Do you believe in Luck?

[BStrong]

I don't know if luck is the right word, but I've walked away from many bike crashes, up to 90-100 mph on the track, and on 26 July 2010, I walked away from an accident where I was rear-ended while riding, the passenger vehicle operator only stoppped when my bike (2004 Yamaha R1) was jammed underneath the car.

After picking up what was left of the bike the next day I received a call at home from the tow company owner telling me to buy a lottery ticket - he told me that in 30+ years in the business he had never seen a bike damaged like mine where the rider wasn't killed or crippled.

Military and OTJ situations have worked out likewise.

Am I "lucky" to have survived all these years or unlucky because I found myself in these sutuation?

[Beth]

Originally Posted by jt512

I had started writing up a Bayesian analysis of your husband's results, but I got sidetracked. Maybe now that the this thread has been revived I'll finish it up.

I'll look forward to that. I'm still kind of flabergasted at how the results are coming out.

That reminds me, one of the hands I added was a pair against two overcards, so it gets added into our 'races' database.

That gives him 22 wins out of 58 contests of that nature. Using the binomial p = 0.5 distribution, the probability of getting 22 or fewer wins out of 58 hands is 0.0435. He has a 50/50 ratio of holding pairs versus two overs.

Originally Posted by Senex

Luck isn't all probability. ... No bulloney, I got lucky to have this woman as my girlfriend. I know what it is like to have a woman as beautiful as Cindy Crawford as a girlfriend. It was just plain luck she decided to chat me up.

You are right. Luck isn't all probability. Thank you for sharing that delightful story!

Originally Posted by BStrong

I don't know if luck is the right word...Am I "lucky" to have survived all these years or unlucky because I found myself in these sutuation?

A good question. I don't know. How do you feel about it?

[Ron_Tomkins]

Luck is one of those words that could either refer to the realistic, casual coincidences that do happen, or then again it could refer to the mystical magical woo woo mental idea that there's some kind of force giving you things when you behave good.

[BravesFan]

About 2 or 3 years ago, I had a run of poker luck that lasted a good 6 months. I was winning around 75-80% of all in calls (even when I was a dog). That was hundreds of hands, guess what happened tho? I went on a bad streak and before you know it I was back within the margins of 50/50....

So, no , I don't believe that luck is a measurable trait inherent in an individual. We just go through periods of good, bad and average draws in a mathematical entity like poker.

If you play ten billion hands everyone will end up pulling what the odds dictate.

[Beth]

Originally Posted by LogicFail

About 2 or 3 years ago, I had a run of poker luck that lasted a good 6 months. I was winning around 75-80% of all in calls (even when I was a dog). That was hundreds of hands, guess what happened tho? I went on a bad streak and before you know it I was back within the margins of 50/50....

Did you collect data and compute those probabilities, or is that based on your recollection?

Quote:

So, no , I don't believe that luck is a measurable trait inherent in an individual. We just go through periods of good, bad and average draws in a mathematical entity like poker.

If you play ten billion hands everyone will end up pulling what the odds dictate.

I agree. And some people will be on the far ends of that distribution.

JT512: Your values are correct. I found my error in the P(Wins = 1) computation. Thanks for the check on those values. I have two more hands to add to the database now if you want to run through the exercise again.

My dh had another poker night Saturday. Interestingly, one of them was the first all-in hand with more than two players since we started collecting data and computing the probabilities. He lost both hands. Here is the complete dataset as of Jan 30, 2012:

1 AK 37 Loss 0.3583

2 A6 K3 Loss 0.027

3 AT AK Loss 0.6864

4 AA 99 Loss 0.1966

5 TT 58 Loss 0.1956

6 KK QQ Loss 0.1856

7 KT AT Loss 0.7019

8 JJ A9 Win 0.3167

9 AK QQ Loss 0.5359

10 AA 99 Loss 0.1966

11 QQ AA Loss 0.9162

12 AK AA Loss 0.7141

13 A9 Q6 Loss 0.8181

14 KK 99 Win 0.1899

15 AQ A9 Win 0.2395

16 78 34 Loss 0.7101

17 KT 77 Loss 0.4629

18 99 77 Loss 0.1364

19 T4 T5 Loss 0.1091

20 A9 K7,A6 Loss 0.4175

21 AT K7 Loss 0.9318

The first column is the observation number. The second is my hubby's hands, the third is his opponents. The fourth column is the win(1)/loss(0) outcome. The fifth column is the probability of my hubby losing the hand.

