Wagering practice – say Zyg-a-Zyg ahhhhh? » Final Jeopardy! wagering practice 20131023 Slide09
Analysis of the Final Jeopardy! wagering from the Back to School Kids Week game Matt Bischoff vs. Becca Portman vs. Josh Woo, which first aired September 26, 2003.
Since Josh could bet small at 3400, I think Becca should NOT bet 4399. I like to think about the 8 possible combinationw of Right and Wrong answers in Final Jeopardy. Call them RRR, RWW, RWR, RRW, WWW, WWR, WRW and WRR where R=Right and W=Wrong.
For purposes of this analysis, let the first position = Matt, the 2nd position Becca and the 3rd position = Josh, so, for example, WRW would mean Matt got it wrong, Becca got it right and Josh got it wrong.
If this game is bet “rationally” by the 2nd and 3rd place players, then the leader Josh should have no more than 4 out of 8 chances of winning. (I think) If Josh bets 3400 and Becca bets 4399 than Josh has 6 chances of winning (RRR,RWW,RWR,WWW,WWR and WRR) and Becca has only 2 chances of winning (RRW and WRW) (only the two cases where Becca is right and Josh is wrong) She can improve her odds to 4 of 8 by betting 2399 which also gives her the win if both she and Josh get it wrong. With a 2399 bet she is still shutting out Matt even if he doubles and she gets it wrong. (This is true even if Josh bets 10201 and gets it wrong.) So, by changing her bet from 4399 to 2399 she significantly improves her chance of winning to counter Josh’s “small” bet potential strategy.