Test for Bad Luck

[RandomElement]

I don't know how to make this post without it sounding like whining, but I I have had incredible runs of mind-boggling bad luck. I could tell story after story that would blow your mind, but I will limit this to something testable.

I wrote Expert Backgammon back in the late 1980s. It was the first computer program to beat humans in a live tournament. It also defeated IBM's entry at the 1992 World Cup Computer Championships even though mine was running on a lowly 386 and they brought a full team and a minicomputer with about 16 times the power. This was right before the advent of neural net programs which surpassed mine.

I actually quit BG for over 20 years when I lost the Nevada State Championship semi-finals in a 100,000,000 to 1 shot. The spectacors could not believe it and experts shown the game notation later thought it was fudged as it was deemed impossible even for such a fickle dice game.

I have two hypothesis:

1. I can prove my bad luck one that I have tested to my satisfaction, but I would like to set up a test to meet with your strict controls. I play for small stakes and consistently roll against all odds in certain positions NOT requiring skill. For example: coming in the from the bar. I have looked at hundreds of consecutive games and consistenly roll negatively against chance day in and day out.

In no contact race situations I roll about 1.2 pips below the average of 8.16 while my higher rated opponents roll about the same 1.2 above average.

The other day the only way I could lose was to roll 11 four times in a row and then get hit by a 11/36 shot. A 5 million to 1. Cherry picking? A little, but weird stuff like this happens daily. My stomach tightens before it happens as somehow I know my impossible-to-lose situation will get turned.

Hypothesis 2: This may be more important as it is not personal. I contend that stronger players have better luck. Now this may seem somewhat obvious, but I am talking about it as a predictor of outperforming a weaker opponent in areas not requiring skill not as a measurement of past performance. It as if they expect better than average luck - and get it!

Now I could whip out my charts and spreadsheets, but they could be doctored or games could be selectively chosen so let's start from scratch.

How can I either prove to y'all that this is mere confirmation bias and selective memory on my part or that something funny IS actually going on? All of my daily games are saved.

If the former, it may help my mental health; if the latter, it would shake science up profoundly.

[Brian-M]

How are the rolls in these computerized tournaments determined?

Do they use a software-based pseudo-random number generator, or a hardware-based true-random number generator? If you're using a pseudo-random number generator, that might be the reason you're seeing a larger than expected outcome of improbable results.

You might be able to examine your "luck" by checking how often both die come up with the same number. This should happen on average one roll in six, or approximately 16.67% of the time.

[WhatRoughBeast]

Originally Posted by RandomElement

The other day the only way I could lose was to roll 11 four times in a row and then get hit by a 11/36 shot. A 5 million to 1.

I hate to quibble, but your math is (I think) badly off. By my reckoning, the odds for your loss were about 344,000 to one. That's more than an order of maginitude error. This makes me uncertain about the rest of your numbers.

[WhatRoughBeast]

Originally Posted by Brian-M

How are the rolls in these computerized tournaments determined?

Do they use a software-based pseudo-random number generator, or a hardware-based true-random number generator? If you're using a pseudo-random number generator, that might be the reason you're seeing a larger than expected outcome of improbable results..

I'm very suspicious that this is the problem. Regardless of shortcomings in the PRNG, you would need to provide a mechanism whereby the resulting deviations from true randomness would consistently work against him, rather than cancelling out.

[RandomElement]

Originally Posted by WhatRoughBeast

I hate to quibble, but your math is (I think) badly off. By my reckoning, the odds for your loss were about 344,000 to one. That's more than an order of maginitude error. This makes me uncertain about the rest of your numbers.

1/36 * 1/36 * 1/36 * 1/36 * 11/36 = what exactly?

[Brian-M]

Originally Posted by WhatRoughBeast

I'm very suspicious that this is the problem. Regardless of shortcomings in the PRNG, you would need to provide a mechanism whereby the resulting deviations from true randomness would consistently work against him, rather than cancelling out.

I'm assuming that there may be some confirmation bias involved.

ETA:

Originally Posted by RandomElement

1/36 * 1/36 * 1/36 * 1/36 * 11/36 = what exactly?

Rolling an 11 is a 2/36 probability, not 1/36. Using this figure, I make it to be a 1 in 343558 outcome.

ETAA:

Just for the record, the 36 outcomes are...

