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Blackjack strategy: Difference between revisions
→{{header|Nim}}
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Loss % staked : 1.801
</pre>
=={{header|Nim}}==
{{trans|Go}}
<lang Nim>import random, sequtils, strformat, strutils
type
Card = 1..10
Deck = object
size: int
cards: array[Card, int]
HandKind {.pure.} = enum Hard, Soft, Pair
Action {.pure.} = enum Stand, Hit, Double, Split
ActionGain = tuple[action: Action; gain: float]
var
# Computed strategy tables.
hTable: array[15, array[10, Action]] # Hard strategy table (round 1).
sTable: array[8, array[10, Action]] # Soft strategy table (round 1).
pTable: array[10, array[10, Action]] # Pairs strategy table (round 1).
hTable2: array[18, array[10, Action]] # Hard strategy table (round >= 2, no doubling).
sTable2: array[10, array[10, Action]] # Soft strategy table (round >= 2, no doubling).
func initDeck(): Deck =
Deck(size: 52, cards: [4, 4, 4, 4, 4, 4, 4, 4, 4, 16])
func `<`(ag1, ag2: ActionGain): bool = ag1.gain < ag2.gain
func dealerProbs(upcard: Card; startDeck: Deck): array[7, float] =
## Returns probabilities of dealer eventually getting:
## 0: 17, 1: 18, 2: 19, 3: 20, 4: 21 (non-blackjack), 5: blackjack (nil), 6: bust.
## It is assumed that the dealer has already checked for blackjack, that one deck is used
## and that the dealer stands on 'soft' 17.
var
res: array[7, float] # Results.
decks: array[9, Deck] # Decks for each level.
scores: array[9, int] # Scores for each level.
elevens: array[9, int] # Number of aces for each level scored as 11.
probs: array[9, float] # Probabilities for each level.
decks[0] = startDeck
scores[0] = upCard
if upcard == 1:
# An ace.
scores[0] = 11
elevens[0] = 1
probs[0] = 1.0
proc drawCard(lev: Natural) =
## Recursive closure.
for c in Card.low..Card.high:
if decks[lev].cards[c] == 0: continue # Card no longer present in deck.
# Temporary variables for current level.
var
deck = decks[lev]
score = scores[lev]
eleven = elevens[lev]
prob = probs[lev]
inc score, c # Add card to score.
if c == 1:
# Score all aces initially as 11.
inc score, 10
inc eleven
prob *= deck.cards[c] / deck.size
if score > 21 and eleven > 0:
dec score, 10 # Bust but can demote an ace.
dec eleven
if lev == 0 and (upCard == 1 and c == 10 or upCard == 10 and c == 1):
res[5] += prob # Blackjack, allow for now.
elif score in 17..21:
res[score-17] += prob # 17 to (non-blackjack) 21.
elif score > 21 and eleven == 0:
res[6] += prob # Bust.
else:
dec deck.cards[c] # Remove card from deck.
dec deck.size
let lev = lev + 1
decks[lev] = deck
scores[lev] = score
elevens[lev] = eleven
probs[lev] = prob
drawCard(lev)
drawCard(0)
# But can't have blackjack, so adjust probabilities accordingly.
let pnbj = 1 - res[5]
for i in 0..6: res[i] /= pnbj
res[5] = 0
result = res
proc dealerChart =
## Print chart of dealer probabilities (as a check against an external source).
echo "Dealer Probabilities, Stands on Soft 17, 1 Deck, U.S Rules"
echo "Up Card 17 18 19 20 21 Bust"
echo "———————————————————————————————————————————————————————————————————"
var deck = initDeck()
deck.size = 51
for uc in Card.low..Card.high:
var deck2 = deck
dec deck2.cards[uc]
let dp = dealerProbs(uc, deck2)
stdout.write if uc > 1: &"{uc:3} " else: "Ace "
for i in [0, 1, 2, 3, 4, 6]: stdout.write &" {dp[i]:.6f}"
echo()
func calcGain(pscore: int; dp: openArray[float]): float =
## Calculates gain per unit staked for a given scenario (helper function).
case pscore
of 17:
result += dp[6] # Dealer is bust.
result -= dp[1] + dp[2] + dp[3] + dp[4] # Dealer has 18 to 21.
of 18:
result += dp[0] + dp[6] # Dealer has 17 or is bust.
result -= dp[2] + dp[3] + dp[4] # Dealer has 19 to 21.
of 19:
result += dp[0] + dp[1] + dp[6] # Dealer has 17, 18 or is bust.
result -= dp[3] + dp[4] # Dealer has 20 or 21.
of 20:
result += dp[0] + dp[1] + dp[2] + dp[6] # Dealer has 17 to 19 or is bust.
result -= dp[4] # Dealer has (non-blackjack) 21.
of 21:
result += dp[0] + dp[1] + dp[2] + dp[3] + dp[6] # Dealer has 17 to 20 or is bust.
of 22: # Notional.
result += 1.5 # Player blackjack.
of 23: # Notional.
result -= 1 # Player bust, loses stake irrespective of what dealer has.
else: # Player has less than 17
result += dp[6] # Dealer is bust.
result -= 1 - dp[6] # Dealer isn't bust.
func playerGain(card1, card2, uc: Card; startDeck: Deck): float =
## Returns player's expected gain per unit staked after hitting once and then standing.
let deck = startDeck
var
score = card1 + card2
eleven = false
if card1 == 1 or card2 == 1:
inc score, 10
eleven = true
for c in Card.low..Card.high:
# Get another card.
if deck.cards[c] == 0: continue # Card no longer present in deck.
