Discount Gambling

Push 22 Side Bet @ Viejas Casino

Posted in +EV, blackjack sidebets, free bet blackjack by stephenhow on August 22, 2013

a91d79570d5b39e5076b8950689c832a_XL My local Viejas Casino just installed Free Bet Blackjack, a game I worked on for Geoff Hall and ShuffleMaster. There’s a side bet on the game called “Push 22″, that I did not work on (until I got back from Viejas last night). I figured I’d check if it was you-know-what.

The bet has some nice payouts, and is a natural match for a game where the dealer pushes all bets on a 22 bust. For a 6-deck shoe, the game has a 5.85% house edge. Not too bad, considering the odds it pays.

Push-22 Side Bet (6 Decks)
Outcome Frequency Payout Return
Suited Dealer 22 0.003327 50-to-1 0.166345
Same Colour Dealer 22 0.011659 20-to-1 0.233174
Other Dealer 22 0.058551 8-to-1 0.468405
Dealer Not 22 0.926464 lose -0.926464
Total 1.000000 -0.058540

Of course, I had to check the EORs (for a single removed card), which showed promise:

Push-22 Side Bet EORs (6 Decks)
Removed EOR Balanced Unbalanced
Deuce -0.44% -1 -1
Trey +0.07%
Four +0.11%
Five +0.13% +1
Six -0.32% -1 -1
Seven -0.12%
Eight -0.06%
Nine -0.03%
Ten/Face +0.03%
Ace +0.52% +2 +2

With the unbalanced blah, you should blah for +24 or better. This will happen 5.1% of the time, with an average +3.6% blah.

Lucky Stiff BJ Side Bet @ 7 Cedars, WA

Posted in blackjack sidebets by stephenhow on May 28, 2013

luckystiffPaigow Dan told me about the new Lucky Stiff side bet his friend recently placed at the 7 Cedars Casino in WA. It looks fun, because you’re paid 5:1 when your initial 12-16 hard total ends up winning the main hand. Also, blackjack pays even-money on the side bet, and an initial pair of 8-8, 7-7, and 6-6 instantly wins 10:1. Anyways, I ran the bet through my BJ analyzer, to see if it was interesting in any way. I understand that 7 Cedars lets you bet $5 on the main hand, and up to $25 on the side bet. So I ran the analysis for a 5:1 side-to-main ratio on a 6-deck, H17, SP4, SPA4 game. The return showed a house edge of 3.5% of the combined (main+side) wager. The optimal strategy for the 5:1 side-to-main ratio only has a few differences with basic strategy.

Hand Dealer Upcard
2 3 4 5 6 7 8 9 10 A
Soft Totals
soft 21 S S S S S S S S S S
soft 20 S S S S S S S S S S
soft 19 S S S S D S S S S S
soft 18 D D D D D S S H H H
soft 17 H D D D D H H H H H
soft 16 H H D D D H H H H H
soft 15 H H D D D H H H H H
soft 14 H H H D D H H H H H
soft 13 H H H D D H H H H H
Hard Totals
hard 20 S S S S S S S S S S
hard 19 S S S S S S S S S S
hard 18 S S S S S S S S S S
hard 17 S S S S S S S S S S
hard 16 S S S S S H H H S H
hard 15 S S S S S H H H S H
hard 14 S S S S S H H H H H
hard 13 S S S S S H H H H H
hard 12 H S S S S H H H H H
hard 11 D D D D D D D D D D
hard 10 D D D D D D D D H H
hard 9 H D D D D H H H H H
hard 8 H H H H H H H H H H
hard 7 H H H H H H H H H H
hard 6 H H H H H H H H H H
hard 5 H H H H H H H H H H
Pairs
A-A P P P P P P P P P P
10-10 S S S S S S S S S S
9-9 P P P P P S P P S S
8-8 P P P P P P P P P P
7-7 P P P P P P H H H H
6-6 P P P P P H H H H H
5-5 D D D D D D D D H H
4-4 H H H P P H H H H H
3-3 P P P P P P H H H H
2-2 P P P P P P H H H H