This is what I compute as the probability of getting a run of bad luck as bad or worse than what we've recorded here:

Prob (Wins = 0) 5.1419E-11

Prob (Wins = 1) 4.3241E-09

Prob (Wins = 2) 1.4285E-07

Prob (Wins = 3) 2.6422E-06

Prob(Wins <= 3) 0.000002789

Earlier in the thread we discussed truncating the distribution. Throwing out the best and worst hands, I get the following probabilities:

Truncated Distribution - Dropping hands 2 and 8

Prob (Wins = 0) 6.01E-09

Prob (Wins = 1) 2.76017E-07

Prob (Wins = 2) 2.37E-06

Prob(Wins <= 2) 0.000002656

[BravesFan]

I was playing in a casino, but I wrote down my hands played/results after every hand (that I bet into including blinds) and then ticked off everytime I was the dealer (to keep track of rounds so I could see how my loose/tight play reflected in winnings)

I disagree that some would be on the low and high end of the spectrum (well in regards to results involving no skill) Of course when one considers player skill/decisions that will spread the results like a bell curve I would suspect. But a player facing coin flip hands, over enough time, they should ALL result in a 48-52% win ration (within the margin of error)

[jt512]

Originally Posted by Beth

I have two more hands to add to the database now if you want to run through the exercise again.

For the Bayesian analysis that I'm writing up, I'm going to cap it at the 19 hands. Otherwise, I'll never finish it.

Jay

[Beth]

Originally Posted by LogicFail

I was playing in a casino, but I wrote down my hands played/results after every hand (that I bet into including blinds) and then ticked off everytime I was the dealer (to keep track of rounds so I could see how my loose/tight play reflected in winnings)

That's cool. Would you mind sharing your data? I'd be interested to see how your all-in results compare to the ones I've been posting.

Quote:

I disagree that some would be on the low and high end of the spectrum (well in regards to results involving no skill)

The no-skill situation is exactly what I'm tracking.

Quote:

Of course when one considers player skill/decisions that will spread the results like a bell curve I would suspect. But a player facing coin flip hands, over enough time, they should ALL result in a 48-52% win ration (within the margin of error)

Yes, they should. We're currently at 22 wins out of 58, that's a ratio of slightly under 38% wins. A binomial approximation using p = .5 yields a p-value of 0.0435.

Originally Posted by jt512

For the Bayesian analysis that I'm writing up, I'm going to cap it at the 19 hands. Otherwise, I'll never finish it.

Jay

I can understand that. It took me long enough to program the probability calculation. It takes my computer a noticeable amount of time to grind through all the calculations too. I'm looking forward to seeing your model and results.

[Ilooklike ACrowley]

Hi Beth

It does seem as though your husband is quite simply not a good player, and that will skew results more than any luck factor. However, if you really want to research this I suggest that you pop over to a forum like 2plus2.com -

Oh and then there's the fact that internet poker is fixed

[Beth]

Originally Posted by Ilooklike ACrowley

Hi Beth

It does seem as though your husband is quite simply not a good player, and that will skew results more than any luck factor. However, if you really want to research this I suggest that you pop over to a forum like 2plus2.com -

Oh and then there's the fact that internet poker is fixed

Whatever his level of playing skill, what we are endeavoring to determine is whether his luck is worse that what would be expected from random chance. The data we are evaluating was specifically chosen because it occurs at a point in the game where skill should not be a factor or have an impact on the outcome.

However, if you have any ideas about how skill could impact these results - i.e. the win/loss outcome of an all-in showdown after the betting is completed - I would like to hear your theory on it. Thanks.

[Ilooklike ACrowley]

Originally Posted by Beth

Whatever his level of playing skill, what we are endeavoring to determine is whether his luck is worse that what would be expected from random chance. The data we are evaluating was specifically chosen because it occurs at a point in the game where skill should not be a factor or have an impact on the outcome.

However, if you have any ideas about how skill could impact these results - i.e. the win/loss outcome of an all-in showdown after the betting is completed - I would like to hear your theory on it. Thanks.

Yes I realise that Beth, but your data is skewed from the start. Your statement:
The data we are evaluating was specifically chosen because it occurs at a point in the game where skill should not be a factor or have an impact on the outcome.
Is completely erroneous.
If action has taken place it has already become a factor and had an impact on the outcome. There are so many variables that measuring only the impact of showdowns is meaningless. The odds vary depending on the games your husband is playing. For example a hand like A6 - which I see he plays - is stronger on a six handed table than a nine or ten handed table. However it has less probability of making a straight than a hand like A5.
Before the heads up situation occurs players can bet, raise or fold. That also gives imperfect information to the players who remain in the hand. Position means that a hand like A10 may be folded UTG but raised in the cut off. In other words the only way you can mathematically judge your husbands luck is by taking a particular hand - say AA - and measuring how often it wins in situations were the money has gone all in pre-flop. Statistically AA should win around 87% of the time against ATC and around 82% of the time against a lower pair be that kings or deuces. However the sample would have to be huge. On top of which there may be variables online depending on the algorithms used by the sites RNG. You would also need a control player to offset your husbands results against playing on the same sights.

