The game is pretty simple, where both dealer and player get 6 cards to make a 5-card poker hand. There’s only an Ante, and a 1x Play bet. The dealer shows 3 upcards, and you decide to either 1x Play or fold your hand. If the dealer doesn’t qualify with Ace-King, then the Ante pushes regardless of the player hand. The 1x Play bet always receives even-money action against the dealer hand. The Wizard of Odds provides a basic strategy, and lists the house edge at 1.27%.

I figured 6-player collusion would help you know when to play Ace-high, and maybe help you fold a pair when a lot of dealer outs remain that beat you. But first, I simulated a bunch of hands finding the optimal decision given confederate card info. This gave me a very close approximation to the ideal edge obtained by perfect collusion. This 6-player edge amounted to only +1.17%. This isn’t much, especially since any actual collusion strategy approaching this limit would be impractically complex.

At this point, I only made a half-hearted attempt at finding a practical collusion strategy. There’s so many cards involved, its difficult to come up with a workable signalling system. Also, I looked over the collusion decision points, and it wasn’t simple to identify the conditions for making a counter decision to basic strategy. For what it’s worth, I came up with the following “simple” 6-player collusion strategy that simulates at +0.15%:

• Call two pairs or better, else
• Call one pair unless there are 7 or more dealer one-card outs remaining that beat you, else
• Call Ace-high when 2 or more Aces and Kings seen with 9 upcard copies, else
• Call Ace-high with 4 or more Aces and Kings seen with 8 upcard copies, else
• Call Ace-high with 6 or more Aces and Kings seen with 7 upcard copies,
• else fold

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.

I made the strategy based on what I normally look for when playing Hold’Em carnival games (like Ultimate Texas Hold’Em). The most common cases are addressed, and I include some less frequent, though interesting situations that you’ll probably want to know about. The strategy is actually very simple, and very easy to remember.

where “scare board” means open-ended or 4-to-a-flush on the turn, and “your” hand means your hand that beats the board.

The game is interesting, because it allows you to discard and replace one of your hole cards before deciding to see the flop. However, you have to pay to see each street (1x to see flop, 1x to see turn, 1x to see river), otherwise you fold. The Ante in the game resembles the Blind in Ultimate Texas Hold’Em, where it only pays for a player’s winning hand according to a paytable, when both hole cards play. But, there’s no qualifier on the dealer hand, so your Flop, Turn, and River bets all get even money action against the dealer hand.

I worked out a fairly simple strategy for the game, which simulates at 3.0% house edge. That’s not too bad, and is comparable with UTH and Texas Hold’Em Bonus.

Rules

1. The Player must wager an Ante before the hand begins.
2. Each Player and the Dealer receives two hole cards.
3. The Player may discard one of his hole cards, and receives a replacement card from the deck.
4. The Player either 1x bets to see the Flop, or folds.
5. The Flop is dealt to the community board.
6. The Player either 1x bets to see the Turn, or folds.
7. The Turn is dealt to the community board.
8. The Player either 1x bets to see the River, or folds.
9. The Dealer turns up his hand, and the Flop, Turn, and River bets receive even-money action against the Dealer hand.
10. If the Player beats the Dealer, the Ante pays according to the paytable if both player’s hole cards play, else the Ante pushes; if the Dealer beats the Player, the Ante loses.

Strategy

The following strategy is fairly simple, and probably doesn’t sacrifice much EV. I’ll guess that the optimal strategy (non-colluding) is better by less than 0.5%, at most.

Discard

Never break a pocket pair. Use the following table to decide whether to replace your lowest hole card:

Flop Bet

Play any pair. Play any suited hole cards, except for 72s, 62s, and 32s. Play T2o or better. Play offsuit {9,8,7,6} with a 5 or better. Fold all others.

Turn Bet

You bet almost all hands on the flop. Bet any hand that beats the board, bet any draw, bet if trips on board. If the board is paired, bet your 86 or better hole cards. If the board is suited, bet your Jack hole card or better, else bet your 96 or better hole cards.

River Bet

You bet most hands on the turn. Bet any hand that beats the board, bet any draw, bet if trips on board, bet if board is double-paired, bet if scare straight on board. Bet your 8-high hole card or better. You can still bet garbage hole cards if the board is paired, and the on-board kicker is 3rd nut or better.