The EORs are fairly small for the 5:1 side-to-main ratio. They’re about only 1/3rd as effective as the EORs for a standard 6-deck shoe main game. So it’s not worth your time to count this side bet. For a single card removed in a 6-deck game, the EORs are as follows:

Lucky Stiff EORs (5:1 side-to-main ratio, 6 decks)
Card Removed Return EOR
None 3.5009%
Ace 3.1324% 0.3685%
Deuce 3.3055% 0.1954%
Trey 3.3723% 0.1285%
Four 3.4423% 0.0585%
Five 3.5247% -0.0238%
Six 4.0443% -0.5434%
Seven 3.7864% -0.2856%
Eight 3.7654% -0.2845%
Nine 3.3903% 0.1106%
Ten/Face 3.4194% 0.0815%

This bet looks like fun. If you bet an equal main and side bet (1:1 side-to-main ratio), the house edge is 4.66% on the combined 2 unit bet (2.33% element-of-risk). That’s not too bad for a carnival-like odds. If you make a small side bet 1/5th of your main bet (e.g., a $1 side bet to a $5 main bet), then the house edge on the combined 1.2 unit bet is 1.38%. That’s not bad for a little bit of fun.

Suit’Em Up BJ Side Bet @ Venetian, LV

Posted in +EV, blackjack sidebets by stephenhow on May 16, 2013

I saw this blackjack side bet in the Venetian last month, and it looked pretty you-know-what. I forgot to post about it until now. I’m pretty sure they use 8-deck shoes at the Venetian.

Suit’Em Up BJ Side Bet (8 Decks)
Hand Combinations Frequency Payout Return
Suited Aces 112 0.001297 60 0.077850
Suited BJs 1,024 0.011863 10 0.118628
Suited Pairs 1,344 0.015570 5 0.077850
Suited 11’s 1,024 0.011863 3 0.035589
Other Suited 17,920 0.207560 2 0.415199
nothing 64,896 0.751807 -1 -0.751807
total 86,320 1.000000 -0.026691
Suit’Em Up EORs (8 Decks)
Removed Card EOR Balanced Count Unbalanced Count
Deuce +0.000767 +1 +1
Trey +0.000767 +1 +1
Four +0.000767 +1 +1
Five +0.000767 +1 +1
Six +0.000767 +1 +1
Seven +0.000767 +1 +1
Eight +0.000767 +1 +1
Nine +0.000767 +1 +1
Ten +0.000116 0 +1
Jack +0.000116 0 0
Queen +0.000116 0 0
King +0.000116 0 0
Ace -0.006601 -8 -8

Using the unbalanced taps, the bet is +EV for RC >= +34 (assuming two decks behind the cut card). This yields 16% betting opportunities, with an average edge of +2.8%/bet. The theoretical max (using full shoe composition, including suits) is 17% opportunities @ +3.0%/bet. It’s not worth much.

Bust Bonus BJ Side Bet

Posted in blackjack sidebets by stephenhow on May 14, 2013

BustBonus-BannerA reader pointed me out to Galaxy Gaming’s Bust Bonus blackjack side bet that the dealer will bust, which you make after seeing the dealer’s upcard. I figured I’d run the numbers to see if it was any good, or if it was countable. Well, it might be a fun bet on a few upcards, but it’s kind of expensive for the (offsuit) odds they offer.

Bust Bonus Side Bet (6 Decks)
Dealer
Upcard
Probability
Suited Bust
Probability
Offsuit Bust
Probability
No Bust
Payout
Suited Bust
Payout
Offsuit Bust
Return
Ace* 0.002222 0.199059 0.798719 50 3 -0.090437
Deuce 0.008751 0.347909 0.643339 25 1 -0.076644
Trey 0.011524 0.365435 0.623042 15 1 -0.084754
Four 0.014574 0.383896 0.601530 10 1 -0.071892
Five 0.017883 0.401749 0.580368 5 1 -0.089206
Six 0.020844 0.418415 0.560741 3 1 -0.079793
Seven 0.011716 0.250219 0.738064 15 2 -0.061881
Eight
888
0.011133
0.000207
0.227312
0.005041
0.756307
 
10
75
2
25
-0.048772
Nine 0.011602 0.217640 0.770758 20 2 -0.103441
Ten/Face* 0.012263 0.217975 0.769761 20 2 -0.088547

*Bust Bonus wagered after dealer peeks for blackjack.

