What the betting really needs is an odds calculator and only allow a fighter's record to be shown.
Then allow the computer to place bets. This will allow the heavily Favorites to only pay out small amounts while the a suprise victory will produce a better payout.
It would make sense to include betting odds based on fighters' records.
An interesting game option might be to obfuscate and/or hide entirely some or all of the fighters' stats. It could then be an effect of your manager character's skill how accurate your estimates of fighters' abilities are. There could even be an element of intelligence gathering - researching the abilities of others' fighters.
Betting for the success (not failure, except as a risky illegal practice) of your own fighter could make sense. And/or, a purse could be offered to the victor, based on the fighter's record, attendance, and/or stage of a tournament.