jpahk wrote:let's say joey estimates himself at 80% on "political terms". (i'm assuming he saw something he liked in that category, since he made a much saner bet yesterday and a very small bet from 3rd on tuesday.) there's no particular reason to estimate john or emily at anything other than the normal 50% FJ get rate, so his win probability if he makes the MSB is at least 85%: he gets it right 80% of the time, and of the other 20% of the time, at least a quarter of the time, neither of the other two can punish him for it. it's probably more like half: if a question is tough enough for an 80% player to miss it, the odds of a 50% player missing it are pretty darn good too. so maybe he's 90% to win making the MSB, and his expected value is 0.9*($19601 + whatever his EV for future episodes is). by going all in, his EV is 0.8*($30000 + future EV), which is higher than his EV with the MSB unless he estimates the value of staying on as champion to be over $64k. and this is only for an 80% confidence in the FJ category, mind you. if he thinks he's 90%, the future EV threshold would more than double.
i noticed i made an error in my calculation: if he makes the MSB, his EV is actually (0.8*19601 + 0.1*10399 + future EV), because in some of his win scenarios, he ends up with only $10399 because he's gotten FJ wrong. this correction makes the all-in bet even more favorable by comparison.
omgwheelhouse wrote:My opinion: I could see it being correct for a "lucky"-type champ who doesn't necessarily love their chances to keep winning*. I don't think it would be correct for a good champ. (Admittedly, I just skimmed Joon's math post and haven't done any of my own calculations on this.) Random example that means nothing: Jason Keller wins game 2 on a TS with pre-FJ scores of 27k to 19k.
well, that's a decidedly non-random example, since jason keller went on to win the 3rd-most games and 6th-most money of all time. i suppose i could look for examples of a returning champ who had a crush in her 2nd game and went on to get it right, but did not turn into an all-time great. this doesn't seem like it would be hard to find. in general, there is no particular reason for any player, even one leading after DJ, to think that he or she is among the top 0.1% of jeopardy players ever, which is where you have to end up before the expected future EV for winning starts to approach the 6-figure range. but perhaps if you are already a dominating 5+ time champ or something and this scenario occurs in your 6th game, then you might be thinking along those lines.