The most countable bet is against a dealer 8 upcard. It has the lowest house edge (4.9%), and has high payouts for the 888o and 888s busts. The EORs are large, and a simple unbalanced count (Eight => -8, Nine, Ten/Face, Ace, Deuce, Trey, Four => +1; bet when running count >= +24) yields an average +7.5% edge/bet on 17.3% of the dealer 8 upcard hands. Of course, a dealer 8 only occurs on 1/13th of the hands, so it’s not a very practical bet. An ideal count (using total shoe composition including suits) yields a theoretical max return of +7.5% edge/bet on 1.6% of the dealt hands.

Sadly, the standard BJ counts (like the unbalanced Knockout count) don’t correlate with the EV of any of these bets, because unlike blackjack, the Ace hurts the Bust Bonus bet. (Ace rich shoe makes it harder to bust.)

Bust It Blackjack Side Bet

Posted in +EV, blackjack sidebets by stephenhow on December 24, 2012

I ran across the Bust It blackjack side bet last weekend at the Palazzo in Las Vegas. It seemed countable, so I ran the numbers today. The bet is simple. You make the side bet before the hand begins, and if the dealer busts on 3 cards, you win according to the paytable. If the dealer doesn’t bust on 3 cards, you lose. The basic house edge for a 6-deck shoe game is -6.91%. The EORs are fairly high, as listed below.

EORs for 6-Deck Bust It Side Bet
Card EOR Balanced Count Unbalanced Count Simplified Count
Deuce +0.006589 +2 +2 +2
Trey +0.005042 +2 +2 +2
Four +0.002963 +1 +2 +2
Five +0.000256 0 0 0
Six -0.006910 -2 -2 -1
Seven -0.001608 -1 0 0
Eight -0.003443 -1 -1 -1
Nine -0.003001 -1 -1 -1
Ten/Face -0.002231 -1 -1 -1
Ace +0.009038 +3 +3 +2

If the cut card is placed after the 5th deck, then an ideal count (using perfect shoe composition) yields 14.7% betting opportunities, with an average +6.73% advatange per bet. That’s an average return of about 1.0% per dealt hand.

Practically, you’d use the unbalanced count in the table above and bet with a running count of +25 or more. This practical count yields 14.4% betting opportunities, with an average +6.1% edge per bet. That works out to an average return of +0.88% per dealt hand.

Depending on the side bet limits, counting this bet could be profitable. But, more likely, they’ll limit you to a $25 max bet. So your profit rate would be (100 hands/hr)(14.4% bets/hand)(+6.1% profit/bet)($25/bet) = $22/hr. Of course, you’ll almost certainly have to make the main bet too (e.g., the Cosmopolitan wouldn’t let me make bonus bets on my friend’s blackjack hand). If it’s only $5, and you get good rules @ -0.6%, then your cost would be (100 hands/hr)($5/hand)(-0.6%) = $3/hr, leaving you with a $19/hr job.

The unbalanced count is fairly complicated, with its multi-level taps. Unless your a very skilled counter, you’ll be better off using the simplified count above. It only uses +2 and -1 taps, and it still performs well, yielding 13.5% betting opportunities, with an average +5.3% edge per bet. Bet when the running count is +24 or more.

Also, the standard blackjack counts don’t work for this bet (there’s no correlation, I checked). You can tell that blackjack counts are very different than this specialised count, because Aces are +3 and Sixes are -2. Those are opposite to blackjack values, and they make sense. Ace-rich shoes are bad for 3-card busts. Also, sixes are valuable because of the 15:1 payouts.

