Do you believe in Luck?

[Ilooklike ACrowley]

If you are simply trying to calculate how "unlucky" your husband is then you do not need to follow the rules of poker. But you do need to know what cards are out of play. For example in the AK v 37.
On the face of it that is a bad beat pure and simple. That's poker.
However if you were able to see the folded hands... and lets assume [as it says the game was online] that it is an eight handed table.
Player 1. Your Hubby is Big Blind with AK
Player 2. Joe has K2 - UTG - Folds
Player 3. Bill has A6 - Folds
Player 4. Mary has K9 - Folds
Player 5. Has the 37 - [low stacked] shoves all in
Player 6. Fred has K10 - folds
Player 7. Lyn has A4 - folds
Player 8. Carlos has A5 - folds

Your husband calls the all in.
He is a 94% dog in that hand.


Now that's me being vicious and setting it up like that.
However using the same method but with random cards selected by the Poker Calculator [I'm using The Hendon Mob Poker Calculator to do this, but I'm sure it's the same as the Cardplayer one.]

I got this scenario:

Player 1. Your Hubby AK
Player 2. Joe has A8
Player 3. Bill has 9 10
Player 4. Mary has 43
Player 5. Has the 37
Player 6. Fred has 46
Player 7. Lyn has AK
Player 8. Carlos has Q8

In that situation your husband is 12% to win and 37 is 10% to win.

The poker calculator only goes up to 8 players but you can see why I say it's important how many players are at the table. And why your calculations will be flawed unless you take into account all the cards. The probability that poker players deal with by necessity has to rule out of the entire deck. Hence a player knows his outs.

Now I then ran ten simulations with an eight handed game. Giving your husband AK and random hands to other players as selected by the computer.

AK percentage chance of winning were:

1 - 12%
2 - 7%
3 - 21%
4 - 3%
5 - 11%
6 - 18%
7 - 26%
8 - 16%
9 - 16%
10 - 21%

That means on average in an eight handed game AK is expected to win 15% of the time.

Same routine but this time with 5 players.

1 - 45%
2 - 33%
3 - 24%
4 - 28%
5 - 42%
6 - 29%
7 - 30%
8 - 29%
9 - 15%
10 - 28%

That means on average in a five handed game AK is expected to win 30% of the time.

Now of course you begin to see why it all makes a difference - although of course my sample is too small I dare say it's a logical assumption to make that the more cards dealt [to players] the smaller the chances are of AK being the best hand by the end of play.

 

[Beth]

But you do need to know what cards are out of play.

Why? If they are unknown at the time of the bet, why should they be included in the computation of the probability of winning? I'm not following your logic here for including them to compute the probability.

Including the cards that all players were dealt at the beginning as part of the computation doesn't seem any more appropriate to me than including the center cards that are dealt after the all-in was called and the players cards are face up.

Now of course you begin to see why it all makes a difference - although of course my sample is too small I dare say it's a logical assumption to make that the more cards dealt [to players] the smaller the chances are of AK being the best hand by the end of play.

I'm sorry, but I'm still not following you. I follow why what other cards are being held can affect the probabilities, that's not an issue. But after most of those people have folded and while their cards are still unknown, why should those cards and players be included in the computations for the probability of win/loss? After all, once players have folded, their probability of winning becomes zero.

Also, how does the analysis you are describing demonstrate only luck and remove skill from the situation? It seems to me that at the point you are suggesting for the win/loss analysis, skill is still a very important factor because it's not the best hand among the ones dealt that wins, it's the best hand among the ones that played to the end that wins. Examining the data in the way you are suggesting doesn't tell us about luck, because skill is very important in deciding which hands to play and which to fold.

 

[Sir Corvus]

Bah Luck is just a word for being that fortunate, or unfortunate, statistic. Coincidence and all that. Chance.

Then again, I STILL knock on wood when appropriate. WHY DO I DO THIS?!?! HAHAH

 

[Ilooklike ACrowley]

I'm seriously beginning to wonder if you are winding me up here.

The cards that have been dealt are out of play, but obviously effect probability - as if all the Aces and Kings have been dealt, as in my extreme example, then your husband's odds of winning the hand have changed dramatically.

Because in the game we cannot know what hands have been folded we have to work with imperfect information... which is how you are working out your odds of probability. But if you could see which cards had been played... in other words knowing which cards were still in the remaining 36 then you could work with exact information. Say it was AK against 33 a typical race. But if all the Aces and kings have been dealt the AK can only hit a straight or a flush to win or hope the board pairs with higher cards than the threes. Without knowing the cards that have been folded and / or burned you are getting an inexact picture of the "luck" involved. As the facts are there were no aces or kings left in the deck. Of course you could argue that that in itself is luck... and I think that's probably your approach, and why you can't understand the point I'm making.

