Discount Gambling

You know what we all need, besides a +EV game, or some ridiculously countable side-bet?  We need more fun at a blackjack table.  We also sometimes need a miracle just to get even at a blackjack table.  Both of these are offered by the new Multiplier Blackjack game at my local Jamul Casino, in Jamul, CA.

I did the math for the game inventors about 6 years ago.  I understand the game won the Best-in-Show award at the table games conference, and is growing in casino placements around the country.   It’s finally available in San Diego county, and I checked it out last night. Woo-hoo, it’s fun, and I actually won at a blackjack table for once!

The idea behind the game is simple.  All the rules are the same as Blackjack, but when you win against a dealer bust, you’re paid odds based on the dealer bust card.  The payouts are higher for a low bust card, and decrease to 1-to-2 for a picture card.  When the dealer busts with a 10-spot card (Ten), your winning wager just pushes.  Of course, the game excitement comes when you’re hoping for a dealer bust with a Six (pays 4-to-1), or any other non-10 valued card.

Why It’s Fun

Regular blackjack is boring for a lot of people.  I almost never play it, because I just don’t care about even-money games.  I walk by all the blackjack tables.  I’ll look at some of the odds-paying side bets, but it’s still not worth the effort of playing the main blackjack game.

The potential 4-to-1 payout of Multiplier Blackjack makes the game fun.  I really don’t care if I sometimes win 1-to-2 on a dealer bust with a picture, because it’s still a win.  It’s all part of the build-up towards a 4-to-1, or 3-to-1 win.  And, if that win comes on a multiply split hand with a double or two, that’s really exciting.  (In fact, that happened during my first short session, where I re-split Deuces to three hands, had a double-after-split, and the dealer busted with an Eight.)

I also like the way the table layout has betting spots for both regular blackjack, and Multiplier Blackjack.  That way, the player has the option of either standard blackjack, or the multiplier version.  This makes it easy for the casino to introduce the game to the player, pretty much at no floor-space cost.  This layout itself is a new innovation, where the player can choose between different blackjack versions on-the-fly, or weight wagers differently for the same hand.

As I mentioned before, there are sometimes during a session when an odds payout becomes attractive (or necessary).

Basic Strategy

The house edge for a six-deck shoe game with Late Surrender (LS), double after split (DAS), re-split up to 4 hands (SP4) including Aces (SPA4) is 1.92%.  So, pretty much for the cost of a 6-to-5 blackjack game, you get a lot of fun, and up to a 4-to-1 payout on wins.

I generated a basic strategy table for the Multiplier Blackjack rules, a six-deck shoe, and the above pay table.  There are a few differences from standard blackjack, notably the hits with hard-12 against a dealer 2-4 upcard.  There are a few more doubles with hard 9 and even hard 8 against a dealer 6 upcard.  Overall, the play is a little more aggressive, including splitting 4-4 against a dealer 5 or 6 upcard.

Countability

I checked the sensitivity of the house edge to the removal of a single card from the 6-deck shoe, to see if the game was somehow especially vulnerable to card-counting, because of the odds payout.  The sensitivity numbers (the effect-of-removal, or EORs) were of pretty standard magnitude.  And, because of the high initial house edge, it takes a much more distorted shoe to attain any +EV opportunities.  So, it looks like the game is fairly uncountable.

I noticed another new AGS game in my nearby Harrah’s Casino, called Premium Hold’Em, extending their products of 3-hole card poker games against the dealer.  I kind of enjoy squeezing these hole cards, catching minimal glimpses of colors and symbols, and making (correct) decisions without knowing my full hand.  Sometimes, this leaves me with emergency outs after seeing the dealer’s hand.

Plus, once you’ve played enough Ultimate Texas Hold’Em (UTH), all those decisions become automatic, and all you seem to notice is that string of miracle dealer hands which constantly scoop the table.  UTH can be boring *and* painful.