Note: a reader says the Palazzo/Venetian deals out of 8-deck shoes. If that’s the case, and they place the cut card @ 6 decks, then the ideal return decreases to 10.7% frequency at an average +4.7% edge. The simplified count return decreases to 8.9% opportunities @ +3.5% edge per bet. You would bet for an RC of +32 or higher.

6-Deck Bust It Blackjack Side Bet
Dealer Outcome
Frequency
Probability
Payout
Return
bust with 888 suited
240
0.001596%
200
0.003191
bust with 888 coloured
1,080
0.007181%
50
0.003590
bust with 6
73,440
0.488299%
15
0.073245
bust with 7
157,536
1.047450%
9
0.094270
bust with 8
245,232
1.630536%
7
0.114138
bust with 9
342,720
2.278729%
5
0.113936
bust with 10
1,782,144
11.849393%
3
0.355482
no 3 card bust
12,437,568
82.696816%
-1
-0.826968
total
15,039,960
100.000000%
-0.069115

Push Your Luck Blackjack Side Bet

Posted in blackjack sidebets by stephenhow on December 20, 2012

pyl-thumbnailI came across the Push Your Luck (PYL) blackjack sidebet yesterday (while browsing, not IRL), and I wondered if it was exploitable in any way. PYL is a simple side bet. You make the bet before you start your blackjack hand, and if you end up pushing your main bet, you win 10:1 on the side bet. The max bet is 1/2 your main bet, and its usually limited to $25.

PYL has been out there for a while, but it’s new to me. It’s pretty simple to code up in my analyzer, which finds the optimal play for the combined (main + side) bet. I don’t know why, but I always expect these bets to be +EV, or somehow exploitable. I’m kind of optimistic that way.

Well, I was very surprised to find the house edge of the side bet is very low. Even when you max the side bet (@ 1/2 your main bet), the house edge of the combined (main + side) bet is only 0.76% for a 6 deck game with good rules (DAS, SP4, SPA4, H17). That’s like a cost of 0.25%, and you’re getting 10:1 odds! Here’s the auto-generated strategy table:

Push Your Luck (PYL) Max Bet Basic Strategy
Hand Dealer Upcard
2 3 4 5 6 7 8 9 10 A
Soft Totals
soft 21 S S S S S S S S S S
soft 20 S S S S S S S S S S
soft 19 S S S S S S S S S S
soft 18 S S S S S S S H S S
soft 17 S S S S D S H H H H
soft 16 H H H D D H H H H H
soft 15 H H H H D H H H H H
soft 14 H H H H H H H H H H
soft 13 H H H H H H H H H H
Hard Totals
hard 20 S S S S S S S S S S
hard 19 S S S S S S S S S S
hard 18 S S S S S S S S S S
hard 17 S S S S S S S S S S
hard 16 H H S S S H H H H H
hard 15 H H H H S H H H H H
hard 14 H H H H H H H H H H
hard 13 H H H H H H H H H H
hard 12 H H H H H H H H H H
hard 11 D D D D D D H H H H
hard 10 D D D D D H H H H H
hard 9 H H H D D H H H H H
hard 8 H H H H H H H H H H
hard 7 H H H H H H H H H H
hard 6 H H H H H H H H H H
hard 5 H H H H H H H H H H
Pairs
A-A P P P P P P P P P P
10-10 S S S S S S S S S S
9-9 S S S S S S S P S S
8-8 P P P P P P P P P P
7-7 P P P P P P P P P H
6-6 P P P P P P H H H H
5-5 D D D D D D H H H H
4-4 H H H H H H H H H H
3-3 P P P P P P P H H H
2-2 P P P P P P P H H H

With a max PYL bet, the game gets a little wild where you’re hitting the majority of your under-17 hands, even against low dealer upcards. People must have a fit at this game. But it looks kind of fun, because you’re trying to get a nice 10:1 payout. It’s a good reason to play crazy.

