (I wrote down my hands played out of pocket in other words, if I bet or called a bet it went down in the book) I kept it in my lap for all my play for a good while. i wrote down what happened and what I was up against in showdowns(or all ins) It ended up being such a PITA I quit doing it. But I had enough info to go back later and analyze my play and look for leaks.

 

[jt512]

I just wrote down what happened everytime i saw a flop and wasnt in the blind) or had activity to the turn (I wrote down my hands played out of pocket in other words, if I bet or called a bet it went down in the book) I kept it in my lap for all my play for a good while. i wrote down what happened and what I was up against in showdowns(or all ins) It ended up being such a PITA I quit doing it. But I had enough info to go back later and analyze my play and look for leaks.

You still haven't explained how you calculated your expected number of winning hands. I was curious about it also.

Not really related, but intuitively (I'm not a poker player), I would think that if your expected win was 74% of your all-in hands, then you weren't going all-in often enough, and are missing out on all-in opportunities with smaller edges. You'd win a smaller percentage of them, but you'd more than make up for that in absolute number.

Jay

 

[BravesFan]

You still haven't explained how you calculated your expected number of winning hands. I was curious about it also.

Not really related, but intuitively (I'm not a poker player), I would think that if your expected win was 74% of your all-in hands, then you weren't going all-in often enough, and are missing out on all-in opportunities with smaller edges. You'd win a smaller percentage of them, but you'd more than make up for that in absolute number.

Jay

i think y'all are misreading my data, My expected number of winning hands were based on the amount of hands I had the odds in my favor going in.(I had no % of hands I expected to win via all ins before I played in other words) Yes, it was a lot, because I play tight and I play smart and I try to always have the best hand. I came from playing limit hold em and as such was a very math oriented player. When limit got killed off, I switched to no-limit and soon discovered the influx of gamblers, wild players and people who apparently thought every hand was like the WSOP. I discovered that playing tight was best because they get so caught up in creating huge pots and "trapping" that they hardly notice when you havn't called a raised blind for 2 button rounds....

 

[jt512]

i think y'all are misreading my data, My expected number of winning hands were based on the amount of hands I had the odds in my favor going in.

If that's what you mean by "expected wins," then I didn't misread your data so much as you made a meaningless calculation. The correct way to calculate the expected number of winning hands is to sum the probabilities of winning each hand.

Jay

 

[rcfieldz]

Luck is Irish isn't it?

If I didn't have bad luck...

 

[BravesFan]

If that's what you mean by "expected wins," then I didn't misread your data so much as you made a meaningless calculation. The correct way to calculate the expected number of winning hands is to sum the probabilities of winning each hand.

Jay

Why is my calculation meaningless? look, I didn't do this math to solve some sort of luck problem as the OP. I did it to detect leaks in my game. So every hand I was involved in got written down. If there was an all in it got written down. I could easily go back and go "well, I had him 60% to 40% and got outdrawn, so that was a good play. Or I was a 80%-20% dog and got lucky," or all the alternatives. This was for the purpose of analyzing my game play. So my calculations were correct for what I needed them for. If I went all in with the best hand , then any winning result was considered an expected win. If I went all in with the worst hand (or behind due to the expected odds of them outdrawing me) then it was considered an expected losing hand.

 

[jt512]

Why is my calculation meaningless? look, I didn't do this math to solve some sort of luck problem as the OP. I did it to detect leaks in my game. So every hand I was involved in got written down. If there was an all in it got written down. I could easily go back and go "well, I had him 60% to 40% and got outdrawn, so that was a good play. Or I was a 80%-20% dog and got lucky," or all the alternatives. This was for the purpose of analyzing my game play. So my calculations were correct for what I needed them for. If I went all in with the best hand , then any winning result was considered an expected win. If I went all in with the worst hand (or behind due to the expected odds of them outdrawing me) then it was considered an expected losing hand.

And what possible use could be made of the number of "expected" winning hands being defined that way?

Jay

 

[BravesFan]

I think you are missing what I'm saying because you aren't a poker player.

