Wrong again (backgammon)
In my life, I have been wrong many times. Just this morning I was quite, quite wrong three times. [Later note: it was wrong in public too. One of them was being wrong about anyone being willing to take 
ciphergoth's bets about Jeremy Corbyn.]
That put me in mind of other times when I've been wrong. The most spectacular in number terms was this example, where I was working out the ratio of aluminium to gold atoms dissolved in a simple electrochemical cell, and got the answer wrong by a factor of 10130. That really is quite wrong. I have a soft spot for
ciphergoth's maxim that it is better to pull numbers out of your arse and use those to make a decision than to pull a decision out of your arse, but I'm not always sure that applies. In that context it's salutary to reflect that numbers I produce with considerable thought, justification and on the basis of robust and really pretty settled science can be wrong by a factor of a billion quadragintillion.
Happily, though, the practical consequences of that particular mistake were no more than a slight loss of face - and even then, not a lot of face, because the guy who set the problem half-expected me to make that very mistake and was very nice about it.
One of the most painful mistakes I've made in terms of cold, hard cash was deciding to play a backgammon hustler. I've probably lost far more money in later mistakes, of course, but at the time it was a share of my disposable income that really hurt, and nothing since has come close.
I was a student, 21 cocky years of age, and had become interested in backgammon. I studied and practiced and got good enough to easily defeat the computer versions available to me at the time. (It was 1992. I strongly suspect they're way, way better now, but I'm much worse and not so interested in backgammon.) The computer opponents didn't play very interestingly, either.
So my issue was finding good people to play. There were some friends who were happy to give me a game, but most of them weren't particularly good, and the rest were only about the same level as me. And none of them were prepared to play for money, which is supposed to be the point. We were all skint.
[Unedifying "in-my-day" rant about how students don't act skint any more skipped for everyone's benefit.]
One lunchtime I went in to one of the student locals. (The Charles, for those who know York.) I was skint but not so skint I couldn't afford a pint now and then. You could get beer for less than a pound a pint at the time, but only in a few places if you knew where to look.
While I was there, I met an older guy who had a backgammon board and was looking for a game. He was offering a pound a point.
For those who don't know: in backgammon, simply winning is worth one point. But there are ways to win more than that, which we will hear more about shortly.
That was real money, but I was so excited to meet someone who was clearly pretty good - otherwise why would he offer to play for money to strangers - and was prepared to play a 'proper' game. Worst case, I thought, was that I get a game with someone really good and maybe lose a gammon (which is two points), which would be much of my beer money gone for the rest of the day, but probably worth it for entertainment value. It did cross my mind that he might have loaded dice, but I thought it was unlikely, and the fact that one can request to swap dice at any point would make it pointless.
(This was obviously wrong, I realised later, and not a defence against loaded dice - see below. Also, I hadn't appreciated how easily one can cheat at dice rolls with enough practice. Coin tosses are relatively straightforward, especially with an unsuspicious audience. I startled my kids the other day by tossing a coin ten times and having it come up heads every time, until they said it must be fixed and heads on both sides, and I said Ok, let's have a tails then, and got one. Hopefully they now understand the importance of a coin toss spinning in the air and landing untouched on the floor.)
Anyway. I sat down, and the game was on. We rolled one die each to see who started. Oops! They were the same. That's an automatic double.
A what? Well, in backgammon-for-money there's a doubling cube. This is mostly used for challenges, which we'll come on to, but sometimes there are events that trigger automatic doubles. Before you start to play, it is important for the players to establish what is and is not a trigger for an automatic double. I hadn't done that. I had little experience of for-money play, but I knew that rolling the same number to start is an almost-universal one: if you have any automatic doubles, that'll be one of them.
Oh dear. Now the stakes were doubled from what I'd thought. Not good.
Then we rolled again. I can't remember what rule he invented that triggered a further automatic double, but I'd never heard of it. He did seem very firm about it, and I lacked the experience to say it was wrong, and nobody around the table (we had a bit of an audience, mostly my friends) objected when I looked round, so I accepted that.
Oh dear oh dear. Now we're at £4 a point and we've not even started.
The game got going. He was playing well - unlike other people I'd played, I didn't spot any obvious tactical mistakes. I was doing Ok, but was definitely behind. Not unrecoverable, but not winning.