I thought with such a low house edge, and with a 10-to-1 multiplier, the game would be easily countable. However, the EORs are pretty tame, and are very similar to standard blackjack:

Max Bet Push Your Luck (PSL) EORs
Card EOR
Deuce +0.076%
Trey +0.069%
Four +0.056%
Five +0.082%
Six +0.122%
Seven -0.066%
Eight -0.057%
Nine -0.008%
Ten/Face -0.031%
Ace -0.142%

You’ll probably need the proper index plays for (not) hitting your under-17 hands on +EV counts. I looked at the strategy for a small +EV count, and the borderline decisions shift towards standard plays. If I get around to learning the lingo for index plays, I’ll post them here for PYL.

Bust Me Blackjack @ Valley View Casino, CA

Posted in blackjack sidebets by stephenhow on October 28, 2012

The new bust me blackjack sidebet is bad, but at least it’s countable. It’s a blackjack side bet you make after seeing your hand, on whether you’ll bust on the next hit. You get different odds, depending on your total. They’ll let you bet table limits on the side bet, regardless of the size of your main bet. So its pretty obvious that the house edge has to be horrendous to avoid it being countable. And it is. (It’s both horrendous, and countable.)

I’m pretty sure anyone can tell just by looking at the paytable, but here’s the numbers anyways.

Total Payout For Bust House Edge
16 1:2 7.692%
15 1:2 19.23%
14 1:1 7.692%
13 3:2 3.846%
12 2:1 7.692%

Yep, it’s that bad. A true sucker bet. You might be able to fool some of the players some of the time, but you won’t be able to fool them for long. Everyone will catch on to how bad this bet is sooner or later.

Of course it has to be bad, since the first thing everyone thinks about is counting for 10’s and 9’s, and waiting until the end of the shoe to whoop out the $500 and $1000 Bust Me bets on hard-13. (The rack cards make it clear you can bet the table limits at any time, regardless of the size of your main bet.) I thought there might be frequent +EV opportunities, so I plotted the distribution of EV’s for the hard-13 bet throughout the shoe:

The Bust Me 13 sidebet gets very good rather frequently. Of course, you must have hard-13 to bet, so this +EV opportunity only occurs on about 2.6% of your hands, with an average edge of +5.4%/bet. That’s not great, but you can make a huge $500 or $1000 table limit bet, until they stop you. So you’ll get about 1.2 betting opportunities per shoe, and even if you bet $1000, you’ll only average about a $65 profit per shoe.

(Thanks to reader fivespot for pointing out my error in the first version of the post; I had one of those one-line bugs, and was shuffling after every hand. Aiyah!)

House Money BJ Side Bet @ Pala Casino

Posted in blackjack sidebets by stephenhow on August 28, 2012

Hooray, another game that I did the math for hits the floor! House Money is a blackjack side bet created by Roger Snow of ShuffleMaster. It’s unique because it allows the player to cap his main blackjack bet with his side bet winnings. The side bet pays when your first two cards make a pair, straight, or straight flush. So, if you’re dealt a suited A-K, the side bet pays 9:1. You always have the option of taking the proceeds (10 units in this case), and adding it to your main blackjack bet. In this case, your BJ nets you a profit of (3:2)(10) + 9 = 24 units on the side bet. (If this reads too much like a paid advertisement, skip to the section on counting for this bet.)

For a 6-deck shoe game with good rules, and the correct capping strategy, the house edge for this side bet is only 2.6%. The basic strategy of when to cap your main bet with your side bet proceeds is presented below.

The game is currently available at my nearby Pala Casino, the Siena in Reno, and the Drift On Inn in WA.

Rules

The rules for the House Money side bet are as follows:

  • The player makes the optional side bet wager before the hand is dealt.
  • The side bet pays for the initial 2-card player hands according to the paytable below.
  • The player has the late (after dealer peeks for BJ) option of capping his main blackjack bet with an amount up to the entire side bet proceeds.
  • The player completes the main hand following normal blackjack rules.
2-Card Hand Paytable
Hand Payout
AK suited 9-to-1
Straight Flush 4-to-1
Pair 3-to-1
Straight 1-to-1
Nothing lose

Basic Strategy

The table below tells you when you should cap your main bet with the winning proceeds of your side bet. “Y” means to cap the bet with the proceeds, because the EV of the hand (after the dealer peeks for BJ) is positive. “N” means not to cap the bet, but just to collect your winnings, because the post-peek EV of the hand is negative. After the capping decision, play your hand according to blackjack basic strategy.