# Temporary variables for current card.
var
deck2 = deck
score2 = score
eleven2 = eleven
inc score2, c # Add card to score.
if c == 1:
# Score all aces initially as 11.
inc score2, 10
eleven2 = true
let prob = deck2.cards[c] / deck2.size
dec deck2.cards[c]
dec deck2.size
if score2 > 21 and eleven2:
dec score2, 10 # Bust but can demote an ace.
if score2 <= 21:
let dp = dealerProbs(uc, deck2)
result += calcGain(score2, dp) * prob
else:
# Bust.
result -= prob
func playerGain2(card1, card2, uc: Card; startDeck: Deck): float =
## Return player's expected gain per unit staked after hitting once
## and then continuing in accordance with the tables for rounds >= 2.
var
eg = 0.0 # Result.
decks: array[9, Deck] # Decks for each level.
scores: array[9, int] # Scores for each level.
elevens: array[9, int] # Number of aces for each level scored as 11.
probs: array[9, float] # Probabilities for each level.
decks[0] = startDeck
scores[0] = card1 + card2
if card1 == 1 or card2 == 1:
inc scores[0], 10
elevens[0] = 1
probs[0] = 1.0
proc drawCard(lev: Natural) =
## Recursive closure.
for c in Card.low..Card.high:
if decks[lev].cards[c] == 0: continue # Card no longer present in deck.
# Temporary variables for current level.
var
deck = decks[lev]
score = scores[lev]
eleven = elevens[lev]
prob = probs[lev]
inc score, c # Add card to score.
if c == 1:
# Score all aces initially as 11.
inc score, 10
inc eleven
prob *= deck.cards[c] / deck.size
if score > 21 and eleven > 0:
dec score, 10 # Bust but can demote an ace.
dec eleven
dec deck.cards[c] # Remove card from deck.
dec deck.size
if (eleven == 0 and (score >= 17 or score >= 13 and uc < 7) or
eleven == 0 and score == 12 and uc >= 4 and uc <= 6 or
eleven > 0 and score == 18 and uc != 9 and uc != 10 or
eleven > 0 and score >= 19) and score <= 21:
let dp = dealerProbs(uc, deck)
eg += calcGain(score, dp) * prob
elif score > 21 and eleven == 0:
# Bust.
eg -= prob
else:
let lev = lev + 1
decks[lev] = deck
scores[lev] = score
elevens[lev] = eleven
probs[lev] = prob
drawCard(lev)
drawCard(0)
result = eg
func stand(card1, card2: Card): array[10, float] =
## Return player's expected gains per unit staked, for each dealer up-card, after standing.
var deck = initDeck()
dec deck.cards[card1]
dec deck.cards[card2]
deck.size = 50
var pscore = card1 + card2 # Player score.
if card1 == 1 or card2 == 1:
inc pscore, 10
for uc in Card.low..Card.high: # Dealer's up-card.
var deck2 = deck
dec deck2.cards[uc]
dec deck2.size
let dp = dealerProbs(uc, deck2)
let eg = calcGain(pscore, dp) # Expected gain for this up-card.
if uc > 1:
result[uc-2] = eg
else: # Dealer has Ace.
result[9] = eg # Ace comes last in tables.
func hit(card1, card2: Card; once: bool): array[10, float] =
## Return player's expected gains per unit staked, for each dealer
## up-card, after hitting once and then either standing (once == true)
## or continuing as per the round >= 2 tables (once == false).
var deck = initDeck()
dec deck.cards[card1]
dec deck.cards[card2]
deck.size = 50
for uc in Card.low..Card.high: # Dealer's up-card.
var deck2 = deck
dec deck2.cards[uc]
deck2.size = 49
# Player's expected gain for this up-card.
let peg = if once: playerGain(card1, card2, uc, deck2)
else: playerGain2(card1, card2, uc, deck2)
if uc > 1:
result[uc-2] = peg
else: # Dealer has Ace.
result[9] = peg
func double(card1, card2: Card): array[10, float] =
## Return player's expected gains per unit originally staked,
## for each dealer up-card, after doubling i.e. hitting once
## and then standing with a doubled stake.
result = hit(card1, card2, true) # Hit once and then stand.
for item in result.mitems:
item *= 2
proc split(card: Card): array[10, float] =
## Return player's expected gains per unit originally staked, for each dealer up-card, after
## splitting a pair and doubling the stake, getting a second card for each hand and then
## continuing in accordance with the rounds >= 2 tables. It is assumed that a player cannot
## double or re-split following a split. It is also assumed (in the interests of simplicity)
## that the expected gains for each split hand (after calculating the gains for the first hand
## as though the second hand is not completed) are exactly the same.
var deck = initDeck()
dec deck.cards[card], 2 # Must be a pair.
deck.size = 50
# Now play a single hand.
var score: int = card
var eleven = 0
if card == 1:
score = 11
eleven = 1
for uc in Card.low..Card.high: # Collect results for each dealer up-card.
if deck.cards[uc] == 0: continue # Card no longer present in deck.
var deck2 = deck
dec deck2.cards[uc]
dec deck2.size
var ix = uc - 2
if ix == -1: ix = 9 # In tables ace comes last.
var peg: float # Player expected gain for this up-card.
# Get second player card.
for c in Card.low..Card.high:
if deck2.cards[c] == 0: continue # Card no longer present in deck.
let prob = deck2.cards[c] / deck2.size
var deck3 = deck2
dec deck3.cards[c]
dec deck3.size
var score2 = score + c
var eleven2 = eleven
if c == 1:
# Score all aces initially as 11.
inc score2, 10
inc eleven2
if score2 == 21:
# Player has blackjack & we know dealer hasn't.
peg += 1.5 * prob
continue
if score2 > 21 and eleven2 > 0:
dec score2, 10 # Bust but can demote an ace.
dec eleven2
let action = if eleven2 > 0: sTable2[score2-12][ix] # Use soft strategy table, no doubling.
else: hTable2[score2-4][ix] # Use hard strategy table, no doubling
let peg2 = if action == Stand: calcGain(score2, dealerProbs(uc, deck3))
else: playerGain2(card, c, uc, deck3)
peg += peg2 * prob
if uc > 1:
result[uc-2] = peg * 2 # Allow for both hands in overall results.
else:
result[9] = peg * 2 # Ditto.