1+1=2
1+2=3
1+3=4
1+4=5
1+5=6
1+6=7
2+1=3
2+2=4
2+3=5
2+4=6
2+5=7
2+6=8
3+1=4
3+2=5
3+3=6
3+4=7
3+5=8
3+6=9
4+1=5
4+2=6
4+3=7
4+4=8
4+5=9
4+6=10
5+1=6
5+2=7
5+3=8
5+4=9
5+5=10
5+6=11
6+1=7
6+2=8
6+3=9
6+4=10
6+5=11
6+6=12

[RandomElement]

Originally Posted by Brian-M

How are the rolls in these computerized tournaments determined?

Do they use a software-based pseudo-random number generator, or a hardware-based true-random number generator? If you're using a pseudo-random number generator, that might be the reason you're seeing a larger than expected outcome of improbable results.

You might be able to examine your "luck" by checking how often both die come up with the same number. This should happen on average one roll in six, or approximately 16.67% of the time.

It has happened in real life with hand-rolled dice and at various BG websites. The dice at Gammon Empire are supposed to the best known random system possible on a computer - either way the dice should balance out.

Just a short while ago I failed to roll a critical 4 for 9 rolls.

A big match 30 minutes ago came to a straight dead even race. He rolled five doubles to my one and picked up an incredible 34 pips. Normal.

And just seconds ago, my opponent admitted he should not have taken the cube in a position where he was a HUGE underdog. He beat me in an $80 tourney on a 1/18 * 11/36 combo - and I knew it would happen. Of course it was worse than this. The previous game was a match winner for me if I did not roll a 51 followed by a 13.

Down 17 straight 4 person tourneys today. Not sure the math on that, but it is huge considering roughly equal skill level.

I could go on and on with stories, but we need a solid test.

[RandomElement]

Originally Posted by Brian-M

I'm assuming that there may be some confirmation bias involved.

ETA:



Rolling an 11 is a 2/36 probability, not 1/36. Using this figure, I make it to be a 1 in 343558 outcome.

ETAA:

Just for the record, the 36 outcomes are...

1+1=2
1+2=3
1+3=4
1+4=5
1+5=6
1+6=7
2+1=3
2+2=4
2+3=5
2+4=6
2+5=7
2+6=8
3+1=4
3+2=5
3+3=6
3+4=7
3+5=8
3+6=9
4+1=5
4+2=6
4+3=7
4+4=8
4+5=9
4+6=10
5+1=6
5+2=7
5+3=8
5+4=9
5+5=10
5+6=11
6+1=7
6+2=8
6+3=9
6+4=10
6+5=11
6+6=12

No, it is a 1/36 shot.

11 = 1 way possible
12 = 2 ways possible (12 and 21)
13 = 2
14 = 2
15 = 2
16 = 2
22 = 1

and so on.

[Zax63]

Ah, WhatroughBeast took 11 as eleven, and randomElement meant double ones.

RandomElement, I would say you are having a run of bad luck but the sample size is just too small to say if there is anything unusual about it. I used to play online poker where all serious players collected the details on all of their hands. A sample size of 10,000 hands was often considered too small to be truly useful.

Also, as you said yourself, you are cherry picking unusually bad results. You have probably had comparable favorable results but accept that as your due or or your own skill.

I'm only a mediocre backgammon player but I've had games playing gnubg where I came close to physical violence against the computer for the amazing luck variance.

[Brian-M]

Originally Posted by RandomElement

No, it is a 1/36 shot.

11 = 1 way possible
12 = 2 ways possible (12 and 21)
13 = 2
14 = 2
15 = 2
16 = 2
22 = 1

and so on.

Ah, by 11 you meant rolling two ones, not rolling a total of eleven. That's not obvious to those of us unfamiliar with backgammon. (Although I should have realized, given that I took a quick look at the Wikipedia page before responding to your OP.)

Originally Posted by RandomElement

I could go on and on with stories, but we need a solid test.

A test is easy. Identify in advance certain rolls in specific conditions as being "lucky" or "unlucky", and keep track of the number of times these rolls occur and the number of times these roll don't occur for a large number of games. Once you've done that, you simply compare the frequency with which you actually got these rolls with the frequency you'd expect to get them by chance.

For example, I would assume that getting the same number on both dice would count as "lucky" because it gives you a double-turn. So as I said before...

You might be able to examine your "luck" by checking how often both die come up with the same number. This should happen on average one roll in six, or approximately 16.67% of the time.

[RandomElement]

Yes, a test is easy, but how to convince the forum is what I am asking so that you know I am not cherry-picking?

[sol invictus]

Originally Posted by RandomElement

Yes, a test is easy, but how to convince the forum is what I am asking so that you know I am not cherry-picking?

If you really had "bad luck", you could win Randi's $1,000,000 challenge.

