I am supposed to be working and not procrastinating so here is my mathematical theory on policy in guns and hookers. The most common scenario this occurs in is with cop dead.

Here are the pure probabilities of town win vs. mafia win with the following very large caveats:

1. Every shot and lynch is random.
2. Gunsmith gunned alive.
3. Mafia always hides gun.
4. Gunsmith always guns in 4way.
5. Hooker always hooks gunsmith if both are alive.

Without policy:

• Town wins 24.27% of the time [1165/4800]
• Mafia wins 75.73% of the time [3635/4800]

With policy:

• Town wins 30.99% of the time [119/384]
• Mafia wins 69.01% of the time [265/384]

Further breakdowns:

• Without policy & villager hooked = 27.5% town win
• Without policy & gunsmith hooked = 14.58% town win
• With policy & villager hooked = 36.45% town win
• With policy & gunsmith hooked = 14.58% town win

As you can see, the main reason policy is effective is that it's more likely that villager is hooked than gunsmith. If gunsmith is hooked then you are at the same odds either way. So never scumhunt and just use policy and you will increase your random win odds by almost 6 percent!