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
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

2 Responses

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  1. Ardent1 said, on January 2, 2013 at 10:41 pm

    There’s no “u” in color(ed) per Americanese; the “u” is far more common for the unbasterdized British English.

  2. Bob Fisher said, on February 24, 2013 at 12:05 pm

    I researched this bet several years ago. My results are different from stevenhow. After looking at both to find the problem, I think I found it. This bet is usually found with Double Attack Blackjack which is dealt from a Spanish 48 card deck The payoffs are also slighlty different. The stevenhow game is for a regular 52 card deck game..Be sure to check this before playing. If 52 card deck use stevenhow if 48 card deck use mine. Mine is at bj21.com USA East 10-07-06.


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