func bestAction(ags: openArray[ActionGain]): Action =
## Return the action with the highest expected gain.
ags[ags.maxIndex()].action
proc printHeader(title: string) =
## Print title and header for a given chart.
echo title
echo "P/D 2 3 4 5 6 7 8 9 T A"
echo "——————————————————————————————————————————————————————————————————————————"
proc printPair(c: Card) =
## Print header for a pair of cards.
stdout.write if c == 1: "AA " elif c == 10: "TT " else: &"{c}{c} "
func dealerPlay(pscore: int, next: var int; cards, d: openArray[Card]): float =
## Simulate a dealer's play for a given player's hand and state of deck.
## Return the player's gain (positive or negative) per unit staked.
var dscore = d[0] + d[1]
var aces = 0
if d[0] == 1 or d[1] == 1:
# Dealer has an ace.
inc dscore, 10
inc aces
while true:
if dscore > 21 and aces > 0:
dec dscore, 10 # Bust but we can demote an ace.
dec aces
if dscore > 21:
return 1 # Dealer is bust and player gains stake.
if dscore >= 17:
# Dealer must stick on 17 or above, hard or not.
if dscore > pscore:
return -1 # Dealer wins and player loses stake.
if dscore == pscore:
break # Player breaks even.
return 1 # Dealer loses and player gains stake.
let nc = cards[next] # Get new card from pack.
inc next
inc dscore, nc
if nc == 1:
# Count aces initially as 11.
inc dscore, 10
inc aces
proc playerPlay(): (float, float) =
## Simulate the playing of a random player's hand according to the strategy tables.
## Return both the gain (positive or negative) and the stake (1 or 2).
var perm = toSeq(0..51)
perm.shuffle()
var cards: array[52, Card]
for i, r in perm:
var card = r div 4 + 1
if card > 10: card = 10
cards[i] = card
var p, d: seq[Card] # Player and dealer hands.
# Initial deal.
p.add cards[0..1]
d.add cards[2..3]
var next = 4 # Index of next card to be dealt.
# Check if dealer and/or player have blackjack.
let dbj = d[0] == 1 and d[1] == 10 or d[0] == 10 and d[1] == 1
let pbj = p[0] == 1 and p[1] == 10 or p[0] == 10 and p[1] == 1
if dbj:
if pbj: return (0.0, 1.0) # Player neither wins nor loses.
else: return (-1.0, 1.0) # Player loses stake.
if pbj: return (1.5, 1.0) # Player wins 1.5 x stake.
var uc = d[0] - 2 # Dealer's up-card as index to access tables.
if uc < 0: uc = 9 # Ace is at last place in tables.
var stake = 1.0 # Player's initial stake.
var fscores: array[2, int] # Final player scores (one or, after split, two hands).
var action: Action
var score, aces: int
proc h(hand: int) =
## Process a hit.
while true:
let nc = cards[next] # Get new card from pack.
inc next
inc score, nc
if nc == 1:
# Count aces initially as 11.
inc score, 10
inc aces
if score > 21 and aces > 0:
dec score, 10 # Bust but we can demote an ace.
dec aces
if score > 21:
fscores[hand] = 22 # Player is bust and loses stake.
break
if action == Double:
fscores[hand] = score
break
# Get further strategy and act accordingly.
action = if aces == 0: hTable2[score-4][uc] else: sTable2[score-12][uc]
if action == Stand:
fscores[hand] = score
break
score = p[0] + p[1]
# Get kind of player hand: hard, soft, pair.
let kind = if p[0] == p[1]: Pair elif p[0] == 1 or p[1] == 1: Soft else: Hard
case kind
of Hard:
action = hTable[score-5][uc]
of Soft: # includes one ace.
let othercard = if p[0] == 1: p[1] else: p[0]
inc score, 10
aces = 1
action = sTable[otherCard-2][uc]
of Pair:
if p[0] == 1:
# Pair of aces.
inc score, 10
aces = 2
action = pTable[p[0]-1][uc]
case action
of Stand:
fscores[0] = score
of Hit:
h(0)
of Double:
h(0)
stake = 2
of Split:
for hand in 0..1:
score = p[0]
aces = 0
if score == 1:
# Count aces initially as 11.
score = 11
inc aces
h(hand)
var sum = 0.0
if fscores[0] < 22:
sum += dealerPlay(fscores[0], next, cards, d) * stake
else:
sum -= 1 * stake # This hand is bust.
if fscores[1] > 0:
# Pair.
if fscores[1] < 22:
sum += dealerPlay(fscores[1], next, cards, d)
else:
sum -= 1
stake = 2
result = (sum, stake)
proc simulate(perDay, days: int) =
## Simulate "perDay" blackjack games for "days" days.
var
winDays, loseDays, evenDays = 0
bigWin, bigLoss = 0.0
totalGain, totalStake = 0.0
for d in 1..days:
var dailyGain, dailyStake = 0.0
for p in 1..perDay:
let (gain, stake) = playerPlay()
dailyGain += gain
dailyStake += stake
if dailyGain > 0: inc winDays
elif dailyGain < 0: inc loseDays
else: inc evenDays
if dailyGain > bigWin: bigWin = dailyGain
elif -dailyGain > bigLoss: bigLoss = -dailyGain
totalGain += dailyGain
totalStake += dailyStake
echo &"\nAfter playing {perDay} times a day for {days} days:"
echo "Winning days: ", winDays
echo "Losing days: ", loseDays
echo "Breakeven days: ", evenDays
echo "Biggest win: ", bigWin
echo "Biggest loss: ", bigLoss
if totalGain < 0:
echo "Total loss: ", -totalGain
echo "Total staked: ", totalStake
echo &"Loss % staked: {-totalGain/totalStake*100:0.3f}\n"
else:
echo "Total win: ", totalGain
echo "Total staked: ", totalStake
echo &"Win % staked: {totalGain/totalStake*100:0.3f}\n"
