In the J! Archive it lists a rule known as "Bridges's Rule" (at
this link) which suggests that you not bet for a tie in a tournament unless betting for an outright win introduces another risk. The rule is said to be named after the 1st runner-up in the 1996 Teen Tournament, Derek Bridges, who had enough to bet for an outright win over Amanda Goad (the winner of that tournament) but bet for a tie instead and forced the game into a tiebreaker.
I was taking a look at a site which discusses some old games of J! (most of the information on the site hadn't been updated since about 2000 or so, but for this tournament the information would still apply) at
this link. From what it shows
here it appears that Derek in that final game did not actually bet to tie Amanda, but bet $201 short of what he needed to cover her maximum possible total. As it turned out, Amanda bet everything but $200 and that's what brought the match to a tiebreaker (if she had bet more than what she did she would've won the tournament outright given Derek's wager).