Tuesday, December 17, 2013

My gambling problem

This isn't going to be a confession, sorry. The problem is this: is gambling rational?

Very often people say that it is not rational to buy lottery tickets, even going so far as to call lotteries a tax on stupidity. I dislike that joke partly because I think it's more accurate to call it a tax on desperation, and jokes at the expense of the desperately poor aren't funny. Partly, also, because I buy lottery tickets from time to time (despite not being desperately poor), and jokes at the expense of me are never funny. There's also the fact that it is rational to buy a $1 lottery ticket if you get $1 worth of pleasure from it. And fantasizing about what you would do if you won can be very pleasant (much more pleasant if you have a ticket than if you don't). Or at least as pleasant as about a third of a latte. But, here's the problem, is that fantasizing rational? It isn't realistic. It's not like fantasizing about what you might do with money you know you are going to inherit or get from selling your business, say. It's not like fantasizing about spending money you know you have a realistic chance of getting either. It's sheer fantasy. It's not taking pleasure in an aspect of reality but in a kind of escape, or looking away, from reality. And 'irrational' might not be the right word for that kind of pleasure, but it's in the ballpark.

A related issue is the rationality of voting. It's often said that voting is irrational because the cost outweighs the likely benefits, much like gambling. Max Black, as I recall, argues that it can be rational if the stakes are high enough. He's right that the likely benefits need to be taken into account, and not just the odds of one vote being the decider, but I don't think this is enough. In many elections the good candidate is not so much better than the bad candidate that voting is rational on some kind of cost-benefit model. But the idea that voting is irrational immediately raises the question: what if everyone thought that way (and acted accordingly)? It would, most people agree, be bad. Can it really be rational to behave in a way that would be bad if universalized?

It depends, of course, on your conception of rationality. The dominant one is roughly Humean and the alternative I'm groping towards is roughly Kantian. The Humean one counts as rational any act that is an effective means to whatever your ends may be. The more effective, the more rational. So buying lottery tickets is irrational if your end is maximizing your expected wealth, but it might be rational if your end is maximizing your expected pleasure. There is no question, though, whether it is rational to have this or that end.

It is slightly amazing that that conception of rationality has caught on, given how counterintuitive it is. As Anscombe points out, it is irrational to want a cup of mud or to put all your green books on the roof (in the absence of something that makes it rational after all, of course). It is irrational--insane--to want to be killed and eaten. If we are going to distinguish the sane from the insane then I think we need this sense of rationality. The mentally ill are not just inefficient or wrong about the facts. Sometimes their ends make no sense. So I think we need something like the Kantian notion of rationality, and if we use this instead of the Humean one then problems about the rationality of voting go away, while the idea that buying lottery tickets is rational (except perhaps in odd circumstances) also goes away. This also speaks in favour of the Kantian notion.

The problem, of course, is that this notion is obscure. It is closely connected with a notion of humanity, of what it means to be human, and that is difficult terrain. It is also essentially normative, which complicates things. Those aren't reasons to give up on it though.        


  1. I'm more or less against gambling on games of chance such as fruit machines ("slots" as Americans would say), blackjack, roulette and so on. But actually I have no problem with people throwing a weekly pound (or dollar) at the lottery.

    The reason for the difference is that you have to take into account the difference the money will make to you if you happen to win. So, with most fruit machines for example (a) the odds are stacked against you (you get back an average of about 85p for every pound wagered which is a whopping edge for the House - compare it to casino blackjack where the average edge is about 3%) but also (b) even when you get lucky you don't win all that much. So if you play regularly for several years you're pretty much bound to be down even if you hit the jackpot more often than the stats say you should.

    With the lottery (a) is still true, of course. In fact the House's edge is enormous. But it's a different matter when it comes to (b). Yes, you're very unlikely to win the jackpot but, supposing you buy one ticket every week then if you do win there's basically no way you can wind up an over-all loser even if you carry on betting at the same level. You're not going to live long enough!

    Really, that's an overly mathematical way of saying that given the small outlay and the life-changing sum you stand to win there's no real harm in having a punt. It's a different matter, of course, if you're a poor person buying 20 tickets a week. Then it really is a problem. (And, by the way, the lottery isn't a tax on the stupid as some claim; it's a tax on the poor.)