Then he offered me a double. This is the strategic, 'challenge' use of the doubling cube in the game. Basically, if someone offers you a double, you can either accept and play for twice the stakes, or decline and immediately lose at the existing stakes. If you accept a double, you gain 'control' of the cube, so you but not your opponent can offer a further double, e.g. if the tide swings substantially in your favour.
A full analysis of the doubling cube is well beyond this post. However, suffice to say, on most analyses, there exist situations where it is rational for a double to be offered and accepted, even if the players agree about the chances of a win.
Of course, in retrospect, I should've refused. (In retrospect I should never have played, come to that.) But he carefully managed it to make it look like I would be chicken and lose face to all my friends round about and would spoil the game were I to decline. I knew I was behind, but I didn't think I was so far behind as to merit refusing a double. And at least if I accepted, there would be no more doubles - I sure as hell wasn't going to offer him one - and my losses would at least be capped.
So I accepted.
We played on, and my relative position deteriorated, and it became painfully apparent that he was playing better than I was ... and things started to look really grim.
If you're losing badly like this, there is a way of playing called a 'back game'. Again, details are beyond this post, but essentially you occupy a couple of points in your opponent's home board while bringing a couple of runners slowly home, and hope that you can hit the blots they inevitably need to leave as they bear off, and leave them a closed board to come in on. It's a long shot, which sometimes works ... but to have any realistic chance, your position has to meet certain criteria (notably, to hold at least two points in their home board and have at least one runner to come round slowly), and mine emphatically didn't.
I sat miserably with pieces on the bar as he efficiently and effectively bore off all of his pieces while minimising the chances that I could get in or hit a blot of his. I did manage to escape a backgammon (where you still have pieces on the bar, or in your opponent's home board, when they finish) but he still beat me by a clear gammon (where one player gets all of their pieces off before the other has started). A backgammon counts for three times the current stakes, and a gammon scores twice the stakes. Which were, by now, 8x.
I paid up £16, feeling wretched. That wasn't just my beer money for the day blown.
He was very consoling, and was full of praise for how well I'd played, how I'd cleverly tried to tempt him in to setting up a back game, and how interesting it had been, and so on. I was not looking happy. He offered me another game, and I said no.
He tried to persuade me, and I was very slightly wavering. Luckily for me he made the tactical error of saying I'd had very unlucky dice.
Now, backgammon is a dice game, and that opens up the possibility of being more or less lucky. The key to playing well is to correctly work the probabilities to maximise gain - and, importantly, minimise the chances of loss - on every move. Sometimes the dice work in line with probability, sometimes not ... but you throw the dice many, many times in the course of a game, and the law of large numbers tells you that they are going to average out pretty close to the correct probabilities over a game.
Nobody as good at backgammon as he was believes that there is such a thing as unlucky dice. At least, not at the level of an entire game. It can and often does happen that unlikely things happen with a single throw. But not on average most of the time. So I knew he was lying ... and it suddenly became obvious I'd been hustled and was being hustled for more.
As the saying goes, I made my excuses and left. It was lucky he said that about the dice and clued me in. If I'd played on I'm sure he'd have taken me for another £8 or £16, or maybe even more if he deliberately let me win a pound in the next match to give me false confidence.
Also, I realised in retrospect - as I mused gloomily on my unwisdom - that the dice could've been fixed. Having his set weighted to roll lots of 6s would've been too obvious, and vulnerable to swapping. But that's not the only way to do it. For example, if one set or both were weighted to materially skew the probabilities from the normal ones - not too obviously, but enough to throw the usual assumptions off - he would know the difference and his opponents wouldn't. That should be enough to have a decisive advantage, even if he were playing someone at about his level or above. If you were really, really good, you might be able spot someone playing the probabilities 'wrong' - but of course, if someone starts to suspect him, he could offer to swap dice, and play the skewy probabilities the other way round.
And much later, when I had got interested in the practicalities of magic and had learned more about sleight of hand, that fixing dice rolls (even with fair dice) is not nearly so impossible as I thought.
Looking back, it was a very useful experience, although mostly in the sense that it has made me very, very wary of anything that looked like it might turn out similar. If you're going to be fleeced, it was one of the more enjoyable ways of it happening. He was very good at both backgammon and hustling, and it's always interesting to observe skilled people at work.