So, what’s new with AGS’s Premium Hold’Em?  Well, first, there’s the novelty and the squeezing of your three hole cards.  Next, the all-in preflop raise is lowered to 3x, which should reduce the variance a bit (from UTH’s 4x).  Then, the entire community board is dealt out at once as a four card “flop”.  Finally, you can either 2x, 1x, or fold after seeing your entire hand!  (Compare to UTH’s 2x decision before the turn+river.)  Of course, the dealer has three unseen hole cards, but the 2x option is still more favorable than in UTH.  Overall, these advantages are offset by the lowered 3x preflop raise, and the higher pair-of-treys Dealer qualifier.  Bottom lime, the house edge of Premium Hold’Em is lower than UTH, at 2.06% of an Ante.

Oh, and the bonus side bet pays down to Jacks Up (two pairs), and has a low house edge of 4.87%.  Again, this offers lower variance than the UTH Trips side bet.

Basic Strategy

I wanted to try out the game, so I worked out a Basic Strategy.  I worked it down to the detail that I like, using hand features that make sense to me.  The table is organized by the two decision points, and divided into mutually exclusive categories for the Player hand, and also for the board.  For each determined sub-category, the selected betting rules should be followed top-down, looking for the first matched condition, or else falling through to the bottom action.

The betting rules are meant to be concise and unambiguous, but I’ll elaborate on some of them below, to clarify with examples.

The Basic Strategy is sub-optimal by only 0.28% from the ideal 2.06% house edge.

You can practice the game for free at the AGS website.

Typical play is actually pretty easy, and the Basic Strategy is intuitive and easy to learn.  The top part of the table tells you what the 3x preflop raising hands are.  They occur about 15.7% of the time, and are easy to remember.

All the river decisions for hands Three-of-a-Kind and higher are simple and intuitive.  Thankfully, you should 2x bet *all* full houses and flushes, independent of the board.  The only time you slow down with a straight is when you 1x it against a 4-flush board.  Notice you still 2x the idiot end straight against an open-ended board, and you still 2x a baby flush against a 4-flush board.  And you still 2x a flush against a double-paired board.

You’ll slow down with Three-of-a-Kind when they’re on board.  You will 2x them with a nut (best) kicker in the hole.  For example, say you’re holding Kh 9s 6h, and there’s trips on board with 8s 8c 8h Ad.  You have the nut (best) kicker in the hole (Kh), so you can still 2x your hand.  However, if your hole cards were Qh 9s 6h, you should only 1x the hand since your Qh is only 2nd nut kicker.  You could still 1x call with Jh 9s 6h (3rd nut kicker), but you would fold with anything lower than the 3rd nut kicker.

If you have Three-of-a-Kind and the board is a scare flush (4-flush), then you can still 1x your hand.  For example, if your hole cards were 7d 3s 3h and the board was 3c Kc Jc 6c, you’d only 1x your trip 3’s.

You’ll generally 2x your two pairs, unless the board is dangerous.  So, against a scare flush (4-flush) or a scare straight (open-ended) board, you’ll just 1x your two pairs.  You should 2x raise your two pairs any time you can beat a double-paired board, or even if you just have the nut kicker.  If the board is paired, you’ll 2x raise your top pair or over pair.  You can 2x raise with bottom pair, just as long as you have 3rd nut kicker or better.  You’ll never fold two pairs when you beat the board.  The only time you’ll fold with two pairs is when you’re playing the board, and don’t have 4th nut kicker or better.

Note: “bottom pair” on a paired board means you’ve paired the lowest singleton on the board.  For example, say the board is 3s 3h Kd 7h.  If you’re holding a 7, you’ve made bottom pair on the board.  If you’re holding a K, you’ve made top pair on the board.  If you have a pair of wired Aces, they’d be an over pair to the board.  If you have a pair of wired Deuces, they’d be an under pair to the board. Also, if you held a pair of wired Fives in the hole, they’d be an under pair to the board too (lowest board singleton is a Seven).

There are a few occasions when you can 2x raise one pair against a safe board (no 4-flush or 4-straight board, including gutshot board).  Against a safe board, you can 2x raise one pair if it’s an over pair, top pair, or second pair.

Generally speaking, you’ll at least 1x call any pair made with the board.  You will fold 3rd or bottom pair against a scare board.  You’ll only call a wired under pair to the board if it’s qualifying, and there’s no 4-flush or 4-straight on board.