At the end of the day there are many people much smarter than me who can work out the mathematics... you are one of them... but I know poker inside out and can tell that the method your using is not taking into account enough variables. In my experience there are players who run through periods of perceived "Bad luck" but then run into periods of perceived "Good luck" psychologically during the perceived period of bad luck a player makes bad decisions due to frustration and impatience. It may well be that your husband is going through one of these periods.

[Beth]

Originally Posted by Ilooklike ACrowley

Yes I realise that Beth, but your data is skewed from the start. Your statement:
The data we are evaluating was specifically chosen because it occurs at a point in the game where skill should not be a factor or have an impact on the outcome.
Is completely erroneous.
If action has taken place it has already become a factor and had an impact on the outcome.

Thanks for your response. I can certainly understand how this affects the probability of ending up in a showdown. But how does this affect the outcome after all the bets have been placed?

Quote:

There are so many variables that measuring only the impact of showdowns is meaningless.

It's certainly meaningless in terms of improving his play. That isn't the purpose of this data collection exercise. This is purely to determine if his outcomes match those expected for random chance alone when skill is taken out of the picture. What additional variables would need to be included to more accurately compute the probability of a win through random chance alone, taking skill as completely out of the picture as possible?

Quote:

The odds vary depending on the games your husband is playing. For example a hand like A6 - which I see he plays - is stronger on a six handed table than a nine or ten handed table. However it has less probability of making a straight than a hand like A5.

Why would this affect the probability of a win after all bets have been made and the probability computed based on the cards the players in the showdown are holding and the center cards that have already been played?

Quote:

Before the heads up situation occurs players can bet, raise or fold. That also gives imperfect information to the players who remain in the hand. Position means that a hand like A10 may be folded UTG but raised in the cut off. In other words the only way you can mathematically judge your husbands luck is by taking a particular hand - say AA - and measuring how often it wins in situations were the money has gone all in pre-flop.

We were, at first, taking data only on 'races' (a pair against two over cards) and only when the money went all-in preflop. Currently, our data on that situation has a p-value of less than 0.05.

Antiquehunter convinced me that all showdowns could be used by computing the probability of a loss at the point the all-in occurs and the cards the players are holding have been shown. and then doing a precise probability computation based on the actual hands that were played. If you disagree and feel that these outcomes are affected by play and should not be computed using probability theory alone, I would like to understand why and try to figure out a way to eliminate the effect of that variable so that probability theory is sufficient to compute the odds.

Quote:

Statistically AA should win around 87% of the time against ATC and around 82% of the time against a lower pair be that kings or deuces. However the sample would have to be huge. On top of which there may be variables online depending on the algorithms used by the sites RNG. You would also need a control player to offset your husbands results against playing on the same sights.

Since the U.S. shutdown of gambling sites like full-tilt poker, the data are from the garage games he plays in. Further, removing the on-line poker hands does not affect the results very much so I don't think that is a factor contributing to the results.

Quote:

At the end of the day there are many people much smarter than me who can work out the mathematics... you are one of them... but I know poker inside out and can tell that the method your using is not taking into account enough variables.

Are you sure you are not misunderstanding why we are doing this? It seems to me that the additional factors are mainly useful in attempting to improve one's play, not compare outcomes to random chance to determine if his actual outcomes match the expected outcomes computed using probability theory.

Quote:

In my experience there are players who run through periods of perceived "Bad luck" but then run into periods of perceived "Good luck" psychologically during the perceived period of bad luck a player makes bad decisions due to frustration and impatience. It may well be that your husband is going through one of these periods.

That's certainly what I thought before we started collecting data. We have been doing this to assess just how accurate his perception of bad luck has been. My attitude used to be that it was just confirmation bias and he was remembering the losses more often than the wins. Instead, the data seems to be bearing out his assessment of poor luck rather than the computations of what would be expected by random chance alone.

Thanks for your insights and any ideas you might have to make better sense of this data.

[bigred]

I dunno. He looks great on paper but how do you replace Manning?? You don't.

[Ilooklike ACrowley]

Hi Beth

Like I say I'm not a mathematician... but the point is that play will always have an influence on the figures. A good player will have a better idea of the hands that his / her fellow players hold.