proc main() =
# Print dealer probabilities chart.
dealerChart()
# For hard scores (i.e. different cards, no aces).
const Tuples = [(2, 3),
(2, 4),
(2, 5), (3, 4),
(2, 6), (3, 5),
(2, 7), (3, 6), (4, 5),
(2, 8), (3, 7), (4, 6),
(2, 9), (3, 8), (4, 7), (5, 6),
(2, 10), (3, 9), (4, 8), (5, 7),
(3, 10), (4, 9), (5, 8), (6, 7),
(4, 10), (5, 9), (6, 8),
(5, 10), (6, 9), (7, 8),
(6, 10), (7, 9),
(7, 10), (8, 9),
(8, 10),
(9, 10)]
# Number of tuples for each player score from 5 to 19.
const Counts = [float 1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 3, 2, 2, 1, 1]
# Expected gains for each player score & for each dealer up-card.
var
segs: array[15, array[10, float]] # if stands.
hegs: array[15, array[10, float]] # if hits.
degs: array[15, array[10, float]] # if doubles.
for t in Tuples:
let i = t[0] + t[1]
let sg = stand(t[0], t[1])
let hg = hit(t[0], t[1], false)
let dg = double(t[0], t[1])
for j in 0..9:
segs[i-5][j] += sg[j]
hegs[i-5][j] += hg[j]
degs[i-5][j] += dg[j]
# Calculate the average per tuple for each score.
for i in 0..14:
for j in 0..9:
segs[i][j] /= Counts[i]
hegs[i][j] /= Counts[i]
degs[i][j] /= Counts[i]
printHeader("\nHard Chart - Player Expected Gains per unit (Stand)")
for i in 5..19:
stdout.write &"{i:2} "
for j in 0..9:
stdout.write &"{segs[i-5][j]: 0.3f} "
echo()
printHeader("\nHard Chart - Player Expected Gains per unit (Hit)")
for i in 5..19:
stdout.write &"{i:2} "
for j in 0..9:
stdout.write &"{hegs[i-5][j]: 0.3f} "
echo()
printHeader("\nHard Chart - Player Expected Gains per unit (Double)")
for i in 5..19:
stdout.write &"{i:2} "
for j in 0..9:
stdout.write &"{degs[i-5][j]: 0.3f} "
echo()
printHeader("\nHard Chart - Player Strategy (Round 1)")
for i in 5..19:
stdout.write &"{i:2} "
for j in 0..9:
let ags = [(Stand, segs[i-5][j]), (Hit, hegs[i-5][j]), (Double, degs[i-5][j])]
let action = bestAction(ags)
hTable[i-5][j] = action
stdout.write &"{action:^6} "
echo()
# For hard scores (no aces) - after round 1 (no doubling or splitting).
# Based on hard table figures (round 1) with scores of 4, 20, and 21 added.
var
segs2: array[18, array[10, float]] # Expected gains if stands.
hegs2: array[18, array[10, float]] # Expected gains if hits.
for i in 5..19:
segs2[i-4] = segs[i-5]
hegs2[i-4] = hegs[i-5]
let sg4 = stand(2, 2)
let hg4 = hit(2, 2, false)
let sg20 = stand(10, 10)
let hg20 = hit(10, 10, false)
let sg21 = stand(1, 10)
let hg21 = hit(1, 10, false)
for j in 0..9:
segs2[0][j] += sg4[j]
hegs2[0][j] += hg4[j]
segs2[16][j] += sg20[j]
hegs2[16][j] += hg20[j]
segs2[17][j] += sg21[j]
hegs2[17][j] += hg21[j]
printHeader("\nHard Chart - Player Strategy (Round >= 2, No Doubling)")
for i in 4..21:
stdout.write &"{i:2} "
for j in 0..9:
var action = Stand
if hegs2[i-4][j] > segs2[i-4][j]: action = Hit
hTable2[i-4][j] = action
stdout.write &"{action:^6} "
echo()
# For soft scores (i.e. including exactly one ace).
# Expected gains for each player second card (2 to 9) & for each dealer up-card.
var
segs3: array[8, array[10, float]] # if stands.
hegs3: array[8, array[10, float]] # if hits.
degs3: array[8, array[10, float]] # if doubles.
for c in 2..9:
let sg = stand(1, c)
let hg = hit(1, c, false)
let dg = double(1, c)
for j in 0..9:
segs3[c-2][j] += sg[j]
hegs3[c-2][j] += hg[j]
degs3[c-2][j] += dg[j]
printHeader("\nSoft Chart - Player Expected Gains per unit (Stand)")
for c in 2..9:
stdout.write &"A{c} "
for j in 0..9:
stdout.write &"{segs3[c-2][j]: 0.3f} "
echo()
printHeader("\nSoft Chart - Player Expected Gains per unit (Hit)")
for c in 2..9:
stdout.write &"A{c} "
for j in 0..9:
stdout.write &"{hegs3[c-2][j]: 0.3f} "
echo()
printHeader("\nSoft Chart - Player Expected Gains per unit (Double)")
for c in 2..9:
stdout.write &"A{c} "
for j in 0..9:
stdout.write &"{degs3[c-2][j]: 0.3f} "
echo()
printHeader("\nSoft Chart - Player Strategy (Round 1)")
for c in 2..9:
stdout.write &"A{c} "
for j in 0..9:
let ags = [(Stand, segs3[c-2][j]), (Hit, hegs3[c-2][j]), (Double, degs3[c-2][j])]
let action = bestAction(ags)
sTable[c-2][j] = action
stdout.write &"{action:^6} "
echo()
# For soft scores (at least one ace) - after round 1 (no doubling or splitting).
# Based on soft table figures (round 1) with scores of 12 and 21 added.
# Assumes one ace counted as 11.
var
segs4: array[10, array[10, float]] # Expected gains if stands.
hegs4: array[10, array[10, float]] # Expected gains if hits.