    Over and above that, there's something fascinating about the mind-set of people who gamble. It's not that they're stupid - most of them know full-well the odds are against them. The real attraction is not at a rational level at all (and therefore isn't irrational either). I think it's much deeper than that. In fact, I'd almost be inclined to say it's about testing yourself against fate. You put yourself on the line and see if you're one of the chosen ones. And if you weren't chosen today then perhaps you will be tomorrow. But, as Jesus said after blowing all his wages playing dice, "Many are called but few are chosen".

    1. Yes, buying the occasional lottery ticket seems fine to me. The cost is almost nothing (as long as you're not buying lots of tickets on a low income, as you say) and the potential profit is enormous. But you aren't going to win. It's an exercise in fantasy. I don't think it's immoral or crazy, but I wouldn't call it rational either.

      the lottery isn't a tax on the stupid as some claim; it's a tax on the poor


      I don't know what the mind-set of people who gamble is. The only gambling I've ever done is of the "just a bit of fun" variety, and I'd be just as happy, if not happier, gambling when nothing real was at stake at all. It's gambling as a game that I like. But there are people who gamble huge amounts and/or don't seem to treat it as a game at all. Perhaps they are testing themselves against fate. That seems vaguely crazy, to be honest, but perhaps I'm misunderstanding your point. It isn't stupid but it sounds very superstitious.

    2. It's probably a mistake to suppose there's one type of gambler. People gamble for all sorts of reasons, and insofar as it administers to something deep within them the nature of that "something" will obviously vary from person to person.

      But one thing I've noticed, both in myself and others, is that we do not have a straightforward, functional relationship with numbers in action. In particular, random processes (picking numbered balls out of a cage, working the roulette wheel, etc) trouble us when we have something vested in the outcome. It's all obvious and clear-cut when we're just watching the dice roll, but bet $100 on the result and see how things change! It's not just that you hope you win (and dread losing) though obviously that's true. Your attitude to the process itself is transformed.

      Imagine a gambling game where a computer said "Take 3/1 on a 7/2 shot?" and if you clicked "yes" it simply informed you that you'd lost (or won). No-one would play that game even if they were certain nothing crooked was going on. We want to see the dice roll, the cards turned, the ball drop. We want to see fate work itself out.

      I'll stop because I'm doing a poor job of putting this into words. But our attitude towards a random process when it's being used to decide something important to us is (for me) a fascinating, subtle and multi-layered phenomenon.

    3. It's probably a mistake to suppose there's one type of gambler.


      Imagine a gambling game where a computer said "Take 3/1 on a 7/2 shot?" and if you clicked "yes" it simply informed you that you'd lost (or won). No-one would play that game

      I think some people would, although it doesn't much affect your point.

      We want to see fate work itself out.

      This is interesting. Is it something to do with wanting to know whether the world is currently on your side or not, whether things are going your way? If you think that way, as many people do at least some of the time, then it would be fascinating to see the unfolding of events. Almost as if the fates are right there in front of your eyes making the dice roll this way or that.

    4. Something to do with it, yes. But I'm not sure there's any tidy description that fully captures the complexity of what's happening. It links to some very strange corners of our lives.

      For example, one way I'm inclined to put it (which connects but not directly with what we've been saying) is that our attitude towards random events in that type of situation resembles our attitude to the ideal of the machine. And my best attempt at characterising that attitude would be to say that it's a curious mix of abhorrence and worship. Does that make any sense at all?

    5. Some, yes. Less the fates and more a cosmic machine, then. Or the cosmic machine. Or an attitude towards randomness that resembles an attitude toward a cosmic machine. (I'm not sure I've completely got it, to be honest.)

    6. Ha! That wasn't my most lucid comment was it? (I promise I've not been on the Brown Ale.) I'll try to elaborate.

      On the one hand a machine can symbolise a kind of pureness or ideal form of rationality. It's precision, economy, and so on. At the same time there's something disturbing about it. It does things, like a person, yet it is sterile, implacable and at times brutal. It is like us and yet utterly unlike us.

      In either case, though, it is more powerful than we are: faster, stronger, quicker, more efficient. And so it can be an object of both fear and desire, abhorrence and worship.

      And I think there's a hint of all this in relation to certain gambling scenarios as well. The analogy is not exact, but (hopefully) provides an illuminating comparison. Think of the implacability of fate, the purity of randomness, and yet also the sense that a decision is being made.

      Hmm. I might just have made things even more confusing.

