Yes, this is your first hint that my blog will be all over the place thematically, LOL.  Future posts may be about poker, tennis, politics, music, random things that annoy me, or even esoteric intellectual/philosophical questions of epistemology or the like.  This one is about a cheesy game show, though it does involve some discrete mathematics (probability calculations) and psychological “risk of ruin” issues that economists like to study.


[UPDATE: Those unfamiliar with the game should read the explanation here.]

A recent contestant (with the ironic surname Einstein, I kid you not) accepted an offer for $23,000 with six cases left (five on the stage and one she is holding), including the $500,000 (top amount), plus one containing $25,000, and four small amounts of $1,000 or less.  If she passed up the offer, she would have had to open two more cases before getting another offer.  This is right at the point just before when the offers usually improve markedly, in terms of what percentage of the average expected value (EV) is offered.  (To get the EV, you just add up all the amounts left and divide by the number of cases left.)

In this situation, her EV was about $88,000; so the offer was barely over 25% of her EV.  And for some context if you don’t watch the show, $23,000 is a generic offer you might get really early in the game (she had passed up $24,000 a couple offers earlier).  If you go one more round, your offer’s going to be more like 70% of your EV; the round after that (when there are two cases on the stage and one with the contestant), over 80%; and then the final offer (which you have to either take, or take what’s in your own case) is for some reason always just a titch over EV, like 101%.

And the show makes you go through the whole “what if” scenario, opening the cases in the order you think you would have opened them if you kept playing.  It turned out this contestant actually had the half million in her case, so as she went along, her next (hypothetical) offer was $84,000, the one after that $139,000, and the final offer was $251,000. 

Now of course she couldn’t know she actually had the big money in her case.  But in this scenario she definitely should have gone one more round.  She only would have really badly screwed herself if she had eliminated precisely the top two amounts.  I’m not sure exactly how the math is affected by the fact that she couldn’t choose to eliminate her own case, but I’m thinking it doesn’t matter, based on poker (you don’t know what the other players have, but you compute your odds of hitting your flush as if the deck the dealer draws from includes the cards that have been dealt out to players).  And if indeed it doesn’t matter, then as long as her own case is a mystery to her, here are the odds of various scenarios (not bothering with the specifics of the four negligible amounts) after playing one more round:

(1) Worst case.  The chance of eliminating the $500,000 and the $25,000 with two picks is 2/6 * 1/5, which is 1/15, or less than 7%.

(2) Best case, keeping both the $500,000 and $25,000 in play is 4/6 * 3/5, or 40%. 

(3) Knocking the $25,000 out but keeping the $500K in play has a 27% chance of occurring.

(4) Likewise, knocking out the half mil but keeping the $25K also has a 27% chance of happening.

Scenario (3) is what actually would have happened, which would have meant an offer of $84K which she probably would have been right to take since she had no “safety net” of more than one significant number left.  Had the best case scenario happened, the offer would have been slightly more, but it would have been a little more tempting to continue (but still a reasonable, safe move to stop).

Scenario (4) would have hurt, of course, but she would still get an offer of about $4,000 which she could take as a consolation prize, or she could gamble and continue with that $25K still up there.

Einstein carried “lucky dice” with her and handed them to Howie (his disgust was evident–he is a germaphobe like I am).  I wonder then if she would have made the same choice had it been a dice game, with the following proposition:

“You can keep $23,000 or make one roll with two dice.  If you get a three or less, you get five hundred bucks.  If you roll a six or an eight, you get $4,000.  If you roll a four, five, seven (most common roll), nine, ten, eleven, or twelve, you get $87,000.  Deal or No Deal?”

I couldn’t make the dice odds fit the game odds exactly, so I erred toward actually decreasing slightly (down to under 64%) the chance of hitting one of the two scenarios where the offer gets increased substantially.  I still suspect though that she would have passed up the offer had it been framed this way!

Or at least, that the things they do to their kids are morally wrong. 

A lot of people don’t, as you might imagine, appreciate being told the way they parent their children is unethical.   They insist “you raise your kids your way, let us raise ours as we see fit”.  When it comes to a lot of parenting decisions, I think that’s valid as far as it goes.  I might not think letting kids drink soda is the best parenting practise, but I’m not going to campaign to make it illegal.

There are however lines many parents cross that are simply beyond the pale.  These are lines that are not (yet) recognised by the majority as abusive or neglectful parenting, but which I as an AP activist (and lactivist) believe are deserving of that kind of recognition.  Once societal consensus is strong enough, we might reach the point where a bright red legal line is drawn.  But on the way to that consensus, there are many milestones along the way, with their own lines (some things, for instance, are widely frowned upon even if not strictly illegal–but the social pressure is no less real for that technical legality).  Progress along these milestones always starts with a vocal minority loudly challenging the status quo, and refusing to bow to reactionary pressure to stop challenging the conscience of the majority, refusing to stop making them uncomfortable.

Specifically (and tip of the hat to Rachel at Free Childhood for inspiring me to see these in their own category), I think circumcision, spanking, and “cry it out” (CIO) sleep training are particularly heinous; there is no excuse (other than perhaps ignorance) for inflicting any of them on a child, and I will never acknowledge them as a valid choice for a parent to make.  For this post, I’ll focus mostly on CIO, but the point holds for the other two as well.

The process of social change, as pushed forward actively by activists (that’s after all why they are not called “passivists”, right?) can be best seen by using three examples that are at different stages of this process: child labour, corporal punishment, and CIO. 

A century or a little more ago, it was commonplace for children in low income families in urban areas to work long hours in dirty, dangerous factories.  A group of (mostly female) reformers started kicking up a lot of ruckus about this, and highlighting the plight of these poor kids, and social attitudes changed, followed by changes in the law.

Many people alive today can remember when it was generally understood that a parent had a right to beat their children with a belt or a stick–even if most people didn’t do it, they didn’t feel they had the right to tell other parents how to raise their children (sound familiar?).  In those days, schools commonly used wooden paddles to punish errant pupils.  Today, the process of reform is still ongoing, as spanking continues to be tolerated as more brutal beatings once were.  However: a parent who uses a belt or stick is likely to get into legal trouble; schools don’t dare strike children; and the last bastion left (open hand spanking by parents) is under increasing pressure of negative social opinion.

CIO is clearly at an earlier stage than either of these other examples.  But just a couple decades ago, parents could easily go about their lives without ever being confronted by those who consider CIO immoral.  These days, if they want to avoid being confronted with this kind of disapproval, they had better stay off the Internet and stick to a narrowly proscribed social circle.  This is a change for the better.  To those who insist that we should back off, let parents make their own decisions about CIO without being pressured or criticised, I defiantly declare just the opposite: these complaints show we are having an effect, and if anything, we need to turn up the heat, tighten the screws! 

I want parents to feel that if they CIO, it’s going to be something they have to feel nervous and at least a bit guilty about.  If that gets a bunch of mainstream parents pissed off at me, I can deal with it.  If you think I’m wrong, step up and say so.  I don’t want an echo chamber here.  I am confident enough of the rightness of my argument that I don’t shrink from debating it with any and all comers.

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