Bonus Bet

The game also has a final hand bonus with the paytable below. It’s interesting that the bonus bet allows you the discard, and it still pays on “folded” hands. However, the discard strategy for the main game is not optimal for the bonus bet. The bonus bet simulates at a 9.9% house edge using the discard strategy for the main game. If you optimize the discard strategy for the bonus bet, then you’ll reduce the house edge to about 3.5% (while destroying your main game EV).

My Blind Review

I have no idea if this game is any fun. I haven’t played it. I know I don’t like the 9.9% house edge on the Bonus bet, but I don’t play most bonus bets either. Of course, you can mess around and bet $5 on the Ante and $100 on the Bonus, and discard for bonus (never break suited cards or pairs; keep 0-gap connectors except for AK, KQ, 43, 32, A2; otherwise keep the card closest to an 8 and discard the other). That’ll get the floorman’s attention.

It’s simple enough to follow the above strategy, but it’s not very poker-like. You make a lot of “crying calls” with nothing (e.g., you call to draw to a pair of 8′s on the river, even against a scare board). I guess the discard option is fun, but I can see breaking A7s, and getting a worse hand more than half the time.

If anyone out there tries it, tell us how you liked it.

Rules

The game is played between the dealer and each player. Each player and the dealer receives two hole cards, and combines them with the community cards on the “board” to make their best 3-card poker hand. You do not need to use any of your hole cards to make a hand (i.e., you may “play the board”).

1. Player posts an Ante before the start of the hand.
2. The Player and the Dealer are each dealt two hole cards.
3. The dealer turns up the Flop card on the community board.
4. The Player decides whether to 1x bet the Flop, or to fold his hand and lose his Ante.
5. The dealer turns up the Turn card on the community board.
6. The player decides to either 1x bet the Turn, or check.
7. The dealer turns up the River card, then turns up his hole cards.
8. The Dealer requires a pair of 4′s or better to qualify, else the Antes push.
9. All remaining bets receive even-money action against the Dealer hand.

Strategy

I constructed a reasonably simple strategy, and was very surprised to see it simulate at only a -0.60% EV! This is pretty good for a carnival game, which usually has between a 2.5% to 3.5% house edge. My simple strategy isn’t very optimal, and I estimate the actual house edge is very close to 0. (The error EV of my simple strategy simulates around 0.5%, so an optimal strategy would yield close to 0 EV.)

On the Flop, you should always make the 1x bet (never fold your Ante).

On the Turn, use the following table to decide when to bet your hand, else check. You should only bet a pair under the stated conditions, and when your hand beats the board by more than just kickers, except when betting the nut flush draw.
(Glossary: “scare straight” means the board has connected cards; “scare flush” means the board is suited; “good straight draws” (GSDs) mean the number of River card ranks that make you a straight, excluding the “idiot end” straight draws. For example, if your hand is Kc 6h and the board is Qd 7s, then your 3 GSDs are {A,J,5}. Note that an 8 is not a GSD, but an “idiot-end” draw, because a dealer 9 would beat your 8-high straight. Basically, a GSD is an out that makes a straight which can’t be beat by a single dealer hole card.)

This simple strategy decisions are occasionally wrong by more than 10% of the Turn bet, but overall, it works out well enough. The mistakes are pretty obvious when you look at them, it’s just not worth optimizing the strategy unless you want to play it seriously. The game will probably be gone in a few weeks anyway, I just wanted to see what a reasonably strategy would yield.

Bonus Bets

The Straight-or-Up bonus bet has a 4.49% house edge, which isn’t too bad, as far as side bets go.

The Pair-or-Suited side bet on your two hole cards is a little better, costing only about a 4.8% house edge.

I figured they wouldn’t like that post. The calculator showed all the players hands face-up, like it’s played at Barona, and showed you the exact value of your hand, and the best decision (3x, 1x, or fold). I guess if the regulars saw it, and all started playing optimally, it’d be a problem. But that will never happen; I’ll bet any amount of money on it. People don’t play optimal strategy, that’s not why they’re there. People play the way they want to, and that’s the way it should be. I pretty much just wrote the calculator for myself, and one or two guys who wanted to see it.

At any rate, someone at Barona thought it best to bar me, and I can’t argue with their decision. I doubt I influenced any players about the game, but everyone got the idea that I played tight. (People also thought I played too aggressively at Ultimate Texas Hold’Em.) Worse-case, I took up a weekend seat playing tight $5 Antes, and locked out a bigger player when the game was full. Best-case, I “prop’ed” up the game on weekday nights, when an additional player helps build up critical mass in the game. (Everyone agrees it’s better to have more players and see more cards per hand.)