You can 1x call playing one pair on board, if you have the nut kicker.  You can also 1x call the pair on board if you hold the 2nd nut kicker, and the board is 2-flush or less.

There’s only one case to 1x bet a no-pair hand on the river.  You should 1x play an Ace-King high hand against a rainbow flop when holding the nut kicker, and the board isn’t 4-cards to a straight.  For example, if your hole cards were Qh 8d 3s and the board was Ac Kh 9d 4s, then you should 1x your hand, because your Qh hole card is the nut kicker.

Collusion Analysis

The game is not vulnerable to even 5 confederates colluding at a full-table sharing perfect information.  Ideal decisions using all known player hole cards (15 of them at a full table) yield only about a +1.4% improvement over Basic Strategy (about +0.5% from counter-strategy pre-flop decisions, and about +0.9% from counter-strategy river decisions).

Bonus Side Bet

An optional bonus on your final hand, or the Dealer’s final hand, is available before the hand begins.  The table below shows the payouts and their frequencies and returns.  The house edge is a reasonable 4.87%, and it pays down to Jacks Up (two pairs), instead of the UTH Trips or better bonus.

Detailed Stats

The total outcomes for every possible starting hand, for every possible flop, and every possible dealer hole cards are shown in the table below, following optimal decisions.  The player will 3x about 15.7% of his hands, will 2x about 37.4% of his hands, will 1x about 23.9% of the hands, and will fold about 23.0% of the hands.

I saw this new variant of Casino War at Barona Casino, where they player gets an option to swap his card and make a 1x Raise bet. Of course, the catch is the dealer gets two cards, and gets to use the highest one. I wanted to see what the strategy and house edge were, and to check if it was at all countable out of the One-2-Six CSM they use.

The rules are pretty simple. You’re dealt one card face up, and the dealer is dealt two cards face down. The dealer will use his highest card. You have the option to replace your card with the next card out of the shoe (CSM), but you must wager an additional 1x bet to do make this swap. Finally, you may wager an optional 1x Raise on your final hand.

The dealer reveals his hand, and all your bets receive action against the dealer high card. Wins win a Six or lower pay 2:1, else it pays even-money. Ties push, and there’s no “going to War”.

For a 6-deck CSM game, the house edge is a fair 2.56%.

The basic strategy is pretty simple. You should swap an Eight or lower card. You should Raise a Jack or higher final card.

I checked the countability in a CSM by assuming perfect play given 16 known cards before every hand. The EV barely changes by +/- 0.3%, and thus is never +EV.

According to Dan Lubin, there’s a version that pays 2:1 for a win with a Six, 3:1 for a win with a Five, 5:1 for a win with a Four, and 8:1 for a win with a Trey. For a 6-deck game, these payouts reduce the house edge to 1.27%. The basic strategy remains the same. Still, the game never gets +EV with only 16 known cards.

Arizona Stud is a new poker-based table game debuting at the Red Wind Casino in Olympia, WA next week (6 Aug 2014). In this game, both the Dealer and the player each receive three hole cards. The player must discard one of his hole cards before the flop, while the Dealer must use exactly two hole cards to make a hand. After the player discards, he may wager a Play bet of 2x-4x the Ante, or check pre-flop. The two card flop is then revealed, as well as one of the Dealer’s hole cards. If the player checked pre-flop, he must then make a 1x Play bet, or fold. Finally, the community river card and all Dealer hole cards are revealed. The Dealer qualifies with a hand of AK-high or better. The Ante pushes if the Dealer doesn’t qualify. The Play bet always receives even-money action against the Dealer hand.

The set of all possible outcomes for the optimal player is listed in the table below. The total in the lower right corner shows a house edge of 1.34% of the Ante. Note that you should either 4x bet pre-flop, or check. You should never only bet 2x.

The basic strategy for the game is listed in the table below, which returns a 1.70% house edge. The player should 4x his hand about 27% of the time, 1x call about 46% of the time, and fold the remaining 27% of the time.

The game looks like fun. The strategy is actually pretty simple, but you get to make the occasional decision. I’ll actually be in Seattle next week (my first time), so I’ll try to check out the game. Maybe I could hit a nice bad beat for once.

