1 files changed, 182 insertions, 0 deletions
diff --git a/internal/casino/house_edge_blackjack.go b/internal/casino/house_edge_blackjack.go
new file mode 100644
index 0000000..884cf75
--- /dev/null
+++ b/internal/casino/house_edge_blackjack.go
@@ -0,0 +1,182 @@
+package casino
+
+import "math"
+
+// A small infinite-shoe decision model supplies the effect of payout, H17,
+// DAS and the game's unusual doubled-split-21 rule. Deck count and resplitting
+// use the published basic-strategy rule adjustments at:
+// https://wizardofodds.com/games/blackjack/rule-variations/
+// This is a reference estimate, not a finite-shoe/composition strategy solver.
+func blackjackMainEdge(r BlackjackConfig) float64 {
+	r = r.Normalize()
+	base := BlackjackConfig{}.Normalize()
+	no := false
+	base.DoubleSplitBlackjack = &no
+	loss := .0043 - (blackjackReferenceEV(r) - blackjackReferenceEV(base))
+	// Improvements relative to eight decks; interpolate uncommon deck counts.
+	decks := []float64{0, .0048, .0019, .00125, .0006, .0003, .0002, .0001, 0}
+	if r.Decks < len(decks) {
+		loss -= decks[r.Decks]
+	} else {
+		loss += .0006 * (1 - 8/float64(r.Decks))
+	}
+	if r.MaxSplitHands == 2 {
+		loss += .001
+	} else if r.MaxSplitHands == 3 {
+		loss += .0001
+	}
+	if r.MaxSplitHands > 1 && r.AllowsResplitAces() {
+		loss -= .0008
+	}
+	return loss
+}
+
+// The split model allows one split; published adjustments above account for
+// the configured resplit limit. Unlike-ten splitting does not change normal
+// optimal play (tens are stood on). Shuffle penetration is not an off-top rule.
+func blackjackReferenceEV(r BlackjackConfig) float64 {
+	probability := func(v int) float64 {
+		if v == 10 {
+			return 4.0 / 13
+		}
+		return 1.0 / 13
+	}
+	add := func(total, soft, v int) (int, int) {
+		if v == 1 {
+			total += 11
+			soft++
+		} else {
+			total += v
+		}
+		for total > 21 && soft > 0 {
+			total -= 10
+			soft--
+		}
+		return total, soft
+	}
+	result := 0.0
+	for up := 1; up <= 10; up++ {
+		// Outcomes 17..21 and bust (22), conditional on no dealer natural.
+		type state struct{ total, soft int }
+		memoDealer := map[state][23]float64{}
+		var dealer func(int, int) [23]float64
+		dealer = func(total, soft int) [23]float64 {
+			key := state{total, soft}
+			if v, ok := memoDealer[key]; ok {
+				return v
+			}
+			var out [23]float64
+			if total > 21 {
+				out[22] = 1
+			} else if total >= 17 && !(total == 17 && soft > 0 && r.DealerHitsSoft17()) {
+				out[total] = 1
+			} else {
+				for v := 1; v <= 10; v++ {
+					t, s := add(total, soft, v)
+					child := dealer(t, s)
+					for i, p := range child {
+						out[i] += probability(v) * p
+					}
+				}
+			}
+			memoDealer[key] = out
+			return out
+		}
+		natural := 0.0
+		if up == 1 {
+			natural = probability(10)
+		}
+		if up == 10 {
+			natural = probability(1)
+		}
+		var outcomes [23]float64
+		for hole := 1; hole <= 10; hole++ {
+			if up+hole == 11 && (up == 1 || hole == 1) {
+				continue
+			}
+			t, s := add(0, 0, up)
+			t, s = add(t, s, hole)
+			dist := dealer(t, s)
+			for i, p := range dist {
+				outcomes[i] += probability(hole) * p / (1 - natural)
+			}
+		}
+		stand := func(total int) float64 {
+			if total > 21 {
+				return -1
+			}
+			ev := outcomes[22]
+			for d := 17; d <= 21; d++ {
+				if total > d {
+					ev += outcomes[d]
+				} else if total < d {
+					ev -= outcomes[d]
+				}
+			}
+			return ev
+		}
+		memoPlayer := map[state]float64{}
+		var play func(int, int) float64
+		play = func(total, soft int) float64 {
+			if total >= 21 {
+				return stand(total)
+			}
+			key := state{total, soft}
+			if v, ok := memoPlayer[key]; ok {
+				return v
+			}
+			hit := 0.0
+			for v := 1; v <= 10; v++ {
+				t, s := add(total, soft, v)
+				hit += probability(v) * play(t, s)
+			}
+			ev := math.Max(stand(total), hit)
+			memoPlayer[key] = ev
+			return ev
+		}
+		hand := func(a, b int, split bool) float64 {
+			total, soft := add(0, 0, a)
+			total, soft = add(total, soft, b)
+			if split && a == 1 {
+				return stand(total)
+			} // one card on split aces
+			ev := play(total, soft)
+			if total < 21 && (!split || r.AllowsDoubleAfterSplit()) {
+				doubled := 0.0
+				for v := 1; v <= 10; v++ {
+					t, _ := add(total, soft, v)
+					value := stand(t)
+					if split && t == 21 && r.CountsDoubleSplitBlackjack() {
+						value = r.BlackjackPayout
+					}
+					doubled += 2 * probability(v) * value
+				}
+				ev = math.Max(ev, doubled)
+			}
+			if !split && r.AllowsSurrender() {
+				ev = math.Max(ev, -.5)
+			}
+			return ev
+		}
+		for a := 1; a <= 10; a++ {
+			for b := 1; b <= 10; b++ {
+				ev := 0.0
+				if a+b == 11 && (a == 1 || b == 1) {
+					ev = (1 - natural) * r.BlackjackPayout
+				} else {
+					ev = hand(a, b, false)
+					if a == b && r.MaxSplitHands > 1 {
+						split := 0.0
+						for v := 1; v <= 10; v++ {
+							split += 2 * probability(v) * hand(a, v, true)
+						}
+						ev = math.Max(ev, split)
+					}
+					ev = (1-natural)*ev - natural
+				}
+				result += probability(up) * probability(a) * probability(b) * ev
+			}
+		}
+	}
+	return result
+}