Well, if you have access to it, the Pathfinder Gamemastery Guide actually has a short section on gambling games, starting on page 240. I don't think I can get away with quoting the entire section, but I think I can get in the stuff you need.
So to start off, the type of bet you've got here is
Proposition betting: Prop bets are bets on the outcomes of events for which one has imperfect knowledge. Sports bets are the best known of these types of bets. The house sets a line on which it believes half the bettors will pick one side and half will pick the other. The proposition then happens, and the people who picked correctly are paid off. (Gamemastery Guide, 240)
and then the outlines, I can skim some.
Então o casa is basically you decide if this place is "tight" like a fancy casino, where there's always a good house edge and a strict limit on how much you can bet at once, or a "loose" place where there's a lot of gambling with higher stakes and the max bet is based on their ability to actually pay off all the winners, like a gambling hall run by the thieves den.
Tem o probabilidade e payout. Now the payout is based off the odds, but remember that the winner also gets back their original bet on top of it, so the "double or nothing" would be a 1:2 bet, called an "even odds" bet, while something like 1:4 is an "odds on" bet, so the payout is less than the initial bet, but you get the initial bet back so you still make a profit. Generally speaking, this is the only kind that places use, because "odds against" has a payout greater than the initial bet, so that would lose them money if that fighter won the match.
Então vem equipamento. This section is basically what you need to have on hand to be able to calculate/simulate gambling. Usually it's like some dice so players can gamble. It also considers how many people (NPCs) are needed to run the game. So you basically just need the guy taking the bets. As for real equipment, you probably already have everything you need, being the DM. Dice, paper, pencil. Real basic.
Assim, o mehcanics. This is how the gambling is actually simulated at the table. This really depends on what you go for. It could be a coinflip, or it could be running actual combat with two fully stat-fleshed out NPCs.
Para put it all together, lets go for the bare bones game you thought up. Two fighters, one D20, one guy gets evens the other gets odds, whoever gets theirs on the roll wins the fight. (I know you could go for a coin flip, but then the players know you're literally just flipping a coin. When you roll a dice, you can act like you're calculating things out. You can even roll extra dice that you pay no attention to, just to make the players think the game is complex). The odds are 1:2, double-or-nothing payouts. Nice, but it's pretty boring for your players to watch a single dice roll, so you could spice it up a bit by making it like a game of horse, so the first to win a set number of rolls (say the classic first to 3) wins the match, and then you can narrate it like a fight.
Importante: even if you're going basic, I suggest giving these fighters barebones character sheets. I know it seems more than needed, but you never know if one your players is going to decide to take part in the fights, and then you have to run it like actual combat, or if the party is going to want to recruit one of the fighters as a bodyguard or something, and then you'd need to make them a sheet anyway, so even if you've just got a name, stats, AC, HP, weapons, and maybe a few skills, that should be enough to last you until you get the chance to fully flesh them out between sessions. If you don't want to spend too much time on this I would suggest using DonJon's Pathfinder NPC generator, specifically under martial class.
http://donjon.bin.sh/pathfinder/random/#type=npc;order=Martial
Contudo, you're probably gonna want to make your gambling fights more realistic. I know you don't want something too complex, but you never know if your insane players are going to somehow end up making a super important bet (like betting a rare magic item for information) on one of these fights, and then they might try to give their fighter an advantage in the fight, and then if all you're doing is even/odd coin flip, that's not gonna help and they're gonna feel screwed over. So I have some ideas to let you make the odds different, and the only real thought power is setting up the odds, the mechanics should be about as difficult as running two NPCs punching each other.
Now, I say for the match, you can just actually run the two guys fighting. If you don't want it to drag on as these guys slowly hack at each other's hit points, then instead of that you can just do the "game of horse" thing I suggested earlier. Or if it's a big important match that the players made a bet on and could get totally screwed over if they lose it, you might want to just run it like full on combat (again, having sheets for them will help). So the match itself is actually the easy part.