The optional 2 Pair Plus Bonus bet pays for the final hand made by the player. The house edges for the various offered paytables are listed below.

The Player Bad Beat Bonus bet pays when a player’s Jacks-or-Better hand is beat by the Dealer. The following table shows the optimal outcomes for the strategy maximizing the Bad Beat Bonus return. The house edge for the optimal Bad Beat Bonus strategy is 8.00%.

I saw a new Hold’Em type game at Casino Pauma last week, and I thought I’d work out the numbers and give it a try. The game is pretty simple. You bet an Ante before the hand begins. After seeing your two hole cards, you may bet 2x preflop, or check. After the flop, you may 1x bet or check. The turn, river, and the dealer’s hole cards are then revealed. The dealer qualifies with a pair of 6’s or better. If the dealer doesn’t qualify, all post-Ante wagers push. If the dealer beats your hand, you lose all your remaining bets. If you beat a qualified dealer hand, you win all your bets. If you beat a non-qualified dealer, you only win 1/2 your Ante.

The game is a bit calmer than Ultimate Texas Hold’Em, since you only have a single Ante, and you can check it down to showdown (in fact, this happens 69.8% of the time). Plus, players may like the fact that they can make the 2x and 1x bets only when they have an advantage. (I.e., all properly made 2x and 1x bets are +EV.) And the Ante is only a -11.4% loser, on average. The optimal player makes a 2x preflop bet 11.2% of the time, and a 1x flop bet on 25.5% of the time. The dealer qualifies 69.1% of the time. The game has relatively low variance, and I found myself increasing the Ante from the $5 minimum, to $10, and $15. (I’d never do that with UTH.)

The total outcomes for the optimal player strategy are listed in the table below, and show a house edge of 3.2% of the Ante.

I worked out the basic strategy for the game, just in case anyone wants to play the game. The strategy is actually pretty simple. Since the dealer qualifies with a pair of 6’s or better, you generally only bet the flop if there’s a qualified hand to beat. You can bet kickers and draws against a qualified flop, otherwise you should only bet a qualifying pair when there’s a board card lower than your pair, but 6 or higher.

The basic strategy below has an error rate of 4.5%, that only results in a cost of 0.23% to the player. So the practical house edge is 3.5% for the game.

There’s not much opportunity for collusion in the game. Knowledge of the hole cards of all 6 players will modify some of the preflop 2x decisions, but the frequency and value of these counter-(basic)strategy decisions aren’t enough to overcome the 3.2% house edge. Trust me, I’d have worked it out if it was worthwhile.

There’s two bonus bets offered, where the Pocket Bonus pays when your hole cards make a pocket pair, and the Final Hand bonus on your final 7-card hand. The paytables offered at Casino Pauma aren’t very good.

A reader told me about a new ShuffleMaster game at The D Casino, where you try to make a 4- to 7- card flush, starting with 4 hole cards, and paying to see 5th/6th and 7th Streets on a community board. The betting structure is similar to Mississippi Stud, where you post an Ante, then make a 1x Play decision to see 6th Street, and a final 1x Play decision to see 7th Street. The game pays odds on the Ante if you make a 4-card flush or better, and even-money on the 1x Play bets. Otherwise, if you fold or don’t make a hand, you lose your bets.

I believe The D will award the highest possible payout for a given hand. So, if you make a 5-card flush that contains a 4-card straight flush, they’ll pay you 15-to-1 (instead of 9-to-1). With this liberal rules interpretation, the house edge is 3.75%. The total possible outcomes for an optimal player are listed below.

If the rules are interpreted strictly, and you must make a straight flush with all your cards of the same suit, then the house edge is 5.41%.

Of course, the only reason why I analyzed the game was to Monte Carlo the 6-way collusion edge. The return is about +4.07% for 6 players sharing perfect info under strict rule interpretation, and +5.67% under the liberal rules. That’s not much, considering it’s pretty hard to convey suit information between confederates. It’s probably not worth anyone’s trouble to attack the game. I didn’t bother working out a practical strategy.

(FYI, I’m spending a lot more time outside of the casino these days. Before, I used to practically live in the casino. About 9 months ago, I changed obsessions. You can read about my current mania on my other blog.)