This entry crossposted to http://doug.dreamwidth.org/300280.html, where there are
comment(s) not shown here.
ciphergoth's bets about Jeremy Corbyn.]
That put me in mind of other times when I've been wrong. The most spectacular in number terms was this example, where I was working out the ratio of aluminium to gold atoms dissolved in a simple electrochemical cell, and got the answer wrong by a factor of 10130. That really is quite wrong. I have a soft spot for
ciphergoth's maxim that it is better to pull numbers out of your arse and use those to make a decision than to pull a decision out of your arse, but I'm not always sure that applies. In that context it's salutary to reflect that numbers I produce with considerable thought, justification and on the basis of robust and really pretty settled science can be wrong by a factor of a billion quadragintillion.
Happily, though, the practical consequences of that particular mistake were no more than a slight loss of face - and even then, not a lot of face, because the guy who set the problem half-expected me to make that very mistake and was very nice about it.
One of the most painful mistakes I've made in terms of cold, hard cash was deciding to play a backgammon hustler. I've probably lost far more money in later mistakes, of course, but at the time it was a share of my disposable income that really hurt, and nothing since has come close.
I was a student, 21 cocky years of age, and had become interested in backgammon. I studied and practiced and got good enough to easily defeat the computer versions available to me at the time. (It was 1992. I strongly suspect they're way, way better now, but I'm much worse and not so interested in backgammon.) The computer opponents didn't play very interestingly, either.
So my issue was finding good people to play. There were some friends who were happy to give me a game, but most of them weren't particularly good, and the rest were only about the same level as me. And none of them were prepared to play for money, which is supposed to be the point. We were all skint.
[Unedifying "in-my-day" rant about how students don't act skint any more skipped for everyone's benefit.]
One lunchtime I went in to one of the student locals. (The Charles, for those who know York.) I was skint but not so skint I couldn't afford a pint now and then. You could get beer for less than a pound a pint at the time, but only in a few places if you knew where to look.
While I was there, I met an older guy who had a backgammon board and was looking for a game. He was offering a pound a point.
For those who don't know: in backgammon, simply winning is worth one point. But there are ways to win more than that, which we will hear more about shortly.
That was real money, but I was so excited to meet someone who was clearly pretty good - otherwise why would he offer to play for money to strangers - and was prepared to play a 'proper' game. Worst case, I thought, was that I get a game with someone really good and maybe lose a gammon (which is two points), which would be much of my beer money gone for the rest of the day, but probably worth it for entertainment value. It did cross my mind that he might have loaded dice, but I thought it was unlikely, and the fact that one can request to swap dice at any point would make it pointless.
(This was obviously wrong, I realised later, and not a defence against loaded dice - see below. Also, I hadn't appreciated how easily one can cheat at dice rolls with enough practice. Coin tosses are relatively straightforward, especially with an unsuspicious audience. I startled my kids the other day by tossing a coin ten times and having it come up heads every time, until they said it must be fixed and heads on both sides, and I said Ok, let's have a tails then, and got one. Hopefully they now understand the importance of a coin toss spinning in the air and landing untouched on the floor.)
Anyway. I sat down, and the game was on. We rolled one die each to see who started. Oops! They were the same. That's an automatic double.
A what? Well, in backgammon-for-money there's a doubling cube. This is mostly used for challenges, which we'll come on to, but sometimes there are events that trigger automatic doubles. Before you start to play, it is important for the players to establish what is and is not a trigger for an automatic double. I hadn't done that. I had little experience of for-money play, but I knew that rolling the same number to start is an almost-universal one: if you have any automatic doubles, that'll be one of them.
Oh dear. Now the stakes were doubled from what I'd thought. Not good.
Then we rolled again. I can't remember what rule he invented that triggered a further automatic double, but I'd never heard of it. He did seem very firm about it, and I lacked the experience to say it was wrong, and nobody around the table (we had a bit of an audience, mostly my friends) objected when I looked round, so I accepted that.
Oh dear oh dear. Now we're at £4 a point and we've not even started.
The game got going. He was playing well - unlike other people I'd played, I didn't spot any obvious tactical mistakes. I was doing Ok, but was definitely behind. Not unrecoverable, but not winning.
