Lucky Thirteen Blackjack Dice

 Lucky13 ♠  ♥  BLACKJACK PAYS 3 TO 2  ♦  ♣ Dealer must hit soft 11
DICE GAMES:
WINNING PAIR OF FIVES PAYS 5:1
(TIMES ORIGINAL BET)
SEVEN-DIE CHARLIE WINS
(EXCEPT FOR DEALER BLACKJACK)
DOUBLE ON ANY TWO DICE,
LOSE ORIGINAL BET ONLY
ON DEALER BLACKJACK
EARLY SURRENDER

MINIMUM: \$100

winnings:  \$ 0

dice color:

How-to

 = blackjack

Lucky Thirteen Blackjack Dice is what blackjack would be if it had been invented using dice instead of cards.  Each die is worth its face value, except aces (ones) which may be worth one or seven.  A blackjack consists of an ace and a six, for a total of thirteen, and beats everything except another blackjack.  The object of the game is to beat the dealer without busting (going over thirteen).

If you need an introduction to blackjack, the Wikipedia article is a good place to start.  Briefly, start by clicking deal.  Then, assuming that you did not get a blackjack, your options are:

hit me, to receive another die;

double down, to double your bet and take exactly one more die (on the first two dice only);

surrender, to give up half your bet and end the hand (on the first two dice only); and

stand, to take no more dice.

If you get a blackjack and the dealer shows a six or an ace, you will be offered even money for your blackjack; this is the equivalent of insurance.  If you take it, you win your original bet only, not the 3:2 blackjack payout, but you avoid the risk of a push (a tie, for no gain) if the dealer also has a blackjack.  (With cards, insurance is usually offered only when the dealer shows an ace, because there are many more tens than aces in the deck; but with dice, the probability of a six or an ace is the same.)

If you play the hand, click hit me until you either decide to stand, or reach a total of thirteen, or bust.  If you do not bust, the dealer then plays to finish the hand.

 7 + 4 = soft 11 1 + 4 + 4 = hard 9

Start by counting aces as seven.  Such a hand is a “soft” hand; if the total goes over thirteen, compress it to a “hard” hand by counting the ace as one, and keep going.

The original bet is a black chip (\$100).  As the table says, a blackjack pays 3:2 (\$150).  The dealer must stand on hard 11 and hit soft 11.  There is no hole die; but on dealer blackjack, a player who has doubled down loses the original bet only.  If the player busts after doubling when the dealer shows a six or an ace, the dealer deals a second die to “peek” for a blackjack.  (The “original bet only” rule compensates for the absence of a hole die.)  To sum it up in blackjack terms:  H11, DOA, ES, NHC, OBO.

 win pays 5:1

Some concessions were made for the sake of limiting the number of dice, the most obvious being no option to split.  To compensate, if your first two dice are a pair of fives, a win pays 5:1.  (You might be tempted to stand on a pair of fives, but you will usually lose, to your disadvantage.  And the payout applies to the original bet, so don’t double down.)  Also, a seven-die Charlie (seven dice without busting) wins, unless the dealer gets a blackjack.  (As it happens, the maximum number of dice the dealer can take before standing is seven:  2, 2, 2, 2, A, A, A.  So each player needs seven dice.)

The super bets, as always, are gimmicks.  Have fun!

Basic strategy

Dealer hits soft 11
 player hand dealer die hard totals 2 3 4 5 6 A 4-9 H H H H H H 10 H H H H H RH 11 S S S S S RH 12 S S S S S S soft totals 2 3 4 5 6 A A,A-A,4 H H H H H H A,5 S S S S S S
Dealer stands on all 11’s
 player hand dealer die hard totals 2 3 4 5 6 A 4-9 H H H H H H 10 H H H H H H 11 S S S S S RS 12 S S S S S S soft totals 2 3 4 5 6 A A,A-A,4 H H H H H H A,5 S S S S S S

H = hit; S = stand; RH = surrender, or hit; RS = surrender, or stand; P = split.

(Strategies are based on 3,000,000 hands per action (hit, stand, double), per dealer die, per player hand, 756,000,000 hands total.)