Since one has no control of the cards yet to be drawn, one can only determine the quality of one's play in all in situations as determined by the odds at the point of the all in and call of said all in. If you have the best hand before the remaining cards are drawn, that is an expected win. (best hand being determined by the odds of one hand winning relative to ther other(or others). I will explain further:

If player A goes all in after the flop with AcAh and a flop of AsKdTc versus player B's KcKh the set of kings is in serious trouble as they are chasing the remaining K to win (roughly 1 in 45 chance of catching) or two running cards to tie with the straight.
If I am player A and I am recording my hands played to look for weak parts of my game (known as leaks) I would write it down as an expected win because I had the odds in my favor for winning the hand before the remaining cards were drawn. Now, if Player B gets very lucky and catches that lone remaining King , he would win the hand. But I would be able to review this later and think "well, I got my money in good and just got outdrawn so that was a quality play."

The math dictated I SHOULD win the hand 44 out of 45 times I play it roughly, but that time I didn't. Hence an expected win turns into a loss. Just as if I were player B, an expected loss turned into a win. Remember, poker is played with incomplete information, and though there may have been (at a 10 seat table) 16 cards in the discard pile, being that none of these cards have been seen by anyone, they are included when calculating the implied odds of drawing needed cards.(actually 18 cuz of the burn cards)

 

[Beth]

Jay, I really really appreciate the check on my computation. That means my program is properly computing the formula. Thank you again.

I had lunch with my best gf today. She's plays about once a week and says she'll start collecting data on her all-in show downs. That will provide a check on my formula being a reasonable one.

Is there any interest in seeing those additional results and how they compare?

And what possible use could be made of the number of "expected" winning hands being defined that way?

Jay

Actually, I don't think it's a bad way to approximate it. It's not very precise, but it's not unreasonable either. It was suitable for his original purposes, so I give it a thumbs up!

I like to encourage people to collect and analyze data. You don't have to be a professional statistician to make good use of data like that.

I also appreciate the ability to make even a rough comparison to someone else's results. This data tells me that compared to another person's set of show down hands, his do seem to be doing rather poorly.

Using that same method, I counted 19 hands out of the 29 that the probability of a win or tie was greater than 50%. That would make his expected number of wins 19/29 = 65.5% His actual number of wins was 6/29 = 20.7%. This is pretty far apart. Which is consistent with the low probability I'm computing.

LogicFail had 178 hands out of 241 with prob. greater than 50%. 178/241 = 73.9%. He actually won 189 out of those 241 hands. 189/241 = 77.6%. This is reasonably close considering the rough estimate we're using.

 

[BravesFan]

Thanx Beth!!! I wasn't using it for extreme stat analysis as stated, it was there to find out if I was :

a) playing too many hands
b) not enough hands
c)too strong of a bettor , or weak...etc

It was there for me to find my strengths and weaknesses. On that level it worked great! ( i discovered I was probably playing too tight and waiting too long too re-raise anticipating too much payoff when gambling type players were in the pot).

As far as it being statistically useful..... I guess it would be if someone wanted to go back and do the work on all my data. But all I needed to know was rough odds and whether or not I was ahead or behind when certain actions took place and how I reacted to said actions.

 

[jt512]

I had lunch with my best gf today. She's plays about once a week and says she'll start collecting data on her all-in show downs. That will provide a check on my formula being a reasonable one.

Is there any interest in seeing those additional results and how they compare?

Yes. Ask her to carefully record the suits as well as the denominations of the cards involved.

Using that same method [LogicFail's method of counting "expected" wins], I counted 19 hands out of the 29 that the probability of a win or tie was greater than 50%. That would make his expected number of wins 19/29 = 65.5%.

And that number is incorrect. His correct number of expected wins is 16.8, or 16.8/29 = 57.9%.

LogicFail had 178 hands out of 241 with prob. greater than 50%. 178/241 = 73.9%. He actually won 189 out of those 241 hands. 189/241 = 77.6%. This is reasonably close considering the rough estimate we're using.

Close to what? Nonsense? There is no reason to think that the actual number of hands he won should be close to the number of hands that he had a probability greater than .5 of winning. His true expected number of wins could have been as high as 209 or as low as 90, so his calculation does not even indicate whether he's done better or worse than expectation.

And as far as plugging leaks goes, who cares about actual results or probabilities of winning per se? What matters is the expected value of your decisions. There are lots of times in poker when you should be in a hand where your probability of winning is less than .5, so why he's even dichotomizing his analysis based on that is beyond me. And if he's habitually missing those opportunities, he's not leaking, he's hemorrhaging.

