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In my current campaign there's a fighting pit in the town the PCs are in. I want the players to be able to gamble on fights here in a way that feels 'real'. The easiest thing I could come up with is equal odds in a fight, double or nothing rewards.

I don't want to spend a ton of thought power managing this. Has anyone executed something like this in a campaign before?

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    \$\begingroup\$ What level of details are you looking for? Do you want a way to mechanically arbitrate ties, accidental death, fighter progression or do you just want a way to simulate the fight itself. Because the simplest solution is a dice-roll to determine the winner, but even then you can add a lot of interaction with the PCs behind the scene if this is more than a one-session event. \$\endgroup\$
    – 3C273
    Commented Jan 21, 2018 at 22:50
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    \$\begingroup\$ It's worth bearing in mind that the players will likely either try to rig the fights or join in. Or both of course. \$\endgroup\$ Commented Jun 6, 2020 at 11:18

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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.

So the house 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.

There's the odds and 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.

Then comes equipment. 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.

So, the 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.

To 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.

Important note: 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

However, 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.

Advanced: 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.

Calculating: 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

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    \$\begingroup\$ (I didn't realize until the second glance—due to the absence of headers and italics—that this answer cites official sources for its info. You may want to emphasize that.) \$\endgroup\$ Commented Jan 22, 2018 at 2:43
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You couldn't get a more unrealistic way if you deliberately tried

The easiest thing is about the most unreal way you could have come up with because:

  • equal odds almost never happen
  • the bookkeeper is not making any money - they don't run a book for fun.

How a modern, efficient betting market works

Lets take a look at the way a modern, efficient betting market works. The bookkeeper (the person who runs the market) wants to match people who want to back one competitor against people who want to back the other (or others if there are more than 2 in the competition) and charge a cut for doing so. In a computerised SP (starting price) market, the odds constantly change so that the bets are completely matched - the bookkeeper is not a gambler so they have no "skin in the game" - they just take their cut of the turnover.

If this sounds similar to the way a stock market works, this is not surprising. In fact, a market in derivatives futures contracts is a betting market.

For a real example. This morning (22 Jan 2018) I had a look at the market on the Australian Open Tennis at Tabcorp - I won't link the actual page because it will very shortly be stale. There are a lot of things you can bet on but lets just focus on the head-to-head for two matches:

  • Fognini (3.25) v Berdych (1.33)
  • Fucsovics (15.00) v Federer (1.01)

The numbers are the dividends: the amount you will get for a $1 bet (including your original stake). So, if you bet $1 on Fognini and he wins you will win $2.25 ($3.25 - your $1 bet), $1 on Berdych wins you $0.33. This means that the odds are that Berdych will win. But what are those odds?

The nominal odds can be derived from the dividend by taking the reciprocal (1/x) of it. For these 2 matches:

  • Fognini (0.307) v Berdych (0.75)
  • Fucsovics (0.066) v Federer (0.990)

Now if, you add the numbers in each market (match) together, you will see that they are bigger than 1. But that can't be, we know one of them is going to win so the probability must be equal to 1! Well, these aren't probabilities they are odds and the amount greater than one is the bookkeeper's margin; in this case, about 5.7%. To work out the probabilities predicted by this market you need to divide each side by the total of both to give:

  • Fognini (0.290) v Berdych (0.71)
  • Fucsovics (0.063) v Federer (0.937)

Of course, you can bet on all sorts of other things as well, who will win the tournament, who will make the semi-finals, if a match will be won in 3, 4 or 5 sets, how many faults will be served, how many aces etc. Each of these is its own betting market and subject to the same kind of market forces.

Incidentally, betting markets are extremely efficacious at making accurate predictions about the future providing they are large enough. For example, they are more accurate at predicting the outcome of elections than polls are.

How betting markets historically worked

Of course, your fantasy market is not going to be like a modern, computerised betting corporation with millions of customers handling billions of dollars in bets. To work out what it might look like, let's wind back to clock 100 years and see how betting on horse and dog raging worked.

Regulated markets

We'll start with legal gambling and I'll focus on Australia because a) that's what I know and b) Australia has always been cutting edge in gambling - a nation of convicts after all.

Tracks were privately owned and the owners wanted the punters to come to the track, pay to get in, pay to drink and eat and pay to gamble. There were 2 ways of gambling on the track, the "totaliser" run by the racetrack that operated as described above (they were analog computers) and the bookmakers who paid the track for the privilege and kept their own books.

A bookkeepers odds would initially be set by what the bookkeeper though of each horse's chances and they would "keep book" on the bets that came in, adjusting the odds to balance their risk. This is similar to what was described above, however, it was not as accurate and required "overcorrection" to encourage bets on lightly backed horses to make the books balance.

