Discount Gambling

Triple Attack Blackjack (+EV) @ Barona Casino, CA

Posted in +EV, triple attack blackjack by stephenhow on August 14, 2011

My nearby Barona Casino opened up a new Triple Attack Blackjack game last month, and I tried it out this weekend. I really like this game, because of the weird, aggressive hitting like Spanish 21. But more importantly, the game allows you to double your initial bet after seeing your first card, and bet again after seeing the dealer upcard. You’re immediately paid on 21 or any 6-card total, and you can double down at any time. The house gets its advantage by paying even money on blackjack, and pushing on dealer 22.

For the full rules and basic strategy, see the Wizard’s analysis, which yields a 1.18% house edge. But for most cases, his basic strategy charts boil down to the following simple rules:

  • If your first card is an Ace, triple your bet.
  • If your first card is a Face, triple your bet against 2-9, else double your bet.
  • 3rd Attack 2 against a 6.
  • 3rd Attack 8 against 6,7.
  • 3rd Attack 9 against 5,6,7,8.
  • Double 10 against 3-6.
  • Double 11 against 7 and under.
  • The only soft total double is soft-18 against a 6.
  • Double all 5-card 14’s and under.
  • Double-for-less (split aces rescue) soft-17 and under, and soft-18 against 9 and A.
  • Hit all 12’s and 13’s.
  • Hit 14 except against a 6.
  • Hit 15 against a 2 or 3.
  • Hit 16 against a 2.
  • Hit 17 against an Ace, and for some 5-card totals.
  • Never split 4’s, 5’s, 6’s, 10’s.
  • Split 2’s and 3’s against 6,7.
  • Split 7’s against 4-7.
  • Split A’s and 8’s against everything except A.
  • Split 9’s against 6,8,9.

I really enjoyed the game. I also won about $400 in 3 sessions, which is unheard-of for me, since I flat bet for the minimum $5. I never vary my bet. However, in Triple Attack, you often end up betting 3 units, or even 6 or more, if you split hands like Aces. I don’t think I’ve ever won that much money playing blackjack before. The players all loved it, because they make more decisions, and their initial $20 bet can easily become a $120 bet on a good hand, or just remain a $20 bet on a weak hand.

Of course, it immediately occurred to me that card counting should be more effective in Triple Attack compared to standard blackjack. While you might dramatically increase your bet for a good count in regular blackjack, in Triple Attack, you only have to commit 1/3 of this amount on the 1st Attack, then another 1/3 only if you like your first card (an Ace or Face), and another 1/3 only if you like the dealer upcard. So, even though the count may be good, you can get away from a bad hand on the first card, and also if the dealer has a good upcard. Compare that to normal blackjack, where you bet huge on a good count, then get a 6, then the dealer shows an Ace.

Using basic strategy, I looked at the EV sensitivities of each of the card ranks (i.e., the effect of removing one card from the shoe). Interestingly, the effect of removing a Face card was very small. Removing a 5 improved the hand EV the most, but not by much compared to a 2, 3, 4, 6, or even a 7. By far, the Ace was the most powerful card, making the other cards insignificant.

So, I tried out a simple scheme, which only relies on the Ace count, compared to the expected number dealt. You subtract the number of actual Aces seen from the expected number of Aces dealt to get the Ace count. For example, after dealing 1/2 the shoe (192 cards), you should have seen 16 Aces. If you’ve only seen 12 Aces, then the count is +4. The Ace count is a measure of the “extra” Aces left in the shoe. Using a basic strategy simulator, I generated the curves showing the effectiveness of this simple Ace-Count system (including double-1-unit-for-less as Ace-split rescue):

Triple Attack Blackjack EV vs. Ace-Count and Shoe Depth

This effect is huge! Look at the green curve, which shows the effect of the Ace count after 3/4 of the shoe has been dealt (288 cards dealt). At this point, 24 Aces should have been dealt, on average. But if only 20 Aces were dealt, then the count is +4, and the next hand has a 4% player advantage. Similarly, a negative count tells you to bet the minimum, or even Wong (sit out) until the next shoe. The blue curve shows the effect after 1/4 of the shoe dealt (96 cards), and the red curve shows the half-way point (192 cards). You can see that generally speaking, it’s good to increase your bet any time the count is +2 or more (the shoe is “loaded” with 2 or more extra Aces).