It's difficult to comment because take your first hand. AK v 37 I have no idea of suits, if it's an all in and call preflop or if there is a flop, turn or river. Now if it's preflop your odds are correct in that your husband is a 65% favourite to win the hand [you put it as 35% to lose] However as you have informed me this is a garage game.. then presumably the players all know each other. The pattern of play before matey boy with 37 pushes all in could suggest to mr 37 that he is playing with live cards as the action preflop may lead him to believe that others were holding high cards and that your husband may have less cards to hit with his obvious AK. Even one folded ace would drop your husbands odds to around 48% preflop for a win.

Now if your calculations are allowing for all these factors at time of showdown, fair enough. But to be exact surely you would need to examine the folded hands... and indeed the burn cards.. if all you are trying to establish is the luck factor. Maybe you are doing that - I'm not that clear on Antiquehunter's method as you say:
all showdowns could be used by computing the probability of a loss at the point the all-in occurs and the cards the players are holding have been shown. and then doing a precise probability computation based on the actual hands that were played. . So if that's including all hands by all players folded and in play + burn cards ... then maybe you have something. Because you would have a true picture of the cards that have been in play including those that could contribute to straights and flushes for either player. If your dealing with incomplete data - as poker players do - then you are inviting the skill factor to play a part and your husband's play and the play of others will be a factor.

[Beth]

Originally Posted by Ilooklike ACrowley

Hi Beth

Like I say I'm not a mathematician... but the point is that play will always have an influence on the figures. A good player will have a better idea of the hands that his / her fellow players hold.

Yes, that impacts their choices on whether to call or not. But, once the bets are made and the cards are face up, how does that alter how the win/loss probability should be computed? What kind of an impact should their educated guess on what other players were holding have on the probability computation for what comes next?

Quote:

It's difficult to comment because take your first hand. AK v 37 I have no idea of suits, if it's an all in and call preflop or if there is a flop, turn or river. Now if it's preflop your odds are correct in that your husband is a 65% favourite to win the hand [you put it as 35% to lose]

Yes, it was preflop. But not all of the showdowns were. I can provide the center cards and when the all-in was called for those hands if anyone is interested.

Quote:

However as you have informed me this is a garage game.. then presumably the players all know each other. The pattern of play before matey boy with 37 pushes all in could suggest to mr 37 that he is playing with live cards as the action preflop may lead him to believe that others were holding high cards and that your husband may have less cards to hit with his obvious AK.

Again, I see this as impacting the choice of whether or not to bet or call with a particular pair of cards at a particular point in time (definitely a skill aspect), but how does that impact the probability of what comes up next after the bet is called and the cards are shown?

Quote:

Even one folded ace would drop your husbands odds to around 48% preflop for a win.

Yes, knowing those cards would affect the probabilities. So would knowing the bottom card, which is why they use a bottom cover card at his games. And if you know the next cards that will be played from the deck, the probability of loss becomes either 0 or 1. But that's not a fair way to assess his luck.

We wouldn't compute the odds given the turn card if the all-in came after the flop because that information was not available to the players before the bets were completed. Why should knowledge that would only be available after the hand is over be included in computing the win/loss probability?

I'm afraid I don't understand why you feel that information should be included nor do I see any legitimate justification for including it. Frankly, it seems like cheating to me.

Quote:

But to be exact surely you would need to examine the folded hands... and indeed the burn cards.. if all you are trying to establish is the luck factor. Maybe you are doing that - I'm not that clear on Antiquehunter's method as you say:
all showdowns could be used by computing the probability of a loss at the point the all-in occurs and the cards the players are holding have been shown. and then doing a precise probability computation based on the actual hands that were played. .

I do wish he'd include the suits - he never does. But he does mention whenever someone holds suited cards and if any center cards were that suit if they were played before the showdown.

Quote:

So if that's including all hands by all players folded and in play + burn cards ... then maybe you have something. Because you would have a true picture of the cards that have been in play including those that could contribute to straights and flushes for either player.

I don't understand why the burned and folded cards should affect the probability computations. Yes, if they are known, it would impact the computations. But since they are not known, why should the computations of probability take them into account in this situation?

Quote:

If your dealing with incomplete data - as poker players do - then you are inviting the skill factor to play a part and your husband's play and the play of others will be a factor.

How can skill be removed from the computation? What data would you recommend collecting and how should it be analyzed to determine whether or not he is actually losing more showdowns than would be expected according to random chance?


Thanks for taking the time to give me your thoughts and suggestions. I appreciate it.