Occasionally, a large bet might be placed on a particular horse that couldn't be balanced - in that case the bookmaker would "lay off" the bet either to a single larger bookmaker who has the resources to cover the bet or across several other trackside bookmakers. Remember, bookkeepers do not want to be gamblers. Sometimes a bet couldn't be laid off, say because it was placed only seconds before the race jumped, in that case, the bookkeeper could either become a gambler or refuse to take the bet. Watch The Sting to see how all this happens.

Illegal markets

Of course, if there's money to be made and legal ways to do so are restricted, people will find illegal ways. In the late 1800's, early 1900's every pub in Sydney and Melbourne would have its resident "bookie" who would handle the bets of the pub's clientele. Behind them was a network of larger bookies who would lay off bets, make sure the police were paid and get and sometimes fix the results of races.

You see, organised crime had to operate this way because we never had prohibition so they couldn't get rich as bootleggers.

With the rise of radio, there was pressure to allow races to be broadcast. This was resisted by the turf clubs as it would lower patronage (true) and the political establishment as it would assist illegal bookmakers (also true). This led to an amusing game of cat and mouse where the radio stations would have OB vehicles with stepladders on the roof driving around the walled racetracks so they could call the race and being chased off by the stewards and the cops. Eventually, the radio stations offered to pay the clubs and we started the movement from gate takings to broadcast deals as the major driver of income in all professional sports.

Of course, betting on football matches, boxing, cricket etc. was all illegal on the basis that the sport could be rigged. This naturally meant that betting and fixing were riffe.

Using this in your game

If you want to keep things simple, use the net and look up betting markets for any two sided contest - tennis, basketball, cricket, baseball, football (any code). Use those odds and change the names to match your gladiators. Use the technique above to work out the actual odds and roll to see who wins.

If you're not boring, however, you can make a whole campaign that revolves around the crime and corruption that hovers around gambling like flies on s*&t. Let the PCs put real (which is to say not-real) "skin in the game".

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For simplicity sake you could just say that the odds are in favor of contender A at a ratio of 3 to 1 over contender B. Allow your players to make their bets then roll a D12 and if the number comes up from 1-4 then contender B wins and you pay out accordingly. You can go higher on ratios by using different dice for instance a 5 to 1 ratio would be a D20 and 1-5 would be underdog.

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  • \$\begingroup\$ Wouldn't those 3 to 1 odds be a result of 1-3 on a d12? (1 quarter goes to the underdog, 3 quarters go to the other. You don't just divide by three, you need to divide by four.) Similarly, 1-5 to 6-20 corresponds to odds of actually 3 to 1, not odds of 5 to 1. (For that you'd have a d12 with 1-2 vs 3-12, right?) \$\endgroup\$ Commented Feb 1, 2018 at 11:27
  • \$\begingroup\$ Yes you are absolutely correct \$\endgroup\$
    – Mad Morgan
    Commented Feb 3, 2018 at 12:53
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The Profession skill

Profession (Gambler or any other relevant job)! Set up a difficulty with a sliding scale giving a multiplier. Have them make the roll and move on. The roll gives you a way to alter the probability and represent things like: finding a bookie on-time, the current outlook on the odds, etc. You can change the scale and cap the bets value.

DC<20 x0

DC 20 x1.05

DC 25 x1.10

DC 30 x1.5

This allows you to have a simple system, and should be PCs bet bigger sum, they can earn more.

Word of Caution You do not want them to win SO MUCH money that adventuring becomes a means to re-acquire wealth they can multiply while gambling... If that's what they want, tell them of a place called Las Vegas...

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  • \$\begingroup\$ While I think this is normally the best way to handle things like this, the asker said, "I want the players to be able to gamble on fights here in a way that feels 'real.'" Since this answer essentially challenges the frame, it should probably explain in more detail specifically why this way is better than going for that real Vegas feel. \$\endgroup\$ Commented Feb 1, 2018 at 14:25
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Probably super late as I can see but to make super simple if you still play is give percent out of 100. Example: Fighter A vs Fighter B the odds fighter A wins is 62 so then you decide high or low, just keep it low. So then you roll a d100 and if it’s 1-62 fighter A is victorious but if it’s 63 or higher it’s fighter B. Then you just describe the fight as it happens and for deciding on payout. Just multiple percent of losing by two times money bet. So fighter A had a 38 percent chance at losing. Double it to .76 and multiple by bet say 15gold. You get a winning of 11.4 round up to 12 and player would receive 27 gold (15 original bet and 12 winnings) If fighter B would have won it would have been 62 x 2, = 1.24 times 15 to get 18.6 round to 19, player would get 34 gold (19 winnings and 15 original). But it’s you to decide the percent of winning for each person and if they get the high or low side of the d100 For a player who wants to actually fight to determine winnings roll a d100 for how many of people bet on them, then give them basic winnings like 75 gold(your choice bigger arenas bigger basic winnings) times CR so if it was a 1/2 it’s 75+37.5 round up and you get 113 gold for winning. Again I know I’m super late but it’s a thought.

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