1 files changed, 61 insertions, 0 deletions
diff --git a/internal/casino/house_edge_fire.go b/internal/casino/house_edge_fire.go
new file mode 100644
index 0000000..3bb1697
--- /dev/null
+++ b/internal/casino/house_edge_fire.go
@@ -0,0 +1,61 @@
+package casino
+
+import "math/bits"
+
+// crapsFireReturn is the fire bet's exact expected return (profit plus stake
+// where the bet wins; nothing where it loses) per unit staked. The bet
+// resolves only on a point-phase seven-out — a come-out seven keeps the
+// shooter's hand and the bet alive — paying 24/249/999:1 for 4/5/6 distinct
+// made points. The state is the six-bit mask of distinct points made in the
+// hand; come-out rolls and rerolls of an already-made point are self loops.
+// Solved by fixed-point iteration over the 64 masks (the chain is absorbing
+// and monotone, so iteration converges to the exact solution).
+func crapsFireReturn() float64 {
+	numbers := []int{4, 5, 6, 8, 9, 10}
+	ways := make([]int, len(numbers))
+	for i, n := range numbers {
+		ways[i] = diceWays(n)
+	}
+	pay := func(made int) float64 {
+		switch made {
+		case 4:
+			return 25 // 24:1 profit plus the returned stake
+		case 5:
+			return 250
+		case 6:
+			return 1000
+		}
+		return 0
+	}
+	vCome := make([]float64, 64)
+	for it := 0; it < 2000; it++ {
+		next := make([]float64, 64)
+		for mask := 0; mask < 64; mask++ {
+			sum := 0.0
+			for i := range numbers {
+				w := ways[i]
+				nm := mask | 1<<i
+				// Point-phase value of an established point n: making it
+				// moves to the come-out with the grown mask; a seven (6/36)
+				// resolves the bet at the CURRENT mask (not the grown one —
+				// the point has not been made).
+				made := bits.OnesCount(uint(mask))
+				pointValue := (float64(w)/36*vCome[nm] + 6.0/36*pay(made)) / (1 - float64(36-w-6)/36)
+				sum += float64(w) / 36 * pointValue
+			}
+			next[mask] = sum / (24.0 / 36.0)
+		}
+		done := true
+		for i := range next {
+			if diff := next[i] - vCome[i]; diff > 1e-12 || diff < -1e-12 {
+				done = false
+				break
+			}
+		}
+		vCome = next
+		if done {
+			break
+		}
+	}
+	return vCome[0]
+}