We don’t need to look at the distribution of Ace counts to know that +1, +2, +3, +4, +5 counts happen all the time, especially at the end of shoe, where the effect if largest. Note that the green curve shows about a 1.25% EV improvement for each surplus Ace left in the shoe.

A simple counting strategy bets the minimum for the first 2 decks of the shoe, then a large bet if the Ace count is +2 or better. Using basic strategy, and assuming the cut card at 48 cards left in the shoe, the following returns are obtained:

Triple Attack Return vs. Large Bet On +EV Ace Count
Small Bet Large Bet Return
(relative to small bet)
1x 1x -1.10%
1x 5x +0.08%
1x 10x +1.60%
1x 20x +4.40%
1x 30x +8.80%
1x 40x +11.8%

On the other hand, the shoe is +EV about 20% of the time (+2 or better count) after the first 1/4 of the shoe is dealt. So, if you just like varying your bet on a good count, you’ll really enjoy this game. Overall, if you Wong and only bet +EV Ace counts, then you’ll extract about +17% total EV out of a shoe (i.e., +0.17 bets/shoe). The Ace-count system is very easy to implement (e.g., use the height of muck cards to estimate the expected Ace count), and is very fun. Some people have a good idea of when the shoe is Ace-rich or not. That’s all you need to know for this Triple Attack game!

And there’s no time to (possibly) bet big like the last hand of the shoe (purple curve, cut card @ 1 deck left):

Note that unless the Ace count is 0 (unlikely, only 22% of the time), you’re either a big favorite, or a big underdog on the last hand. It’s easy to get the Ace count right on the last hand, assuming the cut card was placed with 48 cards behind it. At the last hand, you should have seen 28 Aces. If you only saw 24, then you have a +4 count, and the EV of the next hand is almost 10% in your favor (a $100 1st Attack bet will return a $9.80 profit on average, including possible 2nd and 3rd Attacks, doubles, etc.). But, if you saw 30, then the count is -2, and the house has a 6.2% edge on the last hand, so bet the minimum, or Wong.

I suggest you simply count the number of Aces seen, even using chips if it helps you keep track. Compare your Ace count to the number of decks (48 cards/deck) seen in the muck rack. There are 4 Aces per deck. If the number of Aces seen is less than 4*(mucked decks), then the Ace count is positive. If your count is +2 or better, you’re +EV, and can increase your 1st Attack bet.

Get an idea of what a deck (48 cards) looks like in the discard rack. Ask the dealer for their estimate of the number of decks in the muck. You’ll find it’s pretty easy to estimate the number of dealt decks. Thus, you should be able to determine the Ace count very easily. Also, by watching the level of cards in the discard rack, you’ll know how powerful your count is (see above graphs for 1/4, 1/2, 3/4, and 7/8 shoe dealt depths).

Example: You look at the discard rack, and it looks like 3 decks have been dealt. This means that 4*3 = 12 Aces should have been dealt. Your actual Ace count is 15. The Ace count is -3, and you’re -EV, so bet the minimum. However, if the actual Ace count is only 9, then the Ace count is +3, and you’re +EV, so you should bet more.

This counting system couldn’t be any easier, or any more powerful. It doesn’t get much better than this.

Finally, I saw that at request, Barona increased the limits on the Triple Attack game to $25-$1000. I was locked out until the guy left, and the table returned to $5-$1000. In general, Barona is very flexible about increasing table limits.

30 Responses

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  1. Terry said, on August 19, 2011 at 9:36 am

    Stephen,
    The game looks like fun. I was wondering what the effect on EV would be if you added the 10’s back into the deck and played with real 8 card decks not Spanish 21 decks?
    Lost the last 2 outing at Mississippi Stud game but still beleive in it. we had 4 of us pool our money and only played at a full table.
    Thanks again for the great site. Hope to see you at Barona sometime.

  2. curiousgamer said, on August 24, 2011 at 4:15 pm

    Sorry for the amateur question, but what does “Double-for-less (split aces rescue) soft-17 and under, and soft-18 against 9 and A” mean and can you provide an example?

