A look back at previous posts has convinced me that a change of pace is in order. Since this blog is free to concern itself with all forms of “spirited reasoning,” I thought I’d turn, for at least one post (and maybe two or three), to a light-hearted topic, one of my favorite hot button issues: the wrong-headed wagering I keep seeing at the end of Jeopardy, America’s timeless gameshow.
In a nutshell, my gripe is that contestants who reach the Final Jeopardy stage in third place–that is, in last place behind the other two contestants–too often park their rational brain outside the television studio. Their thought process appears to go something like this: “Gee. I’m in third place. So, the only way I can win is to bet everything on the final question, hoping I’ll get it right while the other two contestants get it wrong.” And, time after time, the third place candidate either watches his/her winnings drop to zero after getting a very hard Final Jeopardy answer wrong, or they manage to get it right, only to see one of the other two contestants win the Jeopardy match because, after all, those other two contestants had more money to bet with.
There is often, however, a working strategy for the third place contestant, and that is to bet zero or close to zero, in almost every case. Let’s take a look first at why that strategy often makes more sense than betting the farm.
To keep things simple, let’s suppose the leading contestant is facing Final Jeopardy with $10,000, followed by the second-place contestant at $7,500. You, in third-place, are sitting on only $6,000. How can you possibly win with only one bet remaining?
Here’s how. Instead of trying to be the one lucky stiff who get’s it right, you only need to hope for a Final Jeopardy answer that’s so extremely difficult, or tricky, that all three contestants get it wrong. If you watch Jeopardy as often as I do, you’ll know that a tough one like that comes along approximately once a week.
Now, let’s look at why the strategy works. In the situation described above, the leading contestant will probably wager exactly $5,001 dollars. Why so? Because contestant number 2 can wind up with $15,000 by betting everything, and the leader wants to close out that possibility with the smallest bet possible.
What, then, should your wager be? By betting zero, you can be sure to wind up with a score of $6,000, regardless of whether you get the answer right or wrong. If all three contestants get the answer wrong, contestant number 1 will wind up with only $4,999 (after that $5,001 wager.) If contestant number 2 followed suit and wagered everything, he or she would wind up with zero. And even if contestant number 2 wagered less than everything, any wager greater than $1,500 will drop him or her below $6,000. You wind up in first place!
Note that if you had made a large wager, you would limit your opportunity of winning to exactly one extremely rare situation–the one where you somehow manage to nail the Final Jeopardy answer correctly while both of your opponents get it wrong. (Very unlikely odds, especially since the other two contestants are smart cookies, as proven by the fact that they outscored you during the Single and Double Jeopardy rounds.)
By betting zero, you have given yourself two chances to win. You still win in that very unlikely scenario–the one in which you’re the only person to nail the final answer. You didn’t need to bet the farm. Why not? Because the other two contestants were forced to wager an amount that was too high. Let them be the ones who take the hit!
But here’s the beautiful part: By adopting this strategy, you also stand a good chance of winning in the more common case, the one that occurs when all three contestants get the answer wrong.
This strategy will only work if you have not been mathematically eliminated–meaning those situations where you are so far behind that the first two contestants can afford to keep their wagering small, get the answer wrong, and still finish ahead of you. But I’ve seen far too many cases of third-place contestants going for broke on the final question, all to no rational end, when they would have won the game if only they had practiced a more disciplined wager.
The only situations in which the third place contestant should make a large wager happen when (a) they are so far behind that they can only win when the most unlikely scenario occurs, as described above, or (b) the leading contestant cannot be caught, and they are just aiming to finish in second place rather than first. (The Jeopardy rules used to provide nothing for second and third place finishers, but now the second place finisher takes home $2,000 and the third place finisher receives $1,000.)
Maybe next week we can look at things from contestant 2’s point of view!