for i in 1..8:
segs4[i] = segs3[i-1]
hegs4[i] = hegs3[i-1]
let sg12 = stand(1, 1)
let hg12 = hit(1, 1, false)
for j in 0..9:
segs4[0][j] += sg12[j]
hegs4[0][j] += hg12[j]
segs4[9][j] += sg21[j]
hegs4[9][j] += hg21[j]
printHeader("\nSoft Chart - Player Strategy (Round >= 2, No Doubling)")
for i in 12..21:
stdout.write &"{i:2} "
for j in 0..9:
var action = Stand
if hegs4[i-12][j] > segs4[i-12][j]: action = Hit
sTable2[i-12][j] = action
stdout.write &"{action:^6} "
echo()
# For pairs.
# Expected gains for each pair (A to 10) & for each dealer up-card.
var
segs5: array[10, array[10, float]] # if stands.
hegs5: array[10, array[10, float]] # if hits.
degs5: array[10, array[10, float]] # if double.
pegs5: array[10, array[10, float]] # if split.
for c in 1..10:
let
sg = stand(c, c)
hg = hit(c, c, false)
dg = double(c, c)
pg = split(c)
for j in 0..9:
segs5[c-1][j] += sg[j]
hegs5[c-1][j] += hg[j]
degs5[c-1][j] += dg[j]
pegs5[c-1][j] += pg[j]
printHeader("\nPairs Chart - Player Expected Gains per unit (Stand)")
for c in 1..10:
printPair(c)
for j in 0..9:
stdout.write &"{segs5[c-1][j]: 0.3f} "
echo()
printHeader("\nPairs Chart - Player Expected Gains per unit (Hit)")
for c in 1..10:
printPair(c)
for j in 0..9:
stdout.write &"{hegs5[c-1][j]: 0.3f} "
echo()
printHeader("\nPairs Chart - Player Expected Gains per unit (Double)")
for c in 1..10:
printPair(c)
for j in 0..9:
stdout.write &"{degs5[c-1][j]: 0.3f} "
echo()
printHeader("\nPairs Chart - Player Expected Gains per unit (Split)")
for c in 1..10:
printPair(c)
for j in 0..9:
stdout.write &"{pegs5[c-1][j]: 0.3f} "
echo()
printHeader("\nPairs Chart - Player Strategy (Round 1)")
for c in 1..10:
printPair(c)
for j in 0..9:
let ags = [(Stand, segs5[c-1][j]), (Hit, hegs5[c-1][j]),
(Double, degs5[c-1][j]), (Split, pegs5[c-1][j])]
let action = bestAction(ags)
pTable[c-1][j] = action
stdout.write &"{action:^6} "
echo()
randomize()
# Do 10 years of simulation.
for i in 1..10:
echo &"Simulation for year {i}:"
simulate(50, 365)
main()</lang>
{{out}}
<pre>Dealer Probabilities, Stands on Soft 17, 1 Deck, U.S Rules
Up Card 17 18 19 20 21 Bust
———————————————————————————————————————————————————————————————————
Ace 0.183786 0.190890 0.188680 0.191692 0.075137 0.169815
2 0.138976 0.131762 0.131815 0.123948 0.120526 0.352973
3 0.130313 0.130946 0.123761 0.123345 0.116047 0.375588
4 0.130973 0.114163 0.120679 0.116286 0.115096 0.402803
5 0.119687 0.123483 0.116909 0.104694 0.106321 0.428905
6 0.166948 0.106454 0.107192 0.100705 0.097878 0.420823
7 0.372345 0.138583 0.077334 0.078897 0.072987 0.259854
8 0.130857 0.362989 0.129445 0.068290 0.069791 0.238627
9 0.121886 0.103921 0.357391 0.122250 0.061109 0.233442
10 0.124156 0.122486 0.124421 0.356869 0.039570 0.232499
Hard Chart - Player Expected Gains per unit (Stand)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
5 -0.293 -0.248 -0.176 -0.104 -0.122 -0.469 -0.513 -0.533 -0.546 -0.659
6 -0.291 -0.232 -0.172 -0.101 -0.119 -0.467 -0.522 -0.533 -0.547 -0.659
7 -0.283 -0.229 -0.163 -0.098 -0.117 -0.471 -0.521 -0.537 -0.547 -0.658
8 -0.276 -0.229 -0.162 -0.100 -0.130 -0.478 -0.523 -0.539 -0.549 -0.648
9 -0.277 -0.224 -0.160 -0.108 -0.134 -0.480 -0.528 -0.543 -0.542 -0.646
10 -0.279 -0.227 -0.172 -0.120 -0.146 -0.484 -0.531 -0.539 -0.537 -0.644
11 -0.277 -0.231 -0.175 -0.123 -0.147 -0.488 -0.529 -0.537 -0.537 -0.646
12 -0.286 -0.241 -0.185 -0.134 -0.151 -0.485 -0.526 -0.535 -0.533 -0.655
13 -0.282 -0.236 -0.181 -0.133 -0.156 -0.488 -0.529 -0.537 -0.534 -0.649
14 -0.282 -0.238 -0.188 -0.134 -0.159 -0.489 -0.529 -0.533 -0.536 -0.651
15 -0.280 -0.239 -0.190 -0.144 -0.169 -0.494 -0.531 -0.536 -0.531 -0.648
16 -0.287 -0.250 -0.194 -0.152 -0.179 -0.495 -0.526 -0.540 -0.530 -0.648
17 -0.147 -0.120 -0.074 -0.044 -0.011 -0.122 -0.405 -0.414 -0.402 -0.459
18 0.119 0.144 0.164 0.202 0.268 0.389 0.096 -0.196 -0.155 -0.082
19 0.385 0.384 0.404 0.448 0.484 0.610 0.577 0.264 0.103 0.308
Hard Chart - Player Expected Gains per unit (Hit)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
5 -0.131 -0.098 -0.041 0.022 0.019 -0.119 -0.181 -0.262 -0.309 -0.417
6 -0.151 -0.107 -0.055 0.009 0.014 -0.164 -0.234 -0.305 -0.349 -0.443
7 -0.111 -0.072 -0.013 0.053 0.064 -0.069 -0.223 -0.295 -0.332 -0.401
8 -0.015 0.021 0.084 0.136 0.148 0.092 -0.056 -0.213 -0.253 -0.275
9 0.090 0.137 0.181 0.226 0.235 0.194 0.111 -0.052 -0.148 -0.128
10 0.215 0.246 0.277 0.314 0.319 0.277 0.211 0.119 0.030 0.030