Jay

 

[BravesFan]

You don't understand poker sir..... The hands held at the point of all in mean very much as far as the expectation of winning goes... sorry.... but it really does.

 

[Beth]

Yes. Ask her to carefully record the suits as well as the denominations of the cards involved.

Okay. If she does, I'll start a new thread though.

And that number is incorrect. His correct number of expected wins is 16.8, or 16.8/29 = 57.9%.

I wouldn't call it incorrect, but simply a less precise estimate of the expectation. It's quite reasonable to sacrifice precision for convenience in informal situations like this. I computed it because I wanted to compare my hubby's results to LogicFail's, and I needed to use the same formulation to make a comparison.

Close to what?

LogicFail's actual result was close to his expected result.

Nonsense? There is no reason to think that the actual number of hands he won should be close to the number of hands that he had a probability greater than .5 of winning.

While it isn't a very precise estimate, I don't think it will introduce bias so the accuracy should be unaffected. It might be interesting to run a simulation and see how it performs. Or it could be formalized and the potential bias computed. Hmmm...that might be an interesting exercise.

At any rate, I'm not willing to dismiss the results preemptively. Statistical precision and formality are not always required for people to make good use of data. As I said, I generally like to encourage people to collect data and analyze it in order to make improvements. But then, I have a long background of working in quality improvement. A little data can go a long way towards helping people make improvements in whatever they are doing.

My experience in applying statistical quality improvement techniques in manufacturing situations was that the simpler the data collection scheme, the more likely the data was to actually be collected correctly. The simpler the analysis used, the more likely the result was to be acted upon.

Complex and precise data collection and analysis may be necessary for scientific papers, but it isn't required for effective qualify improvement. Very simple techniques, as LogicFail used here, were often the most powerful for that situation because they were more likely to be used by the general population.

His true expected number of wins could have been as high as 209 or as low as 90, so his calculation does not even indicate whether he's done better or worse than expectation.

I'm not sure how you are computing the bounds of 209 and 90 for the expected value in this situation. Could you explain?

 

[jt512]

I wouldn't call it incorrect, but simply a less precise estimate of the expectation.

Well, if you can prove that the expectation of his measure equals the expected number of hands won, then you're right, and I'll believe you. But I think it's measuring something different, so I'd have to see the proof.

I'm not sure how you are computing the bounds of 209 and 90 for the expected value in this situation. Could you explain?

Sure. He had 178 hands where P(win)=P(A)>.5, and 63 hand where P(win)=P(B)<.5. The greatest expectation would be if P(A)=1 for all 178 hands and P(B) were infinitesimally less than .5 for all 63 hands. Then his expectation, rounded to the nearest whole hand, would have been (178)(1)+floor((63)(.5)) = 178+31 = 209.

The least expectation would be if P(A) were infinitesimally greater than .5 for all 178 hands, and P(B)=0 for all 63 hands. Then the greatest lower bound of his expectation would have been (178)(.5)+(63)(0)=89. Since his expectation must be greater than 89, I called it 90, although strictly speaking it could have been less, say, 89.1.

Jay

 

[jt512]

You don't understand poker sir..... The hands held at the point of all in mean very much as far as the expectation of winning goes... sorry.... but it really does.

Obviously it does. Try actually comprehending my post.

Jay

 

[Beth]

Well, if you can prove that the expectation of his measure equals the expected number of hands won, then you're right, and I'll believe you. But I think it's measuring something different, so I'd have to see the proof.

If I get motivated enough to do that, I'll let you know. Regardless of which way the outcome works out.

Sure. He had 178 hands where P(win)=P(A)>.5, and 63 hand where P(win)=P(B)<.5. The greatest expectation would be if P(A)=1 for all 178 hands and P(B) were infinitesimally less than .5 for all 63 hands. Then his expectation, rounded to the nearest whole hand, would have been (178)(1)+floor((63)(.5)) = 178+31 = 209.

The least expectation would be if P(A) were infinitesimally greater than .5 for all 178 hands, and P(B)=0 for all 63 hands. Then the greatest lower bound of his expectation would have been (178)(.5)+(63)(0)=89. Since his expectation must be greater than 89, I called it 90, although strictly speaking it could have been less, say, 89.1.

Jay

Thanks. That makes sense.

Beth