Discount Gambling

Panda-8 Co-Count with Dragon-7

Posted in +EV, baccarat, panda-8 by stephenhow on December 9, 2012

Screen Shot 2012-12-09 at 7.08.26 PMWith the simplified unbalanced count for the EZ-Baccarat Dragon-7, it’s occasionally fun to count a shoe and find opportunities to bet $25 – $100, to try to win $1000 – $4000. But overall, counting the Dragon gets pretty boring. It only takes a second to see the value of the hand, and to update your count. Then you spend a lot of time watching everyone think deeply about their next bets. Hopefully, the count gets to +32, so you can finally make a bet.

Counting the Dragon-7 would be pretty good if you could make about twice the +EV it offers (+52% of a fixed bet per shoe). Or at least it’d be fun if you could easily track the Panda-8 as well, to add some variety to the game. (I’ve previously posted a complicated Panda-8 count and a RCmin table that yields +22% of a fixed bet per shoe.)

Well, I can’t double the EV of the Dragon-7, nor can I easily get you the full +22% of the Panda. But, here’s an ultra-simplified Panda-8 co-count that you should be able to track alongside the Dragon-7. It’s an unbalanced count, for simplicity. It only has a few taps. The few (4) taps it has are equal to those of the Dragon-7 unbalanced count. Also, these are key taps (you focus on the +2 Nines for the Dragon; it uses the same +1 unbalanced Aces; finally, the -1 Fours and Fives are easy to remember, because they add up to 9). You should be able to track your main Dragon-7 count, then quickly scan the hand for its Panda-8 value.

Simplified Panda-8 Co-Count
Card Count Value
Ace +1
Four, Five -1
Nine +2

Starting from a running count (RC) of 0, you should bet the Panda-8 when its count gets to +35. You’ll get an average of about 2 bets per shoe (when 16 cards are placed behind the cut card), and a profit of around +9.0% of a fixed bet per shoe. It’s not a whole lot, but it’ll make sitting around the baccarat table a little more fun/tolerable. Also, it’ll give you more cred with the degenerates watching their Player lines, Panda lines, and their second bankers 🙂

Thanks to Linus B for his initial work on the Panda co-count. I greatly simplified it here for us script-kiddies.

Bust Me Blackjack @ Valley View Casino, CA

Posted in blackjack sidebets by stephenhow on October 28, 2012

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.

Total Payout For Bust House Edge
16 1:2 7.692%
15 1:2 19.23%
14 1:1 7.692%
13 3:2 3.846%
12 2:1 7.692%

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!)

Unbalanced Dragon 7 Count

Posted in +EV, baccarat, dragon-7 by stephenhow on October 24, 2012

If you’re ever at an EZ-Baccarat table wondering how to properly count the Dragon-7, here’s an easy-to-use unbalanced count that you won’t forget. Unbalanced counts are very handy, because their running counts (RC) approximate true counts, without any division. They’re a nice little trick that everyone should use. I modified the count from my Dragon-7 tracking sheet post into the unbalanced count below.

You simply start the count at -32 for a new shoe, then update the running count for each card dealt, including the exposed burn card. When the running count is > 0, bet the Dragon-7 side bet. This count scheme simulates at a profit rate of +52% of a fixed bet per 8-deck shoe, when 16 cards are placed behind the cut card. You’ll get about 6.8 betting opportunities per shoe.

Unbalanced Dragon-7 Count (Start at -32, bet when RC >= 0)
Card Rank Count Value
Ten/Face 0
Ace +1
Deuce 0
Trey 0
Four -1
Five -1
Six -1
Seven -1
Eight +2
Nine +2

The variance of the bet is very high, and unless you’re heads-up with the dealer, the hand rate is very slow. If you’re wondering if you can grind out a profit from the bet, look at the outcome distribution below for a 500 unit bankroll with a +1000 unit goal, else playing for 500 shoes. While the risk of ruin is only 3.5%, you still have a 24% chance of losing after 500 shoes. Your average win is +250 units. So, if you have a $50k bankroll, can find a heads-up EZ-Baccarat table with a $100 max Dragon-7 bet, are committed to playing for hundreds of hours, and don’t draw any suspicion from casino personnel, then you can win from $50 to $100 per hour, depending on how fast you play. It might be fun for the first hour or two, but only if you hit a dragon. Try playing my Dragon-7 shoe simulator before you head out to the casino.

