"""SNG variance simulation used on tourneymanager.net.
9-max SNG, payouts 50/30/20 of the prize pool, buy-in 10+1.
A player's finish distribution is specified by P(1st), P(2nd), P(3rd);
everything else is a bust. We draw N-game samples many times and look at
the spread of the measured ROI. Pure Monte Carlo, no ICM."""
import random, statistics, json, sys
random.seed(7)
BUYIN, FEE = 10.0, 1.0
POOL = 9*BUYIN
PAY = {1:0.50*POOL, 2:0.30*POOL, 3:0.20*POOL}
def roi_true(p1,p2,p3):
    ev = p1*PAY[1]+p2*PAY[2]+p3*PAY[3]
    return (ev-(BUYIN+FEE))/(BUYIN+FEE)
def sample(p1,p2,p3,n):
    r=random.random; tot=0.0
    for _ in range(n):
        x=r()
        if x<p1: tot+=PAY[1]
        elif x<p1+p2: tot+=PAY[2]
        elif x<p1+p2+p3: tot+=PAY[3]
        tot-=(BUYIN+FEE)
    return tot/(n*(BUYIN+FEE))
players={"solid winner":(0.16,0.13,0.12),"marginal winner":(0.14,0.12,0.12),"breakeven-ish":(0.13,0.12,0.11),"loser":(0.11,0.11,0.11)}
out={}
for name,(p1,p2,p3) in players.items():
    rt=roi_true(p1,p2,p3); row={"true_roi":round(rt*100,2),"samples":{}}
    for n in (100,300,1000,3000):
        xs=[sample(p1,p2,p3,n) for _ in range(4000)]
        xs.sort()
        row["samples"][n]={"p5":round(xs[int(0.05*len(xs))]*100,1),"p50":round(xs[len(xs)//2]*100,1),"p95":round(xs[int(0.95*len(xs))]*100,1),"p_neg":round(sum(1 for x in xs if x<0)/len(xs)*100,1)}
    out[name]=row
print(json.dumps(out,indent=1))

# --- ICM (Malmuth-Harville) -------------------------------------------------
def icm(stacks, payouts):
    """stacks: {name: chips}; payouts: list of prizes for 1st, 2nd, ... Returns {name: $equity}."""
    eq={n:0.0 for n in stacks}
    def rec(remaining, place, prob):
        if place==len(payouts) or not remaining: return
        total=sum(stacks[n] for n in remaining)
        for n in remaining:
            p=prob*stacks[n]/total
            eq[n]+=p*payouts[place]
            rec([m for m in remaining if m!=n], place+1, p)
    rec(list(stacks),0,1.0)
    return eq
if __name__=="__main__":
    print(icm({'A':5000,'B':3000,'C':1500,'D':500},[45,27,18]))