Then he offered me a double. This is the strategic, 'challenge' use of the doubling cube in the game. Basically, if someone offers you a double, you can either accept and play for twice the stakes, or decline and immediately lose at the existing stakes. If you accept a double, you gain 'control' of the cube, so you but not your opponent can offer a further double, e.g. if the tide swings substantially in your favour.
A full analysis of the doubling cube is well beyond this post. However, suffice to say, on most analyses, there exist situations where it is rational for a double to be offered and accepted, even if the players agree about the chances of a win.
Of course, in retrospect, I should've refused. (In retrospect I should never have played, come to that.) But he carefully managed it to make it look like I would be chicken and lose face to all my friends round about and would spoil the game were I to decline. I knew I was behind, but I didn't think I was so far behind as to merit refusing a double. And at least if I accepted, there would be no more doubles - I sure as hell wasn't going to offer him one - and my losses would at least be capped.
So I accepted.
We played on, and my relative position deteriorated, and it became painfully apparent that he was playing better than I was ... and things started to look really grim.
If you're losing badly like this, there is a way of playing called a 'back game'. Again, details are beyond this post, but essentially you occupy a couple of points in your opponent's home board while bringing a couple of runners slowly home, and hope that you can hit the blots they inevitably need to leave as they bear off, and leave them a closed board to come in on. It's a long shot, which sometimes works ... but to have any realistic chance, your position has to meet certain criteria (notably, to hold at least two points in their home board and have at least one runner to come round slowly), and mine emphatically didn't.
I sat miserably with pieces on the bar as he efficiently and effectively bore off all of his pieces while minimising the chances that I could get in or hit a blot of his. I did manage to escape a backgammon (where you still have pieces on the bar, or in your opponent's home board, when they finish) but he still beat me by a clear gammon (where one player gets all of their pieces off before the other has started). A backgammon counts for three times the current stakes, and a gammon scores twice the stakes. Which were, by now, 8x.
I paid up £16, feeling wretched. That wasn't just my beer money for the day blown.
He was very consoling, and was full of praise for how well I'd played, how I'd cleverly tried to tempt him in to setting up a back game, and how interesting it had been, and so on. I was not looking happy. He offered me another game, and I said no.
He tried to persuade me, and I was very slightly wavering. Luckily for me he made the tactical error of saying I'd had very unlucky dice.
Now, backgammon is a dice game, and that opens up the possibility of being more or less lucky. The key to playing well is to correctly work the probabilities to maximise gain - and, importantly, minimise the chances of loss - on every move. Sometimes the dice work in line with probability, sometimes not ... but you throw the dice many, many times in the course of a game, and the law of large numbers tells you that they are going to average out pretty close to the correct probabilities over a game.
Nobody as good at backgammon as he was believes that there is such a thing as unlucky dice. At least, not at the level of an entire game. It can and often does happen that unlikely things happen with a single throw. But not on average most of the time. So I knew he was lying ... and it suddenly became obvious I'd been hustled and was being hustled for more.
As the saying goes, I made my excuses and left. It was lucky he said that about the dice and clued me in. If I'd played on I'm sure he'd have taken me for another £8 or £16, or maybe even more if he deliberately let me win a pound in the next match to give me false confidence.
Also, I realised in retrospect - as I mused gloomily on my unwisdom - that the dice could've been fixed. Having his set weighted to roll lots of 6s would've been too obvious, and vulnerable to swapping. But that's not the only way to do it. For example, if one set or both were weighted to materially skew the probabilities from the normal ones - not too obviously, but enough to throw the usual assumptions off - he would know the difference and his opponents wouldn't. That should be enough to have a decisive advantage, even if he were playing someone at about his level or above. If you were really, really good, you might be able spot someone playing the probabilities 'wrong' - but of course, if someone starts to suspect him, he could offer to swap dice, and play the skewy probabilities the other way round.
And much later, when I had got interested in the practicalities of magic and had learned more about sleight of hand, that fixing dice rolls (even with fair dice) is not nearly so impossible as I thought.
Looking back, it was a very useful experience, although mostly in the sense that it has made me very, very wary of anything that looked like it might turn out similar. If you're going to be fleeced, it was one of the more enjoyable ways of it happening. He was very good at both backgammon and hustling, and it's always interesting to observe skilled people at work.
This entry crossposted to http://doug.dreamwidth.org/300280.html, where there are
comment(s) not shown here.