Like I said, being barred is a “win-win” situation. They’re happy, and don’t have to worry about me meddling with their Mississippi Stud game. I’m happy, since getting barred was the only way I’d stop playing 60 hrs/week there. So instead of coming back from the casino every night until 3am, I go downstairs and take hour-long walks through Little Italy and Balboa Park. Although it was pointless, it was easy playing a game with a 1.5% tailwind. It’s like being the house, but without all the expenses, and with comp’ed food. But it was just an attractive nuisance, something that draws you in, but ends up harming you.

There were only a few other people that played the game. Often I was there by myself. The game isn’t hard to play, but there’s not a lot of beginner instruction out there, so it remains very mysterious to most people. So I made some video tutorials, to give people that jump-start to understanding the game. (Look for all my YouTube videos on Pai-Gow tiles.)

There’s a few reasons you should learn Pai-Gow tiles. First, it’s a lot of fun if you like games that require a little thought. Secondly, it’s a very cheap game. If you alternate hands as player and banker (e.g., when you’re heads up), the house edge is less than 1%. It even gets cheaper if the house doesn’t use quarters, and charges only $1 commission on a $25 win (4% commission). Finally, and perhaps most importantly, you get tons of degen “cred” by knowing this game well (especially if you’re lo-fan).

I played about 20 hours of $25 Pai-Gow Tiles at the MGM Grand, and got comp’ed for one night hotel stay (all I needed; my friend got comp’ed the other two nights), and I received $67 in cash comps towards our meals. Other than tokes, the average house vig came out to (20 hours)(30 hands/hour)($25/hand)(1%) = $150, which is about the value of my comps. I call that fair. Plus, I ended up winning on the trip, and came back with more money in my pocket than when I left.

The first times I played, I barely knew how to read a hand, and I didn’t learn any strategy. I often asked the dealer for the house way, which I later found out costs at least 0.5% compared to even a simple strategy. Besides, it’s much more fun to set your own hand (correctly). The Wizard of Odds has a very good calculator, but I still needed a practice trainer that taught a simple strategy.

So I wrote a trainer to teach myself, and other newbies, how to play the Wizard’s Simple Strategy. With some interactive practice, and just a little reading on the basics of the game, I hope that anyone can learn to play.

I wrote up a tutorial page on Pai Gow Tiles, if you need some background on the game.

You can see the game is slightly in your favour, because of the asymmetrical bias towards bigger wins than losses. There’s a nice long tail of huge wins (although rare). On average, the expected win is (5000)(+1.25%) = 62.5 Antes. (This used a slightly older strategy; it could be improved.) However, there’s still a 6% chance of busting out, and you still have a 50% chance of losing after 5000 hands!

So, your +EV lies in the asymmetry of the curve, and the long tail of big wins. Not to mention that playing 5000 hands of normal (-EV) Mississippi Stud would cost you (5000)(-4.5%) = 225 Antes, and the outcome distribution curve would look much worse (I don’t have Basic Strategy coded up, but imagine the curve shifted higher and to the left.)

The best way to look at the face-up game is that it’s gambling with a tailwind. Anything can happen, but overall, you’ll feel the help of the tailwind, especially over the long run. Before I was barred, I really enjoyed playing the game hour-after-hour, week-after-week, because it all worked out in the end. It was like playing cards for free.

Of course, the only real advantage to seeing all the players cards is being able to fold early. The other advantage is knowing when to raise draws, but these are fairly rare (e.g., small pairs with all outs remaining on 3rd and 4th Streets, 6 high outs or 5 high suited outs on 3rd Street, certain straight draws on 5th Street). So folding early is the main use of the other player card info.

I wrote a Java calculator for Mississippi Stud when you can see all 6 player hands. It shows you the best decision at each point of the hand. (It’s a huge .jar file and may take some time to load, sorry.) Click on the screenshot below to try it:

The EV numbers tell you the expected value of the hand if you Fold, 1x, or 3x the bet for the next card. The EVs are normalized to the Ante, and a positive EV means an expected profit, and a negative EV means an expected loss. If you’re playing $5 Antes, then multiply these numbers by $5 for the value of the Fold, 1x, and 3x decisions.