11 0.272 0.296 0.327 0.361 0.362 0.293 0.222 0.146 0.107 0.113
12 -0.256 -0.232 -0.206 -0.181 -0.179 -0.241 -0.308 -0.380 -0.378 -0.413
13 -0.315 -0.293 -0.270 -0.252 -0.251 -0.301 -0.362 -0.389 -0.423 -0.440
14 -0.363 -0.353 -0.337 -0.315 -0.313 -0.346 -0.366 -0.426 -0.455 -0.460
15 -0.419 -0.414 -0.406 -0.392 -0.383 -0.351 -0.406 -0.466 -0.496 -0.487
16 -0.461 -0.460 -0.454 -0.448 -0.397 -0.376 -0.426 -0.481 -0.510 -0.497
17 -0.534 -0.536 -0.538 -0.493 -0.484 -0.450 -0.475 -0.529 -0.558 -0.546
18 -0.633 -0.634 -0.597 -0.591 -0.586 -0.567 -0.565 -0.593 -0.624 -0.630
19 -0.750 -0.713 -0.712 -0.709 -0.707 -0.699 -0.697 -0.698 -0.712 -0.740
Hard Chart - Player Expected Gains per unit (Double)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
5 -0.587 -0.497 -0.352 -0.209 -0.244 -0.938 -1.025 -1.066 -1.093 -1.318
6 -0.560 -0.446 -0.324 -0.186 -0.215 -0.870 -1.023 -1.045 -1.074 -1.295
7 -0.415 -0.317 -0.186 -0.066 -0.059 -0.555 -0.851 -0.936 -0.956 -1.127
8 -0.165 -0.081 0.032 0.143 0.157 -0.140 -0.433 -0.697 -0.743 -0.802
9 0.114 0.193 0.286 0.380 0.393 0.175 0.007 -0.281 -0.442 -0.409
10 0.428 0.492 0.554 0.628 0.638 0.446 0.313 0.164 0.007 0.025
11 0.542 0.592 0.654 0.722 0.724 0.479 0.341 0.223 0.164 0.198
12 -0.511 -0.463 -0.413 -0.362 -0.358 -0.556 -0.690 -0.811 -0.789 -0.827
13 -0.630 -0.587 -0.541 -0.503 -0.503 -0.651 -0.775 -0.807 -0.862 -0.880
14 -0.727 -0.706 -0.673 -0.630 -0.627 -0.723 -0.759 -0.862 -0.915 -0.921
15 -0.838 -0.829 -0.812 -0.783 -0.767 -0.716 -0.826 -0.937 -0.992 -0.973
16 -0.921 -0.920 -0.908 -0.896 -0.793 -0.751 -0.853 -0.961 -1.019 -0.995
17 -1.069 -1.072 -1.076 -0.985 -0.967 -0.901 -0.949 -1.058 -1.116 -1.092
18 -1.265 -1.267 -1.195 -1.182 -1.172 -1.135 -1.130 -1.186 -1.248 -1.260
19 -1.499 -1.425 -1.423 -1.417 -1.414 -1.397 -1.395 -1.396 -1.425 -1.481
Hard Chart - Player Strategy (Round 1)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
5 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
6 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
7 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
8 Hit Hit Hit Double Double Hit Hit Hit Hit Hit
9 Double Double Double Double Double Hit Hit Hit Hit Hit
10 Double Double Double Double Double Double Double Double Hit Hit
11 Double Double Double Double Double Double Double Double Double Double
12 Hit Hit Stand Stand Stand Hit Hit Hit Hit Hit
13 Stand Stand Stand Stand Stand Hit Hit Hit Hit Hit
14 Stand Stand Stand Stand Stand Hit Hit Hit Hit Hit
15 Stand Stand Stand Stand Stand Hit Hit Hit Hit Hit
16 Stand Stand Stand Stand Stand Hit Hit Hit Hit Hit
17 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
18 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
19 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
Hard Chart - Player Strategy (Round >= 2, No Doubling)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
4 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
5 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
6 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
7 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
8 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
9 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
10 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
11 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
12 Hit Hit Stand Stand Stand Hit Hit Hit Hit Hit
13 Stand Stand Stand Stand Stand Hit Hit Hit Hit Hit
14 Stand Stand Stand Stand Stand Hit Hit Hit Hit Hit
15 Stand Stand Stand Stand Stand Hit Hit Hit Hit Hit
16 Stand Stand Stand Stand Stand Hit Hit Hit Hit Hit
17 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
18 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
19 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
20 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
21 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
Soft Chart - Player Expected Gains per unit (Stand)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
A2 -0.283 -0.241 -0.186 -0.119 -0.114 -0.462 -0.508 -0.517 -0.539 -0.662
A3 -0.284 -0.240 -0.170 -0.116 -0.112 -0.460 -0.505 -0.527 -0.538 -0.661
A4 -0.283 -0.224 -0.166 -0.113 -0.109 -0.458 -0.514 -0.526 -0.538 -0.659
A5 -0.266 -0.221 -0.164 -0.111 -0.108 -0.468 -0.515 -0.525 -0.537 -0.659
A6 -0.132 -0.093 -0.037 0.005 0.010 -0.090 -0.385 -0.407 -0.418 -0.483
A7 0.136 0.167 0.204 0.222 0.262 0.412 0.121 -0.179 -0.186 -0.101
