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]

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.

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!

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]

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?

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]

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]

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.

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.

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.

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]

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]

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]

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?

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?

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?

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.

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.

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.

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]

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?

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.

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?

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.

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.

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?

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]

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]

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-tools/odds-calculator/texas-holdem

 

[Beth]

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.