Discount Gambling

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
bust with 888 suited
bust with 888 coloured
bust with 6
bust with 7
bust with 8
bust with 9
bust with 10
no 3 card bust

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
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.

Panda-8 Co-Count with Dragon-7

Posted in +EV, baccarat, panda-8 by stephenhow on December 9, 2012

Screen Shot 2012-12-09 at 7.08.26 PMWith the simplified unbalanced count for the EZ-Baccarat Dragon-7, it’s occasionally fun to count a shoe and find opportunities to bet $25 – $100, to try to win $1000 – $4000. But overall, counting the Dragon gets pretty boring. It only takes a second to see the value of the hand, and to update your count. Then you spend a lot of time watching everyone think deeply about their next bets. Hopefully, the count gets to +32, so you can finally make a bet.

Counting the Dragon-7 would be pretty good if you could make about twice the +EV it offers (+52% of a fixed bet per shoe). Or at least it’d be fun if you could easily track the Panda-8 as well, to add some variety to the game. (I’ve previously posted a complicated Panda-8 count and a RCmin table that yields +22% of a fixed bet per shoe.)

Well, I can’t double the EV of the Dragon-7, nor can I easily get you the full +22% of the Panda. But, here’s an ultra-simplified Panda-8 co-count that you should be able to track alongside the Dragon-7. It’s an unbalanced count, for simplicity. It only has a few taps. The few (4) taps it has are equal to those of the Dragon-7 unbalanced count. Also, these are key taps (you focus on the +2 Nines for the Dragon; it uses the same +1 unbalanced Aces; finally, the -1 Fours and Fives are easy to remember, because they add up to 9). You should be able to track your main Dragon-7 count, then quickly scan the hand for its Panda-8 value.

Simplified Panda-8 Co-Count
Card Count Value
Ace +1
Four, Five -1
Nine +2

Starting from a running count (RC) of 0, you should bet the Panda-8 when its count gets to +35. You’ll get an average of about 2 bets per shoe (when 16 cards are placed behind the cut card), and a profit of around +9.0% of a fixed bet per shoe. It’s not a whole lot, but it’ll make sitting around the baccarat table a little more fun/tolerable. Also, it’ll give you more cred with the degenerates watching their Player lines, Panda lines, and their second bankers 🙂

Thanks to Linus B for his initial work on the Panda co-count. I greatly simplified it here for us script-kiddies.