A8 0.402 0.420 0.415 0.461 0.482 0.615 0.608 0.288 0.064 0.290
A9 0.656 0.644 0.654 0.682 0.694 0.773 0.785 0.766 0.555 0.681
Soft Chart - Player Expected Gains per unit (Hit)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
A2 0.039 0.071 0.110 0.159 0.168 0.107 0.039 -0.014 -0.090 -0.184
A3 0.017 0.044 0.091 0.137 0.147 0.060 0.035 -0.060 -0.124 -0.216
A4 -0.012 0.022 0.061 0.108 0.120 0.034 -0.035 -0.114 -0.172 -0.256
A5 -0.032 -0.003 0.038 0.082 0.116 -0.024 -0.084 -0.167 -0.229 -0.296
A6 0.007 0.036 0.077 0.140 0.133 0.060 -0.065 -0.135 -0.189 -0.242
A7 0.065 0.093 0.156 0.175 0.192 0.175 0.047 -0.087 -0.140 -0.160
A8 0.120 0.173 0.187 0.227 0.241 0.222 0.158 0.005 -0.087 -0.081
A9 0.191 0.196 0.230 0.268 0.280 0.243 0.172 0.096 0.007 -0.008
Soft Chart - Player Expected Gains per unit (Double)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
A2 -0.042 0.028 0.115 0.212 0.230 -0.157 -0.312 -0.373 -0.478 -0.586
A3 -0.047 0.011 0.109 0.204 0.222 -0.175 -0.254 -0.394 -0.479 -0.588
A4 -0.070 0.003 0.085 0.175 0.201 -0.141 -0.314 -0.422 -0.495 -0.613
A5 -0.082 -0.019 0.063 0.148 0.217 -0.189 -0.333 -0.452 -0.536 -0.649
A6 0.013 0.074 0.155 0.280 0.266 0.014 -0.230 -0.345 -0.433 -0.522
A7 0.128 0.189 0.313 0.349 0.385 0.240 -0.015 -0.254 -0.322 -0.359
A8 0.237 0.346 0.373 0.453 0.483 0.325 0.190 -0.060 -0.226 -0.200
A9 0.380 0.392 0.459 0.536 0.560 0.351 0.230 0.111 -0.055 -0.055
Soft Chart - Player Strategy (Round 1)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
A2 Hit Hit Double Double Double Hit Hit Hit Hit Hit
A3 Hit Hit Double Double Double Hit Hit Hit Hit Hit
A4 Hit Hit Double Double Double Hit Hit Hit Hit Hit
A5 Hit Hit Double Double Double Hit Hit Hit Hit Hit
A6 Double Double Double Double Double Hit Hit Hit Hit Hit
A7 Stand Double Double Double Double Stand Stand Hit Hit Stand
A8 Stand Stand Stand Stand Double Stand Stand Stand Stand Stand
A9 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
Soft Chart - Player Strategy (Round >= 2, No Doubling)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
12 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
13 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
14 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
15 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
16 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
17 Hit Hit Hit Hit Hit Hit Hit Hit Hit Hit
18 Stand Stand Stand Stand Stand Stand Stand Hit Hit Stand
19 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
20 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
21 Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
Pairs Chart - Player Expected Gains per unit (Stand)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
AA -0.274 -0.232 -0.178 -0.130 -0.104 -0.452 -0.500 -0.511 -0.531 -0.663
22 -0.291 -0.251 -0.192 -0.107 -0.125 -0.471 -0.515 -0.523 -0.547 -0.660
33 -0.295 -0.246 -0.160 -0.101 -0.119 -0.467 -0.510 -0.542 -0.546 -0.660
44 -0.290 -0.214 -0.152 -0.095 -0.114 -0.463 -0.529 -0.543 -0.547 -0.656
55 -0.256 -0.206 -0.146 -0.090 -0.112 -0.484 -0.531 -0.541 -0.545 -0.653
66 -0.262 -0.211 -0.152 -0.102 -0.165 -0.493 -0.536 -0.549 -0.552 -0.617
77 -0.268 -0.219 -0.164 -0.156 -0.174 -0.502 -0.539 -0.555 -0.510 -0.631
88 -0.275 -0.228 -0.215 -0.165 -0.178 -0.503 -0.551 -0.516 -0.518 -0.644
99 0.137 0.123 0.167 0.203 0.265 0.401 0.065 -0.196 -0.133 -0.055
TT 0.627 0.636 0.645 0.674 0.697 0.765 0.783 0.744 0.583 0.650
Pairs Chart - Player Expected Gains per unit (Hit)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
AA 0.095 0.120 0.142 0.182 0.200 0.158 0.093 -0.003 -0.048 -0.075
22 -0.113 -0.082 -0.035 0.036 0.032 -0.092 -0.141 -0.222 -0.277 -0.395
33 -0.153 -0.118 -0.047 0.008 0.014 -0.164 -0.231 -0.310 -0.346 -0.444
44 -0.013 0.028 0.098 0.154 0.175 0.111 -0.055 -0.206 -0.246 -0.268
55 0.224 0.254 0.295 0.347 0.362 0.279 0.207 0.119 0.032 0.042
66 -0.253 -0.222 -0.190 -0.162 -0.194 -0.265 -0.322 -0.386 -0.386 -0.411
77 -0.406 -0.388 -0.369 -0.370 -0.367 -0.389 -0.408 -0.475 -0.516 -0.510
88 -0.454 -0.450 -0.461 -0.453 -0.397 -0.374 -0.426 -0.487 -0.512 -0.490
99 -0.627 -0.638 -0.597 -0.590 -0.587 -0.566 -0.566 -0.595 -0.626 -0.621
TT -0.847 -0.846 -0.846 -0.846 -0.845 -0.843 -0.843 -0.842 -0.840 -0.882
Pairs Chart - Player Expected Gains per unit (Double)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
AA -0.019 0.055 0.137 0.216 0.248 -0.137 -0.296 -0.421 -0.468 -0.591
