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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
}
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