You're of course imagining it. Confirmation bias is powerful, particularly when you can blame your losses on it. Sorry if that's harsh, but it's obvious.

[Jomante]

Sorry. No way you could win the $1 million in a challenge. If you have bad luck, it would mess up any opportunity to win the challenge, wouldn't it?



(lucky post #13!)

[Halfcentaur]

In a universe of stuff happening, at least you managed to be born against all the odds, um. Turn that frown upside down. Have you heard the good news? He is risen!

[SezMe]

Originally Posted by Brian-M

A test is easy. Identify in advance certain rolls in specific conditions as being "lucky" or "unlucky", and keep track of the number of times these rolls occur and the number of times these roll don't occur for a large number of games. Once you've done that, you simply compare the frequency with which you actually got these rolls with the frequency you'd expect to get them by chance.

That's no good because he has to identify "lucky" and "unlucky". It's much simpler than that. Just record EVERY toss. Every single one. After a while, it will be clear whether the result is in accordance with accepted statistics.

[GlennB]

deleted

[GlennB]

Originally Posted by Brian-M

Ah, by 11 you meant rolling two ones, not rolling a total of eleven. That's not obvious to those of us unfamiliar with backgammon.

I'm very familiar with backgammon and it wasn't obvious to me either.

[Pup]

Originally Posted by SezMe

That's no good because he has to identify "lucky" and "unlucky". It's much simpler than that. Just record EVERY toss. Every single one. After a while, it will be clear whether the result is in accordance with accepted statistics.

I agree with that. Though it's possible the claim is that tosses only are against the odds in crucial situations, being balanced out by luckier-than-average tosses when it doesn't matter, so the overall statistics are normal.

A possibility then would be to state in advance, immediately before the toss, whenever a toss mattered, and record the results from those only. Again, the results should be in accordance with normal statistics. It's similar to Brian-M's suggestion but is simpler in that one doesn't have to figure the odds of each individual toss.

[Zax63]

I thought this was interesting - how luck is evaluated by the gnu backgammon program.

Quote:

The luck of a roll is defined as the difference of equity after the best move after rolled dice and the equity after best move averaged over all possible rolls.

[jojonete]

Originally Posted by RandomElement

Yes, a test is easy, but how to convince the forum is what I am asking so that you know I am not cherry-picking?

The key in other posts' ideas is the "in advance" part. You may cherry-pick all you want, as long as you do it before rolling the die.

The idea is simple: when you get that "I know I'm gonna lose against all odds" feeling, you decice you'll record that roll, then you roll the die, then you record the result. Everything's fine as long as you take the decision of recording the result before rolling the die.

Now, I'll add that I've taken a similar approach in a completely different subject some time ago, and I can tell that it's easy to end up rolling the die and then not being sure what the decision was (i.e. should I record this? well, before rolling I did think about recording it, but I can't tell it was a really firm decision...). For me, this was a problem big enough that I couldn't say to myself in any seriousness that I had any valid data at all.

So you should have a physical object to mark what the decision is. An example:

• Before you start playing, you place on the table, beside you, a cell phone with the screen facing up.
• When you get that "I know I'm gonna lose against all odds" feeling, before rolling the die, you turn the cell phone upside down, so the screen is now facing the table.
• You roll the die.
• You record the result (whatever it is) if and only if the phone has the screen facing down.

With this method, after rolling the die there will be no doubt what the decision was: the phone tells you. Note that this means if you forget to turn the phone, you lost your chance of recording a (possibly hugely unlucky) roll. It might seem like a ridiculous thing to do, moving around a cell phone to remember that 10 seconds ago you took a decision, but I can tell from my experience that it's absolutely necessary.

Of course, you may use any object instead of a cell phone.

From my experience, I expect you'll realize very soon that it's not easy at all to decide when to turn the phone. In fact, if you really try this and you really don't cheat, I'd say you'll end up thinking the cell phone position affects your luck. Then we'll wonder why you are not damn rich yet, as all you have to do to get excellent luck is to put a cell phone upside down on your table

[Pup]

Originally Posted by jojonete

From my experience, I expect you'll realize very soon that it's not easy at all to decide when to turn the phone. In fact, if you really try this and you really don't cheat, I'd say you'll end up thinking the cell phone position affects your luck. Then we'll wonder why you are not damn rich yet, as all you have to do to get excellent luck is to put a cell phone upside down on your table

That's an excellent illustration of how our minds work.

[RandomElement]

While I am no longer the world class player I was 20 years ago, having written the best AI program of it's time and many BG articles, I do have some idea of what I am doing & saying.

