Discount Gambling

Paigow 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.

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:

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.

A 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 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.)

I 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:

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:

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.

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.

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!)

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.

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.

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.