Discount Gambling

Lucky Lucky Blackjack Sidebet (+EV)

Posted in +EV, blackjack sidebets by stephenhow on May 3, 2012

Well, here’s another massively countable side bet that some people might be interested in (advantage players, casino floor supervisors, and the game publisher), but that I’ll never play. I think after this one, designers will know to check their games for vulnerabilities, especially when there’s oversized items in the paytable. And we’ll remember, “It’s not a sucker bet if the count is good.”

Again, Eliot Jacobson pointed this one out to me. (But, if Barona had this side bet, I’d have already looked at it.)

The Lucky Lucky blackjack side bet is played with your first two dealt cards, and the dealer upcard. On these three cards, you get paid for various ways to make 21, and for any 20 and 19 total. The most countable version of this side bet is for the double-deck version with the paytable below. The game is also countable for the 6 deck shoe game, but it’s only 60% as profitable.

Lucky Lucky Side Bet(Double Deck)
Hand Frequency Probability Payout Return
suited 678 32 1.757238E-4 100 0.01757238
777 56 3.075166E-4 50 0.01537583
other 678 480 0.00263586 30 0.07907569
suited 21 936 0.00513992 15 0.07709880
other 21 14904 0.08184334 3 0.24553003
any 20 13792 0.07573694 2 0.15147388
any 19 13344 0.07327680 2 0.14655362
others 138560 0.76088389 -1 0.76088389
total 182,104 1.00000000 -0.02820366

As usual, I program a function that tells me the EV for any given shoe composition. Then I simulate millions of hands, calculating the ideal EV of the side bet at the beginning of each hand. I sum up the times when the side bet is +EV, and find the average +EV bet and +EV frequency. For the double-deck Lucky Lucky, I got

double-deck, cut card @ 75th card
ideal +EV frequency: 0.2769, ideal EV/bet: +0.0591

which is not a practical counting scheme, but the theoretical limit if you used a computer that took into account all info (suits, etc.).

Then I calculated the Effect-of-Removal (EORs) of a given card on the EV, in order to make counting tags. (Outside the gambling world, people would call “EORs” sensitivities, and “tags” coefficients.)

EORs and Tags for Double-Deck Lucky Lucky
Card EOR Tag
Deuce +0.007853 +1
Trey +0.006066 +1
Four +0.004099 +1
Five +0.003171 0
Six -0.010422 -2
Seven -0.017270 -2
Eight -0.012616 -2
Nine +0.002515 0
Ten/Face +0.006270 +1
Ace -0.008477 -1

So, setting the trueCount threshold to 2.4 (bet Lucky Lucky when the trueCount is >= 2.4), you get the practical results in double deck:

practical frequency: 0.2640, average EV/bet: +0.0561

6 Deck Shoe Version

The 6 deck shoe paytable is better than the double deck version, as it pays 200:1 for a suited 777. The EORs are similar, and I came up with the same count tags as the double deck game. Using a trueCount threshold of 2.1, the practical counting scheme yields:

ideal +EV frequency: 0.2311, ideal average EV/bet: +0.0432
practical frequency: 0.2217, practical average EV/bet: +0.0409

which is only 61% of the profit rate as the double-deck game.

4 Responses

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  1. Don said, on May 6, 2012 at 2:19 am

    Thanks for another great post. It’s interesting that EOR of 10 is a positive number. Intuitively, I would think that more 10s left in shoes should be beneficial for the LL side bet.

  2. Agatha said, on July 11, 2012 at 9:06 am

    Lucky Lucky is so popular in Northern CA. Thunder Valley, Sacramento Area, has it on almost every table, with Shuffle Master’s Continuous Shuffling Machine (CSM). So, who cares about the APs? But seriously, what is the impact of CSM to counting Lucky Lucky?

  3. mcallister3200 said, on August 17, 2012 at 2:16 pm

    Any idea about what the variance or standard deviation for this sidebet would be?

  4. bernie said, on August 10, 2013 at 3:36 pm

    The computerized simulation for this game is way off. Playable situations occur less than 10%,not anywhere near the projected 26%.
    Computerized simulations are done when one hasn’t got the mathematical knowledge of Thorpe, Braun, etc..and not many people do. I played 30,000 hands with playing cards. (the real world) and got less than 10% occurrence of playable situations.
    I’ve been a professional BJ player for about 40 years. I’m also a retired computer data systems analyst and have written BJ simulations programs. What many simulators don’t get is you have to prove your results empirically. Blackjack simulation programs don’t need 20 billion plays to produce accurate results. If a random number generator is not producing true randoms numbers the results will be garbage.
    Just take a single deck and deal yourself a few hundred hands using this system. It’s a big time loser and you’ll find out soon enough.

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