Capping Strategy for House Money Blackjack Sidebet
Hand Dealer Upcard
2 3 4 5 6 7 8 9 10 A
Straights and Straight Flushes
AK Y Y Y Y Y Y Y Y Y Y
KQ, QJ, JT Y Y Y Y Y Y Y Y Y Y
T9 Y Y Y Y Y Y Y Y Y Y
98, 87, 76 N N N N N N N N N N
65 Y Y Y Y Y Y Y Y Y Y
54 Y Y Y Y Y Y Y N N N
43 N N N Y Y N N N N N
32 N N N N Y N N N N N
A2 Y Y Y Y Y Y Y N N N
Pairs
A-A Y Y Y Y Y Y Y Y Y Y
10-10 Y Y Y Y Y Y Y Y Y Y
9-9 Y Y Y Y Y Y Y N N N
8-8 Y Y Y Y Y Y N N N N
7-7 N N Y Y Y N N N N N
6-6 N N Y Y Y N N N N N
5-5 Y Y Y Y Y Y Y Y Y Y
4-4 N Y Y Y Y Y N N N N
3-3 N N Y Y Y N N N N N
2-2 N N Y Y Y Y N N N N

Countability

This side bet is only slightly countable, using the counting coefficients (2 => +1, 3 => +1, 4 => +1, 5 => 0, 6 => 1, 7 => 1, 8 => 1, 9 => 1, T => -1, J => -1, Q => -1, K => -2, A => -2) and a true count threshold of 3.1. From a 6-deck shoe with 1 deck behind cut card, you’ll have +EV betting opportunities about 13.4% of the time, with an average edge of +3.4%/bet. So betting $25 when the count is good will yield a profit rate (13.4%)($25)(+3.4%) = $0.11/hand. At 100 hands per hour, this yields $11/hr, which isn’t worth anyone’s time or effort.

Field of Gold (+EV)

Posted in +EV, blackjack sidebets by stephenhow on June 12, 2012

Everybody thank Eliot Jacobson for working for you. He emailed me this morning telling me the Field of Gold blackjack side bet was crushable. And it is. For real. The count is simple, and for a 6-deck shoe game, you’ll be able to bet 19% of the time, with an average edge of +6.5%/bet. That’s a profit of ($25 bet)(19% bet/hand)(+6.5% EV/bet) = $0.31/hand. For double-deck, the numbers are even better, yielding 27% betting opportunities with an average edge of +8.2%/bet. For $25 bets, that yields a profit of $0.55 per hand dealt. That adds up pretty quickly. It’s more than $100/hr.

This is about as good as it gets, as it’s a fast blackjack game. Oh, by the way, Eliot also brought you the equally crushable Lucky Lucky bet, which I probably understated in my post. These are probably the best two countable side bets out there, and nobody but Eliot has noticed them. Oh, and he’s the one that pointed out the Dragon-7 vulnerability.

Anyway, here’s what you’re looking for:

Use the following count:

Field of Gold Count
Card Value
Ace -3
Deuce -1
Nine, Ten, Queen, King +1
others 0

Bet when the true count (= runningCount/decksRemaining) is 2.2 or better. You can see from the graph below that the EV is strongly correlated with the true count.

This side bet becomes highly profitable when the shoe is rich in aces and deuces, and lean in high cards. During some shoes, the deck can easily get really good, or really bad for the Field of Gold bet. The distribution of the side bet EV is plotted below over the course of the 6-deck shoe and the double-deck game. Note the peak of the distribution is centered about the nominal -5.66% return of the bet right after the shuffle. Then, especially towards the end of the shoe, the side bet return can vary wildly. Note all the area under the long tail of the distributions to the right of the y-axis (EV>0). This is why the game is crushable.

(5 deck penetration of 6-deck shoe; 29 cards behind cut card in double-deck.)

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.

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