    • stephenhow said, on August 24, 2011 at 9:26 pm

      Say you’re dealt an Ace. You bet the 2nd and 3rd Attacks. Then, you’re dealt another Ace. You split your Aces, which now have 3 units wagered on each hand. Say the first Ace receives a King. You have 21, and are immediately paid. Say the second hand receives a 3. You have 4/14, but can “double for less”, and bet an additional unit to receive one card. It happens all the time, as you can imagine. Of course you’re not guaranteed to improve your hand with one card, but it’s better to pay 1 unit for a card than to stand and hope the dealer busts.

      If your split aces make soft-18, you’re still supposed to double for less against a dealer 9 or Ace. But, you don’t double for less against a dealer Face. That’s surprising, but I assume the Wizard Of Odds got it right.

      If you make soft-17 or soft-18 against a dealer 6, you should double for the full amount.

      • vgMega said, on August 25, 2011 at 9:12 am

        SO many people flat out refuse to deal with a soft-18, whether its to double or hit against a face. It usually costs them potential winnings or the hand

  3. hmmmmmm said, on August 25, 2011 at 6:26 pm

    this game sounds too easy to beat with ridiculous ev percentages favoring the player if you count correctly which doesnt seem hard to do with your detailed instructions… whats the catch?!!! im contemplating trying this game out with a legitimate bankroll, so id like to know everything before i jump into this venture, thanks!

    • stephenhow said, on August 26, 2011 at 1:28 am

      As always, the catch is variance and bankroll requirements. I’ll post on the various session outcome distributions, and bankroll requirements for the 5x, 10x, 20x max bet on +EV counts. You can then judge for yourself if it’s worth attempting to beat.

      • hmmmmmm said, on August 26, 2011 at 11:24 am

        awesome thank you so much for the advice, i cant wait to try this out! you are the best! 🙂

      • stephenhow said, on August 26, 2011 at 12:32 pm

        I just posted on expected 100 shoe session outcome distributions, so take a look. And don’t forget, this is gambling, and aside from what I see in the movies, I don’t know of anyone that actually grinds out a profit from the casino.

  4. hmmmmmm said, on August 27, 2011 at 4:34 am

    is the counting only effective when you play heads up with the dealer or can there be other players at the table and still be able to play according to your counting/betting strategy? if so, how many and do their actions affect your play?

    • stephenhow said, on August 27, 2011 at 9:43 am

      I just ran the simulator for a 1st base counter with 4 additional players, and I got slightly better results for the overall EV as in the above table. I only simulated the 4 other players receiving cards between your 1st and 2nd cards, but didn’t play their hands out. Overall, there’s probably a small beneficial effect from more players, because they move you to the end of the shoe quicker, and you get to see more skewed Ace counts. You benefit from skewed counts, because you can either Wong, or min bet bad counts, but jump on good counts as much as the casino will allow. So, overall, I’d welcome other players, but I’d take 1st base, since the correlation between Ace count and EV is probably highest there.

  5. TBones said, on August 27, 2011 at 9:56 am

    In spanish 21 it has been documented that the rules are so good that if you only took out half the 10’s in the deck instead of all them that the advantage would swing to the player. I wonder if half the 10’s were put back in triple attack blackjack would the EV turn positive as well? Stephen your site is great!

    • stephenhow said, on August 27, 2011 at 10:50 am

      I’m sure it would, but what did you have in mind? (I can guess what you might be thinking, but don’t forget, the clerk counts down the decks after every card change, i.e., at the end of the day). If the shoe didn’t count down right, they’d go to the cameras. Oh ….. you could sub them back out. Hmmmm.

  6. TBones said, on August 27, 2011 at 11:16 am

    No. Nothing illegal just more of a math and counting question.

    • stephenhow said, on August 27, 2011 at 11:29 am

      I don’t have the analyzer program for Triple Attack, I just used the Wizard Of Odds basic strategy, and developed a counting strategy around it. I’m probably not going to program in Triple Attack, because the Ace count is so good, there’s no point in looking for other optimizations (indices) that people probably wouldn’t use. So I can’t just change the deck (add back the 10’s) and run the analyzer to find your answer.

  7. Steven George said, on October 18, 2011 at 8:41 pm

    Triple Attack has just been added at a local casino. I’ll focus on it instead of the Spanish M-T-D. Thanks

  8. Steven George said, on October 19, 2011 at 9:08 am

    Do you know of any “practice” software programs or online sites for Triple Attack? I have used CVBJ to good advantage in the past to practice counting, estimating discard decks, sizing bets, playing etc… I would buy a good Triple Attack program if it had a nice user interface and triggered on mistakes (either betting or playing). Thank you.

