Up until today I always pretty much assumed that the leader should (maybe with rare exceptions based on the category) always bet at least enough to surpass whatever total the second place person could win.
Today a 6 time champion had a 5000 dollar lead on number 2 who had a lead of approximately 15000 over number 3. Number 2 was clearly an excellent player as it was amply demonstrated during the game and even seemed to adopt many of the champion’s strategies.
It would seem to me the optimum strategy for number 2 should be to bet the amount necessary to overtake number one up to the maximum amount without risking number three overtaking him. And this is basically what number two did. Number one went ahead and bet the amount necessary to win if number two bet the maximum.
Needless to say everyone missed the Final Jeopardy answer and the champion lost. Had he taken number two’s “optimum” strategy into account and assumed he would follow it number one would have bet less and won.
Did number one bet appropriately or should he have given number two more credit?
My POV has always been: if I’m leading going into Final Jeopardy and I get the FJ question correct, I sure as hell better not lose. I’d never live it down. But there’s no shame in going down swinging.
Or has Jeopardy! Changed and there’s a reason to want to score highly while coming in second? (Multi-day tournament formats with cumulative scores being an exception)
Unless the category is one I know I have much less chance than otherwise to get the question right - something pop culturey, like involving movies or TV shows or show biz people - then I’d bet assuming I’ll get it wrong. But in general I assume I’ll know the answer, 'cause I wouldn’t have made it onto the show otherwise
If player 2 bets 10999, he ends with 10,401 if he misses which is just enough to shut out player 3 who can get 10400 maximum. But if 2 bets that way, then player 1 can be assured of a win if both 1 and 2 get the question right or wrong by betting 6000. The totals are then 32400 to 32399 if they’re both right or 20400 to 10401 if they’re both wrong.
It seems to me that both 1 and 2 being right or wrong together is very likely since they seem both to be good players. So the 10999 bet is probably not 2’s best bet.
If 2 bets it all then 1 has to bet 16401 to be assured of winning if they’re both right. This doesn’t help 2 directly as he can still be shut out by 1, but 1 might be reluctant to bet 16401 since if both he and 2 miss 3 can win by betting it all.
I don’t believe there is a dominant strategy in this case for players 1 and 2 – that is one that is best regardless of the probability of of 3 being right or wrong
I’m not at all sure what the 4/5 means in the Jeopardy calculator. That sounds like a rule of thumb and can’t be universally a good strategy.
