For my own reasons, I am very disappointed with the scholarship here. To wit, the paragraph:
...it is a safe assumption that the competitors have watched prior Tournaments of Champions or have visited one of the myriad websites that recap Jeopardy! games question by question, bet by bet, and as a result are aware of qualifying scores.[FN5]
I can't access the first link, but given the 9/11 link I think it must be the one. The later paper is considerably more refined and lengthy. Good thing TPTB don't like me enough for me to have to read it.
Thanks. Now I am not so sure that the 2003 paper is the one I'm thinking of. I do not recall it going into detail about the players' relative decision-making strategies; it was a pretty straightforward analysis of the optimal betting strategy for wildcards in isolation, and pretty plainly concluded that there was a particular cutoff (now I see it was $8000) below which it recommended you bet everything, and above which it recommended you stand pat. (I don't know if that $8000 is in pre-doubled figures.) The name of one of the authors looks familiar, though, so maybe it was a predecessor article.
Based on their discussion of data sources I think they were using pre-doubled figures, but then I question what their numbers actually mean. In their final published paper they say that $8,000 gives "an 80% chance of advancing" on a wildcard. Keith thinks the average cutoff for ToC wildcard slots is more along the lines of $10,800 (postdoubled), but with $5,800 std. dev. His numbers will have to be updated in a couple weeks.
Satisfied that the wager in this case was too small--but not that the wager should have been everything, or even everything but a dollar.
Robert K S wrote:Based on their discussion of data sources I think they were using pre-doubled figures, but then I question what their numbers actually mean. In their final published paper they say that $8,000 gives "an 80% chance of advancing" on a wildcard. Keith thinks the average cutoff for ToC wildcard slots is more along the lines of $10,800 (postdoubled), but with $5,800 std. dev. His numbers will have to be updated in a couple weeks.
Satisfied that the wager in this case was too small--but not that the wager should have been everything, or even everything but a dollar.
A quick glance at the post double cutoffs seems to suggest that a figure somewhere between 11,000 and 12,000 would give you an 80% chance of advancing. So if their math still holds, anything below that range would require an all in and anyone above that should stand pat.