22 -0.582 -0.501 -0.384 -0.214 -0.249 -0.942 -1.030 -1.047 -1.094 -1.320
33 -0.567 -0.472 -0.302 -0.184 -0.215 -0.871 -1.000 -1.065 -1.072 -1.298
44 -0.185 -0.082 0.044 0.162 0.193 -0.108 -0.447 -0.701 -0.741 -0.802
55 0.446 0.510 0.590 0.695 0.724 0.466 0.323 0.175 0.014 0.042
66 -0.505 -0.444 -0.380 -0.325 -0.387 -0.599 -0.711 -0.817 -0.803 -0.823
77 -0.813 -0.777 -0.738 -0.741 -0.734 -0.823 -0.858 -0.978 -1.035 -1.019
88 -0.908 -0.900 -0.922 -0.906 -0.793 -0.747 -0.853 -0.974 -1.024 -0.980
99 -1.255 -1.277 -1.194 -1.181 -1.173 -1.132 -1.133 -1.189 -1.252 -1.242
TT -1.693 -1.693 -1.693 -1.691 -1.690 -1.686 -1.685 -1.684 -1.681 -1.764
Pairs Chart - Player Expected Gains per unit (Split)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
AA 1.192 1.223 1.265 1.321 1.344 1.308 1.201 1.039 0.860 0.921
22 -0.128 -0.070 -0.007 0.128 0.126 -0.054 -0.213 -0.383 -0.463 -0.566
33 -0.202 -0.128 0.009 0.117 0.112 -0.115 -0.265 -0.418 -0.509 -0.579
44 -0.236 -0.127 -0.013 0.095 0.083 -0.223 -0.343 -0.493 -0.580 -0.623
55 -0.232 -0.150 -0.038 0.068 0.056 -0.299 -0.448 -0.608 -0.685 -0.695
66 -0.219 -0.135 -0.028 0.068 -0.011 -0.270 -0.413 -0.570 -0.652 -0.660
77 -0.163 -0.084 0.016 0.039 0.053 -0.123 -0.423 -0.564 -0.634 -0.635
88 0.017 0.077 0.106 0.188 0.234 0.202 -0.100 -0.430 -0.464 -0.378
99 0.170 0.170 0.253 0.339 0.359 0.341 0.179 -0.112 -0.268 -0.109
TT 0.412 0.465 0.518 0.596 0.619 0.576 0.447 0.276 0.146 0.140
Pairs Chart - Player Strategy (Round 1)
P/D 2 3 4 5 6 7 8 9 T A
——————————————————————————————————————————————————————————————————————————
AA Split Split Split Split Split Split Split Split Split Split
22 Hit Split Split Split Split Split Hit Hit Hit Hit
33 Hit Hit Split Split Split Split Hit Hit Hit Hit
44 Hit Hit Hit Double Double Hit Hit Hit Hit Hit
55 Double Double Double Double Double Double Double Double Hit Double
66 Split Split Split Split Split Hit Hit Hit Hit Hit
77 Split Split Split Split Split Split Hit Hit Stand Hit
88 Split Split Split Split Split Split Split Split Split Split
99 Split Split Split Split Split Stand Split Split Stand Stand
TT Stand Stand Stand Stand Stand Stand Stand Stand Stand Stand
Simulation for year 1:
After playing 50 times a day for 365 days:
Winning days: 179
Losing days: 180
Breakeven days: 6
Biggest win: 33.0
Biggest loss: 22.5
Total win: 144.0
Total staked: 20623.0
Win % staked: 0.698
Simulation for year 2:
After playing 50 times a day for 365 days:
Winning days: 168
Losing days: 184
Breakeven days: 13
Biggest win: 25.5
Biggest loss: 25.0
Total loss: 233.0
Total staked: 20553.0
Loss % staked: 1.134
Simulation for year 3:
After playing 50 times a day for 365 days:
Winning days: 177
Losing days: 176
Breakeven days: 12
Biggest win: 25.5
Biggest loss: 22.0
Total loss: 18.5
Total staked: 20646.0
Loss % staked: 0.090
Simulation for year 4:
After playing 50 times a day for 365 days:
Winning days: 193
Losing days: 164
Breakeven days: 8
Biggest win: 26.5
Biggest loss: 22.0
Total win: 210.5
Total staked: 20635.0
Win % staked: 1.020
Simulation for year 5:
After playing 50 times a day for 365 days:
Winning days: 161
Losing days: 191
Breakeven days: 13
Biggest win: 25.0
Biggest loss: 31.0
Total loss: 270.0
Total staked: 20502.0
Loss % staked: 1.317
Simulation for year 6:
After playing 50 times a day for 365 days:
Winning days: 182
Losing days: 175
Breakeven days: 8
Biggest win: 23.0
Biggest loss: 26.0
Total win: 104.0
Total staked: 20610.0
Win % staked: 0.505
Simulation for year 7:
After playing 50 times a day for 365 days:
Winning days: 178
Losing days: 181
Breakeven days: 6
Biggest win: 19.0
Biggest loss: 21.5
Total loss: 86.0
Total staked: 20546.0
Loss % staked: 0.419
Simulation for year 8:
After playing 50 times a day for 365 days:
Winning days: 178
Losing days: 177
Breakeven days: 10
Biggest win: 26.5
Biggest loss: 21.0
Total loss: 127.5
Total staked: 20522.0
Loss % staked: 0.621
Simulation for year 9:
After playing 50 times a day for 365 days:
Winning days: 173
Losing days: 184
Breakeven days: 8
Biggest win: 25.0
Biggest loss: 24.0
Total loss: 14.5
Total staked: 20551.0
Loss % staked: 0.071
Simulation for year 10:
After playing 50 times a day for 365 days:
Winning days: 170
Losing days: 178
Breakeven days: 17
Biggest win: 20.0
Biggest loss: 21.5
Total loss: 93.0
Total staked: 20516.0
Loss % staked: 0.453</pre>
=={{header|Phix}}==
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