Why? To answer that, we'll only deal with scenarios in which Melizza gets it wrong—because if she bets correctly and gets the answer right, the game's over no matter what.
Miles' bet of $4,301 puts him out of Judy's striking range should he answer correctly, as he'd finish with $11,601, or two times Judy's score plus a dollar.
Judy's correct bet, $2,800, gives her that extra chance that Haley should have had in the first example. By betting $2,800, she can win if all three players miss the last question. With correct bets and all players missing Final Jeopardy!, Melizza winds up with $399, Miles finishes with $2,999, and we'll see Judy again tomorrow as our returning champion, as she's just finished with $3,000. (Naturally, if Judy gets it right and the others don't, she wins anyway.)
Sound too theoretical? Consider what actually happened: All three players missed the final question. Melizza wound up with $399—which was good enough to win, as her opponents had wagered absurdly. Miles bet the insane sum of $7,000, which left him with $300. Judy bet the house and wound up with nothing. Had Miles bet correctly (or even close to correctly—six grand would still have won it for him), he would have been champ. Or, barring that, Judy could have won it herself.
You may be wondering: If the first person knows that the second-place person is going to have this back door, why doesn't he simply bet just enough to outstrip the second place player's more modest bet? Because there's always the possibility that the second-place person will bet it all. And in practice, the person in first place almost always bets $1 or $100 over what he needs to put himself out of reach. It's this tendency that the second- and third-place players should take advantage of.
There are also a few subtleties we're glossing over—for instance, Haley, Miles, or Judy would get a bigger payday if they bet everything and won. But the safer bet provides the extra chance of simply surviving and coming back the next day. And anyway, the basic premise is clear: If you're in second or third place going into Final Jeopardy!, don't just automatically bet it all. Your better chance may be backing into victory.
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