  9. zenmasterflash said, on December 24, 2011 at 7:00 am

    This MUST be the most volatile version of BJ ever.
    Can we compute variance coefficients.
    The greatly magnified Risk of Ruin will require a huge
    bankroll in order to stay below 5% a la “½ Kelly”

  10. zenmasterflash said, on December 24, 2011 at 7:05 am

    I would greatly appreciate a set of E.O.R.’s (“effect of removal”) for all ranks.

    T. I. A.

  11. Tthree said, on December 26, 2011 at 3:40 am

    I am looking at you frequency versus EV graphs. We know the sum of all frequencies of the green graph is 1. How can the red graph have 2.5 to 5 or more higher frequencies than the green graph at every EV and still add to a frequency of 1? The red graph even has positive frequencies that are 0 frequency in the green graph. Since all frequencies added together must equal 1, How is this possible?

    • stephenhow said, on January 3, 2012 at 11:59 am

      There are no frequency distribution graphs on this page. Are you talking about graphs on other pages? The graphs on this page show the relationship between the Ace count and EV; there are no frequencies here.

      • Tthree said, on January 4, 2012 at 5:35 am

        Yes , the other page. The frequency vs EV graphs at . The sum of all frequencies is one. Both colors on each graphs can not be correct. The sum of the frequencies of the triple attack EVs looks to be 3 times or more the sum of the frequencies of regular blackjack EVs at both penetration levels that are graphed. They must both equal one. What am I missing? This is pretty basic frequency knowledge.

  12. Charlie Pignatello said, on December 26, 2011 at 11:59 am

    Eliminating 4 cards from an 8-deck shoe, my estimates are -.71%, +.19%, +.21%, +.27%, +.28%, +.28%, +.14%, 0%, -.06% and -.21% for ace thru ten, respectively.

  13. Jim said, on February 12, 2012 at 12:44 am

    From these numbers, it looks like a count of +4, -1,-1,-1,-1,-1,0,0,0,+1 would be noticeably better as a
    starting point. But of course, it would be a lot harder.

    • Tony said, on February 24, 2012 at 2:56 am

      Stephen,

      Am I correct in assuming that each shoe in Triple Attack BJ starts with a zero, if doing the ace count? Zero meaning that each deck has 4 aces.

      • stephenhow said, on February 24, 2012 at 8:21 am

        The “aces seen” starts off at zero for a new shoe, but the aceCount = expectedAces – seenAces. The expectedAces is the average number of aces dealt at a given penetration of a shoe. For example, at the start of an 8 deck shoe, the expectedAces is 0, as is the seenAces. After the first 2 decks are dealt, the expectedAces is 8, and the seenAces is the number of actual aces you observed dealt. A better analysis would use a “true excess Ace count” = (expectedAces – seenAces)/decksRemaining, but I didn’t know counters used “true counts” when I posted this.

        All this might not matter to you; Barona removed this game a few months ago, and replaced it with Blackjack Switch.

  14. jigs said, on January 12, 2013 at 11:30 pm

    So what type of bank is needed to play 100 shoes betting 5-20X? Deviation? Variance? Etc.

  15. johnalbanese said, on March 18, 2013 at 8:29 am

    Very interesting analysis. Do you believe that your analysis here would translate over to Double Attack Blackjack?

    I would imagine a simple Hi-Low approach would be effective – but I’m not quite sure why Aces are so much more powerful in the Triple Attack version.

    • stephenhow said, on March 18, 2013 at 8:38 am

      Thanks for the tip on the game, I never heard of it before. I’ll have to run the EORs when I get a chance!

      Steve

  16. johnalbanese said, on March 22, 2013 at 5:03 am

    I wonder why the Wizard strategy calls for only doubling on 10 against a dealer 6 and below?

    His strategy for Spanish 21 calls for doubling against a dealer 8 and below – and both games use a Spanish deck and employ the 6 card Charlie rule.

    Hmm. I may have to post this question on his boards.

    • stephenhow said, on March 29, 2013 at 7:24 pm

      I’ll probably get around to fully analyzing the Triple Attack game myself. It should be fairly simple, then I can calculate the EORs, and do a better job of describing the counting edge on the game.


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