I don't think I can add any more to the debate, and wish you "Luck" with it Hopefully Brian will hit a hot streak and confound the odds again.

What I would recommend - yet again - is to go to 2plus2 forums... post there and you will get the answers I think you are looking for.

 

[Beth]

I'm seriously beginning to wonder if you are winding me up here.

No, sorry, I'm just not getting why you think this approach will lead to a better evaluation of the 'luck' he is having.

The cards that have been dealt are out of play, but obviously effect probability - as if all the Aces and Kings have been dealt, as in my extreme example, then your husband's odds of winning the hand have changed dramatically.

This only changes the probability computation if you have that knowledge available. By the same token, once the deck has been shuffled and cut, the cards are in a particular sequence. They can't change and the outcome is set as soon as the call is made. But it makes no sense to compute the probability using that knowledge of the remaining center cards because that knowledge wasn't available to the player at that point in time.

Because in the game we cannot know what hands have been folded we have to work with imperfect information... which is how you are working out your odds of probability. But if you could see which cards had been played...

Correct. And if you could see which cards remained to be played in the center, we wouldn't have to work out any probability computation, but that won't tell us anything about what we are trying to measure.

in other words knowing which cards were still in the remaining 36 then you could work with exact information. Say it was AK against 33 a typical race. But if all the Aces and kings have been dealt the AK can only hit a straight or a flush to win or hope the board pairs with higher cards than the threes.

Yes. I understand how this works. That's not the issue. The issue is whether or not it's appropriate to include such information in the probability computation.

Without knowing the cards that have been folded and / or burned you are getting an inexact picture of the "luck" involved.

This I don't agree with. I just just as easily say that without knowing what center cards are coming up, I am getting an inexact picture of the 'luck' involved. The idea is to determine the probability of the different possible outcomes at a particular point in time such that the relative skill of the different players cannot affect the outcome. Using information not available at that point in time, such as folded cards or the center cards that haven't been played doesn't seem kosher in terms of computing the probability.

As the facts are there were no aces or kings left in the deck. Of course you could argue that that in itself is luck... and I think that's probably your approach, and why you can't understand the point I'm making.

Yes, I would consider that just as much a part of the 'luck' we are trying to measure as the sequence of the remaining cards in the deck. I'm trying to understand why you do not feel that way.

I don't think I can add any more to the debate, and wish you "Luck" with it Hopefully Brian will hit a hot streak and confound the odds again.

Thanks for your good wishes and I appreciate your taking the time to make suggestions and explain why you think your approach would be better.

 

[Beth]

I have more data to report. There are 6 more all-in hands added to our database, 2 wins and 4 losses.

Data for the first 21 hands is in Post 245.

Game 22: AT against K8 after a flop of A8T. His probability of a win was 90.1%. He won.

Game 23: A9 against 33 after a flop of A83. His probability of a win was 1.92%. He lost.

Game 24: AJ against 36 preflop. His probability of a win was 64.64%, there was a 0.41% probability of a tie. He lost. The center cards were 24Tj5.

Game 25: AT against 57 preflop. His probability of a win was 63.4%, there was a 0.35% probability of a tie. He lost. The center cards were 34689.

Game 27: K2 suited against 38 preflop. His probability of a win was 61.75%, there was a 0.74% probability of a tie. He lost. The center cards were 336Q3.

Game 28: KQ against AJ and KT after a flop of 9TJ. His probability of a win was 82.5%, there was a 12.96% probability of a tie. He won. The turn was a 4 and the river was a K.


Because the complexity of the exact prob. computation goes up exponentially as we add more data, I have not yet computed it exactly. As an upper bound on the probability of winning five or fewer hands out of 27 all-ins I can compute the binomial probability of getting 5 or fewer hands out of 27 assuming a probability of winning equal to .5. His average probability of a win or tie is actually .583, so using p = .5 will produce a conservative estimate. I've computed both probabilities. Using p=.583 produces a more accurate estimate, but may not be conservative.

P(X<=5|p=.5) = 0.000757.

P(X<=5|p=.583) = 0.000028.​

It has occurred to me that the probabilities of winning/losing that Meg has been using may be subject to a systematic error, namely, a tacit assumption that the cards that remain undealt after a player has gone all-in and been called are a random sample of the cards that remain unseen at that point in the hand; that, is a full deck minus the player's cards, the callers' cards, and the cards on the board. In a heads-up game this assumption is true. However, in a multi-way game, it may not be—cards that have been folded by other players, would be, I think, at least weakly predictive of the composition of the remaining deck. Failing to take this into account could, then, in principle, systematically bias the calculation of the win/loss probabilities. However, I don't know how significant this error is, nor do I think we can correct for it, except, possibly by using a sophisticated poker simulator.