Am down 4 more 4 player tourneys this morning for a total of 21 straight losses AFTER STARTING THIS thread. That is certainly not ad hoc.

Any of you grab a deck of cards and pick out 1 of each suit and mix. Now see how long you go without picking a heart. Some math geek here could tell you the astronomical odds of missing 21 times.

To make this simpler, I will choose one straightforward aspect of the game. Coming in from the bar, as this is often the most critical part of the game and any skill and decision-making is totally absent. One is 100% at the mercy of the dice gods.

To further limit, I will pick situations in which the opponent has either a four point or a five point board and I have a single blot on the bar and I will give an honest tally of the average number of rolls it takes to come in over the next 24 hour period.

Fair enough?

[GlennB]

Originally Posted by RandomElement

To further limit, I will pick situations in which the opponent has either a four point or a five point board and I have a single blot on the bar and I will give an honest tally of the average number of rolls it takes to come in over the next 24 hour period.

Fair enough?

Not quite. This isn't such a common situation that you'd experience it often enough in 24 hrs to make it statistically solid. Unless you play a lot of games.

Then, we'd want to see each game posted when the case arose and then see the roll separately. Screen shots please. It feels like you're wedded to this "bad luck" thing and will cherry-pick bad results.

Sorry, but what you're claiming here invalidates probability theory. The dice cannot be out to get you. You'll only get so much slack cut to you before folks start <sigh>ing.

[RandomElement]

Quote:

It feels like you're wedded to this "bad luck" thing and will cherry-pick bad results.

How are your feelings relevant to the test I proposed? If I present honest results based on an a priori condition? How can that possibly be cherry picking?

Also I am going to change the test slightly BEFORE THE FACT. I am also going to count having more than 1 blot on the bar.

As to the games, unfortunately they are not numbered sequentially according to player, but according to game # on the server, so it will be difficult to prove I am not skipping games. (Would a dishonest person mention this?)

What I can probably do is save the game(s) as an attachment and anyone here can open it with a free Gammon Empire account. No money required - and no I am not spamming for them.

[MuDPhuD]

Originally Posted by RandomElement

No, it is a 1/36 shot.

11 = 1 way possible
12 = 2 ways possible (12 and 21)
13 = 2
14 = 2
15 = 2
16 = 2
22 = 1

and so on.

What? Who plays backgammon like that? When you roll 5 and 6 you get 56? No, you 5 and 6 or 11. It's the same as every other dice game:

http://www.jimloy.com/math/probabil.htm

[Weak Kitten]

Obviously you have angered the Random Number Gods! You must sacrifice a pair of virgin six siders by microwaving them until they melt. Then you must buy a pizza of his/her choice for your game master. Only then can you appease the all powerful RNG!

[GlennB]

Originally Posted by MuDPhuD

What? Who plays backgammon like that? When you roll 5 and 6 you get 56? No, you 5 and 6 or 11. It's the same as every other dice game:

http://www.jimloy.com/math/probabil.htm

This was some confusion that arose earlier. The notation I'm used to is 5-6 or 5,6. RandomElement happens to use 56, but it all became clear in the end.

[RandomElement]

My bad for the confusion. I have seen notation written all three ways, but should have clarified.

[Toontown]

RandomElement:

I'm willing to stipulate that you have had a long streak of very bad luck. It happens, and it is hardly likely that someone who has had average luck will testify to having experienced anything unusual.

Yes, it is selection bias. People who have had streaks of luck, good or bad, tend to notice. People who have had average luck do not tend to suspect anything abnormal is happening.

However, you can rest assured that any streak of luck you might have had is not ongoing. The nature of probability dictates that all streaks of luck, good or bad, can only be recognized in retrospect. There is no such thing as an ongoing streak of luck.

The nature of probability therefore dictates that any streak of luck, good or bad, is due to end immediately. The future is a whole new ball game.

In the future, expect runs of good, bad, and average luck. The past is done.

[EdG]

You're neglecting the Bell Curve. In order for there to be a mean and medium, some people must be on the trailing edge and some on the leading edge of the curve. It is entirely possible for John Doe to hit on 9 of 10 rolls during his entire life while you only hit on 1 of 10 rolls during yours. You could ascribe that to bad luck. Or you could ascribe it to normal statistical probability for a given number of rolls during a given number of lifetimes.

