Stupid Jeopardy! betting strategy

Cafe Society
1

Why do most players do this: bet enough to beat the next player by a dollar? In most cases it doesn’t make sense.

For example, entering Final Jeopardy we have the following scores:

Player 1: $3,000
Player 2: $7,000
Player 3: $12,000

Nine times out of ten, Player 3 will bet $2,001 so as to beat Player 2 by a dollar if they both get the final answer right. But based on the rules of the game, this is not his optimal strategy. (Only the winner gets the final total; the other two get fixed amounts of cash.)

Here’s what he should do: bet against Player 1, not Player 2, i.e. bet $5,999. This way, if he’s right he maximizes his winnings ($17,999) and if he’s wrong, he holds on to second place ($6,001). The difference in his final winnings is almost $3,000. Big upside if right, no downside if wrong.

But time after time, players don’t do this. Why not?

(Full disclosure dept: I won on Jeopardy! with the non-optimal strategy only to be criticized by a know-it-all acquaintance after the show aired. This was 15 years ago, and I can’t figure out why people haven’t wised up since then, like I have.)

2

I lost on my second day of Jeopardy! — by one dollar. :mad:

3

There’s always the chance that Player 2 will not bet all he has. If the Final Jeopardy answer is about internet linguistics and P2 doesn’t have a degree in “elite speech,” then he may only bet a fraction of his money in the hopes that P3 blows a big bet.

So P2 bets $2k. To his surprise, he knows the answer (well, the question) and ends up with $9k.

P3, being an elite haxor, confidently bets $5999, and gets the question wrong. His final tally is only $6001, and he goes home crying.
But yeah, I’m surprised the betting is so consistently conservative (redundancy!). You’d expect to see players go out on a limb at least a little more often. And it’s not much of a limb to go out on usually, anyway.

4

Um, to sum up, if P3 had only bet $2001, he would still have won even though he missed the last answer.

5

The unknown here is how much Player 2 is going to bet. Either way, Player 3 is guaranteed to win if he gets it right, and he’s guaranteed to beat Player 1 even if he gets it wrong. If Player 2 is going to bet it all, then yes, your strategy dominates. But we don’t know that Player 2 is going to bet it all. Suppose, for instance, that Player 2 doesn’t have a clue in that category. He knows he’s unlikely to get it right, so he’s playing for the second-place consolation prize, and wagers $0. If he does that, then Player 3 will win if he wagered $2001 (regardless of whether he gets it right or not), but he’ll get second place if he wagered $5,999 and got it wrong. In this case, unless Player 3 is very confident of his knowledge of the category, he’d be better off with the conventional betting.

6

There is an obvious explanation, apart from any other betting:

With the conservative bet, you know for a fact that Player 2 will have to get the answer right to beat you, even if you get it wrong.

Thus you won’t get burned by a wicked hard final question.
In your example in the OP, I would bet $4999.

Get it wrong, you end up with $7001. Still enough to put you out of reach of Player 3, and Player 2 still needs to get the question right to beat you if it is hard enough that you miss it.

7

And, if both 2 and 3 get it wrong, 3 takes home more money with the conservative bet than with the confident bet.

8

Biggest downside? Second place players can’t come back. Coming back another day means winning at least another few thousand. Therefore, the conservative bet has the biggest possible prize yield, because it leads to another playing day.

9

Right. The amount of money you come away with is secondary to winning.

Overall I think fewer leaders are using the “P2 + $1” strategy these days. They’re counting on the second-place player not to bet every dollar he has, and that’s usually how it plays out.

10

Wouldn’t an even better strategy for Player 3 be to bet $2000? That way if he gets it right and Player 2 bets everything ($7000) and gets it right then both players win $14,000.

Maybe I’m just too socialist–I guess I should think more American-like ('tis better to win $14,000 and deny your rival any winnings than for you both to win $14,000).

Ummm… actually, I’ll admit I’m not even sure that both players get $14,000 in this instance if they tie.

11

Yes, each co-champion gets $14,000 and returns to play the next game. The “share the wealth” counter-argument to this strategy is that your scenario allows only one waiting contestant to “come in from the bullpen” for the next episode, as opposed to the two new competitors who’d take the stage if two were eliminated by the “winner-take-all” strategy you decry.

12

Thanks for all of your well-reasoned and helpful answers. I think this is just another sign that after I appeared on Jeopardy! my brain decided that it had met its hardest challenge and could start taking it easier henceforth. For some stupid reason, I hadn’t thought of the possiblity of winning the game despite getting FJ wrong. But I’ll bet I had considered it at the time, and just forgot it since then.

There’s nothing worse than getting older, except the alternative.

13

I meant to add, on the topic of sharing the win, that although (despite being liberal, if not quite a socialist) I think it’s a bad idea to intentionally play to a tie in a regular game, because it pits you against an experienced player insteard of two newbies, the exception was in the fifth game, back when that’s as many as you could win.

When I was on, one of the other players made it clear before the taping that if he became a five-time champ, he would bet in the final so as to allow the second place player to tie him, thus enabling him to retire undefeated, and the other guy to win and move on as well. I thought that was a great strategy, and good sportsmanship, and always felt it was a little mean when people in that position didn’t do it.

14

I also wonder why so many players start at the top of the board. Starting at the bottom of the board will run up your total more quickly, so that when you hit the Daily Double you have some margin to work with…

15

Starting at the top gives you a better sense of the kind of question you’re likely to face, with lower risk. Knowing the lower value questions can also eliminate possible wrong answers to the bigger questions.

If you’re an expert on the subject, starting at the bottom may not be a bad strategy, but often the categories aren’t what they seem, or there are patterns in the correct questions that are more obvious from top to bottom (although this practice seems rarer now).

I heard of a player who jumped around the board just to throw off his opponents and make it slightly harder for them to find the next clue.

16

Wagering on Jeopardy! is harder than it appears. They don’t give you a calculator, you have a limited amount of time and everyone is watching you.

I kind of panicked when I was up there on my first day and I ended up betting twice as much as I needed to secure victory. It turned out the final question was easy and everyone got it right. I was richly rewarded for my bad arithmetic.

17

Well, let me think. If we disregard wagering based on knowledge (or lack thereof) of the category, let’s assume that each player has about the same chance of getting the question right. Given that, there are 8 possible outcomes of who gets correct answers: +++, +±, ±-, ±+, -++, -±, --+, —.

Given the respective scores, player three has 5 betting options: (1) bet less than $2000; (2) bet between $2000 and $4999; (3) $5000-8999; and (4) $9000-12000. (The break points are related to player #1 and 2’s minimum and maximum bets.)

Betting Option 1: In this case, he wins for certain only if #2 gets the question wrong. Given the 8 scenarios, this is a 50% chance of a certain win, and 50% chance of a possible win (i.e., dependent on the betting strategy of the other players).

Betting Option 2: He wins for certain if he gets the question right or #2 gets it wrong; he may win if #2 gets it right. 75% chance of a certain win, 25% chance of a possible win.

Option 3: He wins for certain only if he gets the question right (50%); he loses for certain if he gets it wrong and #2 gets it right (25%) and has a possible win if they both get it wrong (25%).

Option 4: He wins if he gets the question right (50%), possible win if they all get it wrong (12.5%), and certain loss if he gets a wrong answer and either of the others get it right (37.5%).

Given this, his best strategy for goal #1 is Option #2. To maximize winnings, he should bet at the high end of that range ($4999).

(This could be further refined by analyzing players #1 and 2’s betting options, but I’m too lazy to do that.)