Jay

I've looked at that in more detail now. The distribution of cards in the center does not vary significantly from what would be expected, so this does not appear to be a factor.

 

[BravesFan]

See, you can't judge his luck based on making bad calls or all ins. I would call AJ and AT marginal hands to call all ins with pre flop. It's an awful risk that one is beaten. This makes me suspect your hubby is just not a very good player and/or takes too many risks. This will skew results.

See what I mean? true the post all in results are luck based. But putting oneself into said situation is skill based.It's the debate of what you have versus your opponent. Sometimes you fold winning hands. But a good player can laydown a monster because they know they are beaten. A poor player will push said losing hand to the end and go broke with it... Regardless of what cards may come, it's the decisions made by good players that separate them from bad and why we see so many familiar faces at final tables.

 

[fishtumor]

No I don't because how can luck be measured.

 

[jt512]

No I don't because how can luck be measured.

Read the thread.

 

[Beth]

I have two more all in show downs to add to the database.

KQ against AQ preflop. The probability of losing was 0.7383. He won.
KK against QT after a flop of T84. The probability of losing was 0.2020. He lost.

 

[Beth]

I have two more all in show downs to add to the database.

KQ against AQ preflop. The probability of losing was 0.7383. He won.
KK against QT after a flop of T84. The probability of losing was 0.2020. He lost.

I computed the exact probability of winning six or fewer games out of this set of 29 as 0.00000127.That's just barely above a 1 in a million probability.

We are mystified as to why/how this is happening. If anyone cares to check my probability computation to verify it, that is sincerely appreciated. A binomial approximation using the average prob. of winning or tie (.57935) is 0.000048716. This is an upper limit on the probability, which means it is still a weird result.

 

[jt512]

I computed the exact probability of winning six or fewer games out of this set of 29 as 0.00000127.That's just barely above a 1 in a million probability.

We are mystified as to why/how this is happening. If anyone cares to check my probability computation to verify it, that is sincerely appreciated. A binomial approximation using the average prob. of winning or tie (.57935) is 0.000048716. This is an upper limit on the probability, which means it is still a weird result.

Some of your data are erroneous.

(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)
Hand|Player's|Opponent's|Player's|Your|My|My|My
#|Hand|Hand|Outcome|P(Loss)|P(Win)|P(Tie)|P(Loss)
19|T4|T5|Lost|.1091|.2228|.4436|.3336
21|AT|K7|Lost|.9318|.6433|.0032|.3535

Columns 1–5 are your data from this post. Columns 6 and 7 are the results of my entering your reported hands in the online poker calculator you said you use. Since you did not indicate suit information, I assumed that all four cards were of different suits. Column 8 is 1 minus the sum of column 6 and column 7.

Scanning your data, those two errors jumped out at me. There may be other errors.

As I said in a much earlier post, it is much more likely that your husband's apparent bad luck is due to erroneous data than to supernatural forces.

Jay

 

[BravesFan]

Your sample size isn't big enough yet Beth to be useful. He could deviate from the mean for 2 years, then have a monster run of cards that pulls him even....

Or, as I said, he puts himself in the position too often due to poor choices. I noticed above that there were several all in hands he played that I wouldn't have played, due to the odds he was ,AT BEST a coin flip. Most of the time (depending on situation and stack size) one doesn't want to be going all in pre flop ,with a hand that isn't AT WORST a coin flip. So AT, KQ, AJ..... those are marginal all in hands IMO.

 

[Beth]

Scanning your data, those two errors jumped out at me. There may be other errors.

As I said in a much earlier post, it is much more likely that your husband's apparent bad luck is due to erroneous data than to supernatural forces.

Jay

Thanks, I appreciate the help in error checking. For hand nineteen, I had transposed the hands in post 245. My hubby had the T5 and his opponent had the T4. See post 259 for the correct hands.

When you did the computations for those hands, I don't think you included the flop information (I'm not sure I posted that data) and for both of those, the all-in show down came after the flop. Hand 19 had a flop of QTT while hand 21 had a flop of K66. When I input that data, I get the same values that I originally reported, although it does vary a bit depending on the suits of the center cards, but the variation, as least in my checks was less than 4%. I also assume 4 different suits for the two players cards unless it is specified otherwise.

Incidently, no one is assuming supernatural forces; we are just mystified by the results and currently have no reasonable explanation other than random chance, which is why I'm working to compute that probability.

Erroneous data is always a possibility, as are errors in the computations. As more data is collected and collectively scrutinized, that possibility goes down. That's why I post the results here. I am deeply grateful for the help in spotting and correcting such errors. Thanks for your help in checking those values. As noted above, I can make errors and sometimes those errors have an influence on the probabilities computed.