Keen-eyed observers will note that the strategy never says to double down.  (It does if the house stands on 12; but if the house stands on 10 or 12, the player advantage is enormous, and you wouldn’t see it in a casino.)

“Stiff” hands, those which should be hit but may bust, are hard 8-10.  “Pat” hands, those on which the player generally stands, are hard 11-12 and soft 12.

The house advantage for the game above is 0.27% (10,000,000,000 hands), comparable to a casino.  Without the pair bonus, it would be 2.65%.  Without seven-die Charlie and surrender, it would be 2.85%.

If the dealer stands on all 11’s, the player advantage is 0.23% without the pair bonus, and a casino would have to resort to reducing the blackjack payout or some such.

If you were to split, the house edge would be something like 0.67% without the pair bonus.

Dealer hits soft 11
 player hand dealer die pairs 2 3 4 5 6 A 2,2 P P P P H H 3,3-4,4 H H H H H H 5,5 P P P P P RH 6,6 S S S S S S A,A P P P P H H
Dealer stands on all 11’s
 player hand dealer die pairs 2 3 4 5 6 A 2,2 P P P P H H 3,3-4,4 H H H H H H 5,5 P P P P P H 6,6 S S S S S S A,A P P P P H H

Win rate per hand (without splitting):

Dealer hits soft 11
 player hand dealer die hard totals 2 3 4 5 6 A 4 -0.141 -0.121 -0.095 -0.065 -0.204 -0.372 5 -0.141 -0.117 -0.083 -0.058 -0.195 -0.404 6 -0.013 0.009 0.039 0.073 -0.086 -0.281 7 -0.013 0.009 0.039 0.074 -0.087 -0.282 8 -0.154 -0.134 -0.109 -0.081 -0.216 -0.385 9 -0.275 -0.259 -0.236 -0.212 -0.329 -0.472 10 -0.378 -0.365 -0.345 -0.325 -0.424 -0.500 11 -0.269 -0.224 -0.152 -0.210 -0.324 -0.500 12 0.242 0.272 0.309 0.407 0.206 -0.131 soft totals 2 3 4 5 6 A A,A 0.166 0.186 0.208 0.267 0.078 -0.115 A,2 0.100 0.119 0.143 0.197 0.018 -0.170 A,3 0.029 0.050 0.072 0.121 -0.048 -0.226 A,4 -0.013 0.008 0.039 0.073 -0.087 -0.282 A,5 0.241 0.273 0.309 0.406 0.206 -0.131
Dealer stands on all 11’s
 player hand dealer die hard totals 2 3 4 5 6 A 4 -0.121 -0.113 -0.043 -0.066 -0.204 -0.292 5 -0.118 -0.106 -0.018 -0.057 -0.196 -0.306 6 0.010 0.020 0.100 0.073 -0.086 -0.187 7 0.009 0.019 0.101 0.073 -0.086 -0.187 8 -0.135 -0.126 -0.057 -0.080 -0.217 -0.303 9 -0.259 -0.251 -0.192 -0.212 -0.329 -0.403 10 -0.364 -0.358 -0.307 -0.324 -0.425 -0.488 11 -0.249 -0.215 -0.098 -0.211 -0.323 -0.500 12 0.290 0.293 0.442 0.407 0.206 0.079 soft totals 2 3 4 5 6 A A,A 0.185 0.191 0.273 0.262 0.073 -0.014 A,2 0.122 0.128 0.207 0.195 0.016 -0.070 A,3 0.052 0.059 0.133 0.120 -0.047 -0.129 A,4 0.009 0.020 0.100 0.073 -0.086 -0.187 A,5 0.289 0.294 0.442 0.407 0.206 0.079

Dealer bust probability (10,000,000 hands):

Dealer hits soft 11
 dealer die 2 3 4 5 6 A 0.246 0.271 0.309 0.240 0.206 0.134
Dealer stands on all 11’s
 dealer die 2 3 4 5 6 A 0.234 0.266 0.274 0.240 0.206 0.080

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