Discount Gambling

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.

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.

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.

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.

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:

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.)

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.

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.)

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.

My local Barona Casino offers the Royal Match blackjack side bet which pays 75-to-1 when you’re dealt a suited K-Q on your first two cards, and 2-1 for any other suited hand. Normally, the house edge is 4.06% for this side bet, but as readers of this blog know by now, sucker bets are often countable. Using a simple true K-Q count, the bet yields an average 5.4% player edge.

I always play this bet for $1, and get really excited when I hit it for $75. The last time I hit it, I decided to analyze it’s countability.

I first looked at the bet’s distributions of EVs at the last hand of the shoe. This would show me if there was any potential for a counting scheme. I’d see how often and how strongly the bet went +EV. Here’s what it looks like with one deck remaining:

I could tell from the graph that the bet was exploitable. So I calculated the average profit per shoe, assuming heads-up play with the dealer. This theoretical limit comes out to a profit of +0.504 bets/shoe. That’s a really good profit rate (compare to the Dragon-7 profit rate of 0.54 bets/shoe). That means a player betting a fixed amount on the Royal Match will net an average profit equal to half his bet per shoe, when heads up with the dealer. On a per bet basis, the average Royal Match bet EV is +5.9%, assuming perfect knowledge of the dealt cards.

I then looked for a simple (practical) counting scheme that would capture most of the theoretical edge. As it worked out, the second idea that came to mind happened to be very effective. A simple true count of excess Kings and Queens yields about +0.43/shoe (85% of the theoretical edge):

trueCount = (8*decksDealt - countedKingsAndQueens)/decksRemaining

where decksDealt and decksRemaining are floating-point numbers.

The relationship between the true KQ-count and the Royal Match side bet EV is shown in the following graph:

Note that you should bet the Royal Match when the true count is >= 0.8.

In heads-up play, you’ll get an average of 8.0 bets/shoe, with an average bet EV of +5.4%. The scheme is very comparable with the highly profitable Dragon-7 counting scheme (EV +0.54/shoe), but it’s much faster, and has much lower variance.

So if you don’t find me at the full-exposure Mississippi Stud game, look for me in the i-Table pit counting the Royal Match.

I recently saw the Instant-18 blackjack side bet, and I thought it was funny. It’s an even-money side bet that plays against the dealer as a hand of value 18. Hence, the name “Instant-18″. You put up a bet, and it’s an 18. It has a 2.036% house edge for a 6-deck shoe, but it’s still kind of interesting. It’s an optional side bet where (typically) you can bet an amount less than or equal to your main blackjack bet. Of course, I had to see if this bet was countable.

First, I looked at the distribution of EVs after 5 of 6 decks were dealt from the shoe:

This looked promising, so I checked out the EORs for the bet:

From the EORs, I made a simple count system, where Aces are +3, Sevens are -2, and Deuces are -1. Then I plotted the EVs of the main and side bet vs. the true count:

Unfortunately, when the count for the side bet gets good (true count >= 4), the main bet is -EV. However, for a good enough count (true count >= 7), the combination of (main bet + side bet) is +EV. Also, for a bad enough count (true count <= -3), them main bet is +EV.

So, by itself, the Instant-18 side bet gets good (true count >= 4) about 7.8% of the time, with an average return of +1.53%.

Of course, you can’t just bet the side bet when it gets good. You have to have a main bet to bet the side bet. If you bet both when the combination gets good (true count >= 7), or just the main bet for true count <= -3, and Wong all others, you'll bet 13.9% of the time with an average EV of +0.47%.

As usual, these things are interesting, but not practical.