 

[Beth]

Your sample size isn't big enough yet Beth to be useful. He could deviate from the mean for 2 years, then have a monster run of cards that pulls him even....

How much data do you think is needed? At this point, we have 6 months of all of his all-in results and are continuing to collect data. Posting it as we go allows other folks to spot errors and question my assumptions, which I find very helpful in more accurately computing the probabilities.

Or, as I said, he puts himself in the position too often due to poor choices. I noticed above that there were several all in hands he played that I wouldn't have played, due to the odds he was ,AT BEST a coin flip. Most of the time (depending on situation and stack size) one doesn't want to be going all in pre flop ,with a hand that isn't AT WORST a coin flip. So AT, KQ, AJ..... those are marginal all in hands IMO.

The point of this is to determine whether his actual outcomes are in line with is expected based on the random chance. Whether or not the choice to go all-in was a good or poor, once the all-in is called and the cards are shown, the probability of winning is independent of that choice. That's why we are using all-in showdowns as a way to make that determination - at that point, the results from that point on are unaffected by the skill of the players involved.

 

[jt512]

When you did the computations for those hands, I don't think you included the flop information (I'm not sure I posted that data) and for both of those, the all-in show down came after the flop.

That's correct. I didn't see any info on board cards, so I didn't take board cards into account. If you're reasonably confident about the accuracy of the data, I can calculate the probability of the result after I've ingested a little more caffeine.

Incidently, no one is assuming supernatural forces; we are just mystified by the results and currently have no reasonable explanation other than random chance, which is why I'm working to compute that probability.

Your husband's original hypothesis, that he is "unlucky," is a supernatural hypothesis. According to the known laws of physics, there is no property of "luckiness" that attaches to certain persons.

Erroneous data is always a possibility, as are errors in the computations. As more data is collected and collectively scrutinized, that possibility goes down.

If the error is systematic, then having more data doesn't help. In fact, it arguably makes it words, because you end up with a highly significant, but wrong, result.

Jay

 

[Beth]

That's correct. I didn't see any info on board cards, so I didn't take board cards into account. If you're reasonably confident about the accuracy of the data, I can calculate the probability of the result after I've ingested a little more caffeine.

Yes. Many thanks if you care to do that. I find the programming difficult; it's not one of my stronger skills. I test the program by computing exact results for a smaller dataset and comparing the results, but I would appreciate any additional checks on the computations.

Your husband's original hypothesis, that he is "unlucky," is a supernatural hypothesis. According to the known laws of physics, there is no property of "luckiness" that attaches to certain persons.

You're reading more into the word 'unlucky' that was intended. The hypothesis was that his outcomes were worse than expected. So far, that hypothesis has been supported by the data. Unlucky seems as good a description as any and was not, in my usage, intended to imply a necessarily supernatural hypothesis, only playfully suggest the possibility. My hubby actually has no belief in anything supernatural.

Unfortunately, we have yet to come up with ANY cause for these results. Random chance is appearing increasingly unlikely as more data is collected. With only 6 wins out of 29 hands, even assuming a binomial probability with a prob of .5 (this is less than his average prob. of wins and has the largest variance of any binomial distribution), the p-value is only .0012. Using a p-value equal to his average prob. of winning yields a p-value of 0.000048716. Either of which is sufficient to reject the null hypothesis and accept the alternative, that his outcomes are worse than can be reasonably expected by random chance only.

If the error is systematic, then having more data doesn't help. In fact, it arguably makes it words, because you end up with a highly significant, but wrong, result.
Jay

It's the process of putting the data and analysis out for review and answering questions like yours that will (hopefully) reveal any such systematic errors. For example, I started out using a binomial approximation on only one type of hand (a pair vs. two over cards for pre-flop all-ins only). I was convinced by others on this thread to go to exact computations and to collect data on all all-in showdowns.

Thanks for all your help and taking the time to look over the data and consider possible problems.

 

[jt512]

I computed the exact probability of winning six or fewer games out of this set of 29 as 0.00000127.

I get the same result.

Jay

 

[BravesFan]

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.

 

[Almo]

I computed the exact probability of winning six or fewer games out of this set of 29 as 0.00000127.That's just barely above a 1 in a million probability.

We are mystified as to why/how this is happening. If anyone cares to check my probability computation to verify it, that is sincerely appreciated. A binomial approximation using the average prob. of winning or tie (.57935) is 0.000048716. This is an upper limit on the probability, which means it is still a weird result.

Once, I rolled 8 dice at the same time and go ALL sixes. The probablility of that happening is pretty damned small. But just because it happened I didn't suddenly believe in luck, or thought something "weird" was going on. It was just a random occurrance.

The bummer was, I only needed a few fours or higher to win the fight I was in. Had I been attacking my opponent's Titan with that roll, I would have won the whole game outright.