[jt512]

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

[jt512]

Originally Posted by Beth

Yes, it was preflop. But not all of the showdowns were. I can provide the center cards and when the all-in was called for those hands if anyone is interested.

Your P(loss) figures are taking the known board cards into account, aren't they?

Jay

[Beth]

Originally Posted by jt512

Your P(loss) figures are taking the known board cards into account, aren't they?

Jay

Yes. I'm using this poker calculator to get the win/loss/tie probabilities:

http://www.cardplayer.com/poker-tool...r/texas-holdem

[Beth]

Originally Posted by jt512

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

Hmmm....are you saying that because small cards are more likely to be folded and large cards are more likely to call that it biases the deck towards larger cards?

That might have some validity. I'm not sure how it would be dealt with, but it's a testable hypothesis. I can look at the center cards that were dealt and determine if they fit a random distribution or if larger cards are slightly more likely.

I'll try to pull that analysis together this week-end and see how it plays out.

If you're interested, here is the data on the center cards. It's just a cut and paste from excel, so the formatting sucks. (I really wish I knew how to align columns. But I don't.) I'll be glad to answer any questions about the notes I've jotted down. I don't have all the center cards, just I have all the ones that were played pre-flop.

As we got further into the project, I started keeping notes on more stuff, so the later games are recorded in more detail.

Date Venue Mark Mark Cards Opponent Cards Win/Lose Flop Prob of losing

On line A K 3 7 0 387 All in pre flop 0.333333333

10/22/2011 Brians six's full of threes versus threes full of sixes at all in after the turn. River comes a 3. 0 0.02

10/22/2011 Brians A T A K 0 All in pre flop 0.666666667

10/22/2011 Brians A A 9 9 0 All in pre flop 0.2

10/8/2011 Patricks T T 5 8 0 All in pre flop 0.333333333

10/8/2011 Patricks K K Q Q 0 All in pre flop 0.2

10/8/2011 Patricks K T A T 0 All in pre flop 0.666666667

Combined probability of losing all of them in a row

0.00004

Date Mark's Cards Opponent's Cars Flop Prob of losing

11/5/2011 Patricks J J Q 9 3 4 5 Rainbow 0.2

All in after the flop. Mark wins.

Prob of losing

11/5/2011 Patricks AC KC Q Q Mark had suited AK 0.5

All in pre flop. Mark Loses

Combined Probability with previous

0.000142222

Flop Turn River Prob of losing

11/19/2011 Brian's AA 99 Flop 5 6 7 8 A 0.2

All in pre flop. Mark Loses

Combined Probability with previous

0.0000316

Prob of losing Tie

12/3/2011 Patricks QQ AA Flop 9 high rainbow. Called all in. 0.9162

AK Suited AA Flop K, J 10 high flop. One of suit. Called all in. 0.7141 0.1717

A9 Q6 Flop A, 6, ? (not nine), checked around, Turn Q, Called all in 0.8181

12/17/2011 Brians KK 99 all- in Preflot Mark Won 0.1899 0.0039

AQ A10 all- in Preflot Mark Won 0.2395 0.0568

78 Suited 34 Offsuite Flop 2, 5, 6. Mark Lost 0.7101

0.4629 0.0049

1/14/2012 Brians KT 77 all- in Preflot Mark Lost 0.1364 0.0909

99 77 all-in Turn 4567 Mark Lost 0.1091 0.7566

T5 T4 All in after flop QTT Mark Lost

Prob of losing Tie Prob. Of Win

1/28/2012 Patricks A9 suited K7 clubs Flop A, 5, 5, two clubs 0.4175 0.3887 0.1938 0.5825

A6 offsuit A6 pushes all in. Mark and K7 call

turn is 10 hearts

River 7 clubs

AT off suit K7 Flop K,6,6, 0.9318 0 0.0682

Turn 4

Mark goes all in (low in chips)

River doesn't help

[Bill Thompson]

People say The Force is just simple tricks and 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]

Originally Posted by Ilooklike ACrowley

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.

Quote:

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]

Originally Posted by Ilooklike ACrowley

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.

Quote:

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.

Quote:

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.

Quote:

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.

Quote:

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.

Quote:

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.

Quote:

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.

Originally Posted by jt512

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]

Originally Posted by fishtumor

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]

Originally Posted by 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]

Originally Posted by Beth

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]

Originally Posted by jt512

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]

Originally Posted by LogicFail

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.

Quote:

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]

Originally Posted by Beth

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.

Quote:

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.

Quote:

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]

Originally Posted by jt512

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.

Quote:

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.

Quote:

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]

Originally Posted by Beth

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]

Originally Posted by Beth

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.