## Thursday, May 10, 2012

### Care To Bet on That?

In all the preparing for Jeopardy, the most dreaded aspect was wagering. Everyone can remember a time when they watched someone completely blow a game because of a wager that was too large or too small. Heartbreaking. Of course I wanted to avoid that, but here's the thing - I've never really enjoyed math. Besides that, though, wagering is less like plain old math and more like chess crossed with probability. I was terrible at probability when we did that section in school. I could never understand how many tries it would take to pull out a pair of socks from that drawer.

Now I'm married to a mathematician. That would seem to make it easy. In fact, when one of my fellow contestants heard that, she said, "oh, so he could tell you what to do." Well, it's not quite like that. I have a hard time memorizing things like math - I need them to make sense to me. I can't believe "just because" or "just do this, it works" as a reason. Here's a case in point: a couple of months ago, someone online brought up the Monty Hall problem. I had never heard it before, and so I talked to Morgan about it. Well, actually, it's more like we argued about it for an hour. He explained the right answer to me, but it still didn't make sense. So I argued my position, and asked "but why..." a million times, and in the end, I got it. I not only knew the answer, but I understood it.

Which brings me back to why it very quickly became clear that the wagering calculator at the Jeopardy archive, while an incredibly useful tool, was just not going to work for me. It explains all the various rules for wagering - there's a 3/4 rule, and a 4/5 rule, and a 2/3 rule, and all kinds of other permutations (are scores evenly spaced? Do two scores add up to another score?) that started making my head swim. So I asked Morgan to look through the whole mess and explain it to me in a way I could make sense of. He did a fabulous job, but overall after many days we were still at the "but why ..." stage for me, and I wasn't feeling any more confident at betting. One mental block I had centered around wagering recommendations that seemed to create a loss - betting big, where clearly you'd win if you were right, but you'd not only not win if you were wrong, you'd be dropped all the way to 3rd place. This seemed wrong to my risk-averse mind. Eventually, though, I started to understand that the probabilities mostly take into account winning vs. losing (2nd and 3rd are both losing - you either win or you don't, after all), and additionally are trying to prevent situations that actually turn a win (you got the answer right) into a loss (you bet too small and someone was able to pass you). So I was able to get into the right mindset, which is summed up in three little words: play to win. Seems simple, but it was hard for me to get over the fear of ending up last.

Anyway, once that was straightened out, I had the right attitude but I still lacked the skills to consistently come up with the right answers, let alone do it quickly. First I was looking at the scores and trying to figure out what situation they fell into, and then I was doing the math for what I thought my bet should be. But when I checked my answers against the wagering calculator, I kept finding things I hadn't thought about or realizing that the scores actually fell into a special case. I was a mess, and Morgan's explaining wasn't helping me any. Worse than that, I couldn't tell him exactly what it was I needed from him. So I asked him to go away for a while and I would figure out where the disconnect was happening for me, and then he could help fill in the blanks.

This resulted in me coming up with a chart of all the numbers, and then asking him to show me what they all meant for wagering. Morgan was impressed that my little chart really did provide all the info necessary to make a wager, and once I had it, he was able to help me learn to interpret it. Here's what you do, step by step (this one focuses on 2nd place, because 1st place normally has it easiest, needing to bet to cover second's doubled score, and 3rd place's figuring often needs to know what 2nd should do).

First, write down all three scores. I start with third on the left. The lines in between them are for the differences between the scores. (I chose to work with round numbers and put "R" or "W" next to them so I would know if I should add a one, thus removing a place where I could make stupid computational mistakes.)

Next, fill in second and third's doubled scores.

Now that you have the doubled score for 2nd, you can fill in what first place's bet to cover should be. I write the number up above first's score and then actually add it, putting the total below to make sure I'm not making any dumb math errors.

The final math steps are to subtract first place's covering bet and put that under his column, and then figure out the difference between your current score and that number, then between your current score and third place's doubled score. Fill in those numbers along with an R or W designation.

Now you have all the information you need to figure out how to wager. Ideally, you want to make a wager that will meet these conditions: if you get it right, you will stay above third place's doubled score (this is your minimum bet), and if you get it wrong, you'll be above first place's wrong answer (this is your maximum). In the example above, it works out that you can do exactly that by wagering between 4101 (add the dollar for the "R") and 4900 (it's a "W," so leave the number as is).

This is a basic example, but using this will cover all the eventualities - if your minimum bet turns out to actually be more than your maximum bet, you're in what they call "Stratton's Dilemma," where you have to decide whether you hope to win on a right answer or a wrong one. There are also a couple of situations where you have to take into account double the difference between your score and first place's current score, but again, if you practice with this and check your conclusions against the wagering calculator, it'll become clearer. If you're interested in more examples or how to use this system, feel free to drop me a message.