    7. Oh, btw - here's a wager that kind of represents the flip-side of my point about the lottery.

      Suppose you're an extremely poor family man and someone offers you a bet. A number between one and five million will be picked. If it's seven then you lose. Any other number then you win. If you win you get a million dollars. If you lose your daughter dies.

      Do you take the bet? What's the right decision? What's the rational decision? Are they the same?

    8. That's a good example. It's probably rational to take the bet in the sense of 'rational' that I want to reject. It's not right, though. And therefore not reasonable. And therefore not rational in the sense of 'rational' that I prefer. But then it might depend how poor you are. Do you need the money? Does your daughter need it? It sounds like a short story (in which, of course, seven is the number that comes up.)

      The machine business sounds (a bit) like Kafka's penal colony story. There's a sort of fascinating horror. But I can't really see it appealing to anyone much (despite the fascination). Is gambling part of any religions? It seems as though it ought to be if many people feel the way you describe. There's fortune-telling, of course, but lotteries for human sacrifice sound more like it. The Beltane cake, for instance.

    9. Funnily enough when I read back my description of the machine Kafka's story occurred to me too. That's an interesting connection for reasons we'll get to shortly.

      Aside from fund-raising raffles, I can't say that gambling has ever played much of a role in religion (though your Beltane cake example is fascinating). I'd say that was because the mythic outlook in which religious practices developed was far more organic in character. The machine was not an ideal or symbol for them - or, at least, not a particularly powerful one. Religion has of course developed over the millennia, but it seems to have retrained that organic character. God, as a symbol, is patriarchal not mechanical.

      But the machine and its correlates are symbols for us. From actual machines, to pseudo-machines (bureaucracies, time-keeping, job selection processes, etc, etc) they dominate our lives. They have replaced (or transfigured) the organic outlook in which religion developed (indeed the very concept of an organism has received a mechanistic make-over).

      And as the machine becomes a powerful symbol there is a corresponding urge to deify it. Think of the strong pseudo-religious flavour of New Atheism - they even have their own saints (Newton) and martyrs (Galileo).

      Kafka comes in here too, because both his penal colony and his trial take the idea of religious judgement and recast it a modern form: a machine on the one hand, a bureaucracy on the other.

      From this point of view, it could be that at times gambling represents an outlet for a spiritual urge - but one that has been distorted to fit the myths of modernity. Think of the similarities (and differences) between gambling and praying.

      I agree with your analysis of the wager. There's simply something not right about taking it no matter how much consequential reasoning suggests otherwise. I put the question to Twitter last night. Interesting results: four women answered quickly with an emphatic "no". When I mentioned the potential benefits to the child (including an over-all increased chance of survival) they refused to budge. A little later three men responded. They all said "yes, of course". Hardly statistically significant, but still...

    10. Yes, God is not mechanical. That's one of the best things about him. And you're probably right that gambling can be an outlet for a spiritual urge.

      I had just read your tweets about the wager before I came here and saw your comment. More proof that women are better than men.

    11. Maybe, but as a friend pointed out to me tonight: how far were they speaking from their heart and how far were they merely saying what they'd been taught women ought to say?

      Same goes for us men, of course.

    12. Yes. I should have put scare quotes or something around "women are better than men." There's the point about women and men, of course, but also about ideas of moral goodness. I feel an incoherent ramble coming on...

  2. van fraassen, the empirical stance, 'bridled irrationality':


  3. Thanks.

    If rational belief is belief within the bounds of reason, though, then isn't there still a question about where these bounds are? It isn't insane to vote or not vote, play the lottery or not play the lottery, but there is a kind of unreasonableness in not voting and a kind of irrationality in voting. And the unreasonableness of not voting, the anti-social, anti-democratic aspect of that kind of (non-)behavior also exists in the judgement that voting is irrational. I.e. the use of that notion of rationality (at least sometimes) is itself unreasonable in the way that not voting is unreasonable. A puritanical refusal to gamble ever might also be unreasonable. It might be anti-social, for instance, even if not strictly anti-democratic. But excessive gambling is certainly unreasonable too. As is living in a fantasy world, although not every bit of day-dreaming is a crime against reason.

    I should add that when I say that not voting is unreasonable I mean adopting the principle of not voting on the grounds that it is not in one's self-interest is unreasonable. Not voting because the candidates are all bad, or because they aren't great and it's raining, etc., seems reasonable enough. But I don't think there's a very clear place to draw the line.