Since my players now have a strong incentive to visit arenas, theatres, and casinos, I need to price out accessing each block. I'm still working on ticket price rules for performances, but for arenas and casinos, I need gambling rules. Furthermore, arenas and casinos offer very different gambling experiences, and I want gambling at each type of establishment to feel very different.
For casinos, I think blackjack works just fine as a game mechanic. Most know how to play, the casino player runs on autopilot, the betting possibilities are fairly simple, the odds are minimally in the players' favor, and the players are able to collaborate against the casino player. While adapting your favorite casino game is fine, I like that blackjack has fairly simple choices for the player each round and that the players are gambling on the same team.
Arenas offer a very different set of circumstances. I want to offer odds that adjust for multiple fighters with different levels of fighting ability, durability, and equipment that I can quickly output at the table. I do this by converting turning each of these parameters into numbers for a given fighter and then combining fighters' numbers to give the payout for a given type of bet. Right now, this only supports win/lose bets, but with time and player interest I can probably expand it to cover different types of winning conditions.
Fighting Ability: combatant notches * attribute
While I need to post my revised combat rules (since my outline here is legible probably only to me), I'll summarize the relevant aspects as needed. A character's combat ability is represented by their Combatant skill, which comes in three flavors: Strength, Dexterity, and Mindfulness. Each flavor is trained separately, uses the appropriate attribute, and controls a different group of weapons. Skills are ranked descriptively (Novice, Apprentice, Professional, Expert, Master, Sage) based upon the number of notches possessed (0, 1, 3, 6, 10, and 15 respectively). Thus, the product of the character's Combatant notches multiplied by the appropriate attribute (Strength, Dexterity, or Mindfulness) is a rough approximation of their overall fighting ability. This gives me a number ranging from 0 (treat as .5) to 90.
Durability: health * wagered injuries
Also relevant is the character's physical endurance, which I measure in two ways: health and injuries. Health represents the character's level of endurance, while injuries measure their bodily integrity. Damage taken is removed from the character's health total, and when that total reaches 0 they gain an injury and refresh back to full health. Death occurs when taking an injury past their normal bodily maximum. Most creatures have 1 or 2 injuries, and this number can never improve. In a fight to the death, a fighter will wager every injury they can safely take, but in a friendly skin brawl, a fighter will bow out after taking 1. We multiply the number of wagered injuries by the character's health to get a rough estimate of their fighting fitness. This number will reasonably range from 1 to 14.
Equipment: weapon damage / (1+ opponent's DR) * weapon reach / opponent's weapon reach
Lastly, I want to account for what the fighters are wielding. Unlike combat ability or fitness, gear is only beneficial in the context of the other gear on the table. Since armor provides damage reduction, we can divide the base damage of the chosen weapon by 1+ the damage reduction of the opponent's armor to get a baseline for how effective that weapon is. Weapon damage ranges from 0 (treat as .5) to 6, while fighters can have a damage reduction of 0 to 3.
The range of that weapon is also critically important. Clashing occurs whenever the weapons of two opponents overlap. I use 1-yard hexes, so a clash normally happens when fighters are 1 hex removed from each other (as their weapons occupy the hex in between). Long weapons like spears or claymores have a longer range and can engage a foe at a greater distance, possibly 2 or 3 hexes. If the opponent has a shorter weapon, they can't deal damage while clashing, and, since mobility is limited during the clash, it will take them time to get close enough to actually threaten their opponent. I am interested in the comparison, so I divide the reach of the fighter's weapon by the reach of their opponent's. The maximum reach of a melee weapon 3, while some weapons have a reach of 0 (treat as .5).
The product of each of these three terms gives us the combat number, with one modification. Zeroes are no good because I need each of these numbers to be invertible. I don't want to set the value of the whole term to 1, either. Instead, I treat all zeroes as .5 except for damage reduction. The range of these combat numbers is quite large: 0.0834 to 45,360 (although I'd never put someone in an arena with a combat number less than 1). Because of this, take the geometric mean of all three terms (raise the product to the 1/3rd power), which reduces the range considerably: 0.4369 to 36.
If two fighters are on the same side, add their combat numbers together.
For a bet on side A, divide the combat numbers of side A by the combat numbers of side B to get the combat ratio, the numerical representation of the two sides compared against each other. This equals the amount necessary to bet in order to return a payout of 1 gold.
Most arena-style fights are just two fighters using only their fists and no armor to the first injury, which obviates a lot of the rules above. This lets us ignore the equipment term entirely and simplifies the durability term to just the character's health.
EDIT - forgot to post arena fight resolution rules
If no player character is fighting, each side will make a Combatant test (both sides rolling), resolving damage as normal. The first side to take an injury loses.
If a player character is fighting, treat as a normal combat.