The big issue you're going to have for brainpower is figuring out the odds. In real life people actually use a bunch of crazy statistics to work out odds on MMA fights, but that's a bunch of jargon that sent me down a half hour rabbit hole, so let's make it simpler. After all, it doesn't have to be realistic to how they actually do it, and its not like your players are going to become professional gamblers, so what do they care.
avançado: So there are a couple levels of complexity I can think of, which are basically how many things you take into consideration: Hit Points (or Hit Dice), AC, attack bonus, etc. Now to start off, you can use that "game of horse" idea and say that a fighter's number of Hit Dice equals how many times "he can get hit", i.e. how many rolls the opponent needs to succeed on to win the match. You could also make it their HD plus their Constitution modifier. It's pretty simple, but it lets you easily change up the odds of the bets. Lets say a basic one of fighter 1 has 4HD and fighter 2 has 6HD. Now normal mathematical statistics would say the odds are 4:6 and 6:4, but that puts the payout for fighter 1 at 1.5 times the initial bet, and bookies don't want to risk money on that. So the way you could calculate the odds to ensure that the payouts stay under the initial bet is adding their HP together for the second number, and so you'd get 4:10 and 6:10, So if they bet 1 gold, they would win either 4 silver or 6 silver (plus getting their gold piece back) Sure that's not a big difference, but it's one on one so who cares. Now keep in mind that fighter 1 has the 6:10 odds because there's a higher payout and he's less likely to win, and fighter 2 has the 4:10 odds because it's a lower payout but he's more likely to win.
Going off of this, you could start adding other stats together to get the total, such as their armor class bonus (going of base 10 as 0, because adding 7 is easier than adding 17), their total attack bonus, their initiative bonus, etc, and then just like before add the totals together and put that as the second number.
So lets try an example with Hit Dice and Constitution modifier, Armor Class, and Attack Bonus (base plus strength mod), and Initiative modifier. This will let you use that "game of Horse" style match where you ignore damage and actual HP and just go for a set number of hits, in this case set as their Hit Dice plus their Constitution modifier. Also for attack bonuses of +6/+1 and the like, I would just add those together as +7 for the calculation. the initiative bonus is just keeping in mind that whoever goes first in the round has a chance to take the other guy out first. So, lets say you've got Steve and Joe, two basic fighter NPCs you got the ability scores for from the generator, and you spent a minute or two figuring out their stats. Then you just get the numbers needed and total them up
Steve has 4 Hits (3HD, +1 Con), +5 AC (15 - 10), +5 attack bonus, +2 initiative, total: 16
Joe has 6 hits (4HD, +2 Con), +3 AC (13 - 10), +7 attack bonus, +3 initiative, total: 19
So then the total is 35 and Steve's odds are 19:35 (27:50) and Joe's are 16:35 (23:50). Sure you could go into more depth like how many attacks and the weapon damage, but again, the players aren't going to be gambling professionally so who cares. Now you pick who goes first by initiative and make two attack rolls each round, which will be about as complex as doing a one on one fight with a player.
Calculando: Now, when you're calculating odds like this, you're probably gonna want to use this, as it's a nice little calculator that you can probably just keep bookmarked in your phone.
http://www.therx.com/odds-converter-payout-calculator
it'll make it simple for you and change it to the smallest fraction. If it doesn't change it from the original input, copy the decimal box, change it to 0, hit convert, and then paste the amount back into the box and hit convert again. It should round it to a nicer amount. If that's still too big, just divide each fraction number in half and round the first number down and the second number up (the bookies would do it that way for smaller payout). You can ignore the "moneyline" box, it's a different style and is too confusing for converting from dollars to coin. Also keep in mind it calculates on the basis that the winner is given their payout on top of earning back their initial bet.
It is in USD, but fortunately, the money in game is pretty much our version of coins, copper to a penny, gold to a dollar, etc., so you can just use the Standard Exchange Rates chart in the Core Rulebook on page 140