[Toontown]

Originally Posted by EdG

You're neglecting the Bell Curve. In order for there to be a mean and medium, some people must be on the trailing edge and some on the leading edge of the curve. It is entirely possible for John Doe to hit on 9 of 10 rolls during his entire life while you only hit on 1 of 10 rolls during yours. You could ascribe that to bad luck. Or you could ascribe it to normal statistical probability for a given number of rolls during a given number of lifetimes.

It is not possible for John Doe or anyone else to correctly expect to hit on 9 of 10 rolls in the future based on anything that has happened in the past. If John Doe does turn out to be unlucky for his entire life, then that statistical fluctuation from the norm will only be seen in retrospect - after it has already happened. And it would be wrong to predict anything about John Doe's probabilistic future except the 'mathematical expectation', if there is one - irrespective of John Doe's probabilistic past.

[RandomElement]

Quote:

The nature of probability dictates that all streaks of luck, good or bad, can only be recognized in retrospect. There is no such thing as an ongoing streak of luck.

So the 21 consecutive lost matches immediately AFTER the post were in retrospect? Is that how it works?

If it was not bad luck then I must be prescient. Can't have it both ways. How could I possible know when writing this post that yet another million to 1 shot would occur right away with no gaps?

Can someone do the math on missing 1/4 21 times?

[RandomElement]

Originally Posted by EdG

You're neglecting the Bell Curve. In order for there to be a mean and medium, some people must be on the trailing edge and some on the leading edge of the curve. It is entirely possible for John Doe to hit on 9 of 10 rolls during his entire life while you only hit on 1 of 10 rolls during yours. You could ascribe that to bad luck. Or you could ascribe it to normal statistical probability for a given number of rolls during a given number of lifetimes.

True, but I am saying that there may very well be a predictive element. I know this does not jive with probability theory, yet were my losses after the fact just a meaningless fluke despite my predicting it?

To anyone interested I could post all of the time-stamped tournaments if it is a credibility question.

[SezMe]

RandomElement, are you claiming that you personally, somehow, directly affect the results of the throws?

[Toontown]

Originally Posted by SezMe

RandomElement, are you claiming that you personally, somehow, directly affect the results of the throws?

That's easy enough for RandomElement to check. If so, then the run of bad luck will continue indefinitely into the future. If not so, then the expectation is for average luck in the future.

[EdG]

Originally Posted by Toontown

It is not possible for John Doe or anyone else to correctly expect to hit on 9 of 10 rolls in the future based on anything that has happened in the past. If John Doe does turn out to be unlucky for his entire life, then that statistical fluctuation from the norm will only be seen in retrospect - after it has already happened. And it would be wrong to predict anything about John Doe's probabilistic future except the 'mathematical expectation', if there is one - irrespective of John Doe's probabilistic past.

Who said anything different? Why are you paraphrasing what I said as though it is some new insight?

[Toontown]

Originally Posted by RandomElement

So the 21 consecutive lost matches immediately AFTER the post were in retrospect? Is that how it works?

Again, you are talking about something that happened in the past. And I didn't see where you specifically predicted the 21 consecutive losses before the fact. Therefore, you are backfitting.

Originally Posted by RandomElement

If it was not bad luck then I must be prescient. Can't have it both ways. How could I possible know when writing this post that yet another million to 1 shot would occur right away with no gaps?

Every specific sequence of dice rolls is highly improbable.

Given a choice between you being prescient (or) you having experienced a run of bad luck, I will dispose of prescience. If I am correct, your future luck figures to be unremarkable.

Originally Posted by RandomElement

Can someone do the math on missing 1/4 21 times?

That's backfitting. The post hoc probability is the same as any other sequence of hitting and missing.

[RandomElement]

I didn't predict 21 straight losses, I predicted the dice would continue to go against me. And they did - well beyond expectation. And yet everyone here can just disregard a negative million to 1 shot as if it were meaningless ?

I am trying very hard to follow, but cannot.

[EdG]

Originally Posted by RandomElement

True, but I am saying that there may very well be a predictive element. I know this does not jive with probability theory, yet were my losses after the fact just a meaningless fluke despite my predicting it?

Likely a meaningless fluke. Perhaps you are inadvertently affecting your roll because you EXPECT to lose. If you simply improved your mindset and expect to win, your fine motor control may respond with a steadier hand, thus resulting in more wins.

It all boils down to math. The orientation of the dice in your hand, the force with which you throw them and anything that materially alters their path will affect which surfaces end up. It can be modeled with computer software but no known humans control their motor skills finely enough to consistently alter the outcome in a positive fashion. Remember, a superstar professional baseball player only hits about 1 of 3 balls thrown at him.

[RandomElement]

At least no one here will do the simple card test I suggested.