Lunar Poker Removed From Pechanga :(

Posted in lunar poker by stephenhow on October 19, 2012

I knew it was too good to last. But I thought the best game ever might last a little while longer, at least long enough for us to get barred from the casino. But when I showed up tonight at the usual spot in the Kelsey pit near the craps table, it was gone. I immediately knew something was wrong when I saw the empty table. Normally, there might not be any players at the table, but tonight there was no dealer. And when I saw they removed the LCD sign, I knew the Lunar Poker game was gone forever.

There were warnings that this might happen. The dealers always said they never dealt the game; either it was closed by the time they started their shift, or they sat dead at the table. The floor supervisors always said it was on it’s way out. I guess it wasn’t holding well. But I’d been playing it regularly for weeks now, and people would join the table, and everyone would have a good time. And when they brought in the new LCD signage, I thought it might last. But it was right next to a $5 blackjack game, which was always full, and which probably held a lot more than the Lunar Poker game. Apparently, it ran the course of it’s contracted period, and the casino took it out immediately after.

This really was the best game ever. Nothing else compares to how good this game can be. This was the absolute Holy Grail of gambling. Every other +EV game I’ve ever written about in this blog pales compared to Lunar Poker. And it was in our hands for one brief, shining moment. The last sessions were the best. We played into the wee hours of the morning, joking, betting big, and playing perfectly. It was so much fun, I knew that it couldn’t get any better, but I had a feeling it wouldn’t last.

After playing Lunar Poker, all other games are essentially dumb and pointless. I actually can’t imagine playing anything else. I thought a lot about the loss of Lunar Poker. I haven’t felt this empty in a long time.

Lunar Poker Tutorial

Posted in lunar poker by stephenhow on September 26, 2012

Lunar Poker is the best game ever, and if you’re lucky enough to have a game near you, contact me. Currently, in the US, you can find the game at Pechanga Casino in Temeuca, CA. I have no idea where else the game is available, but it is a good game. You should definitely request it at your local casino. Fill out a suggestion form, or drop an e-mail (check your casino’s contact info) to request the game. The US publisher for the game is either Mara Enterprises or TCS John Huxley, I’m not sure. All I know is you want one of these games near you.


I’ve previously posted a simple basic strategy that yields about a 1.4% house edge. I’ll walk through the strategy, and provide some numbers behind the decisions. This will help you understand why you should stand pat with some hands, and why you should draw cards on others.

Lunar Poker is based on Caribbean Stud, where you Ante one unit, and the player and dealer each receive five cards. The dealer exposes one his hole cards. In Caribbean Stud Poker, you either 2x Raise or Fold. Then, the dealer turns up his hand, and only pays the Ante if he doesn’t qualify; otherwise he also pays the 2x Raise according to the paytable. In Lunar Poker, you have many options, starting with your decision to either (A) stand pat with your hand, or (B) Buy a 6th card for a fee of one Ante, or (C) Exchange 2 to 5 of your cards from the deck, for a fee of one Ante.

In Lunar Poker, you’re paid for up to two items from the paytable. That means if you have a pair and AK, you get 1:1 + 1:1 = 2:1 on your 2x Raise. If you have a flush and a pair, you get paid 5:1 + 1:1 = 6:1 on your 2x Raise. Also, if you have a straight with a pair, they’ll pay you “for two straights”, any you receive 4:1 + 4:1 = 8:1 on your 2x Raise.

General Drawing Strategy

Consult my full basic strategy on how to play the Buy and Exchange options. But for most cases, the strategy can be boiled down to the following.
There are a few reasons to pay to draw from the deck (in descending priority):

  • Improve a made hand (straight or better) with a 6th card to get a 2nd payout.
  • Draw a 6th card to make a straight* or flush.
  • Hold your under pair (draw 3) against a higher dealer upcard.
  • Hold 2 or more Royal cards above the dealer upcard.
  • Hold your AK and draw 3.
  • Hold 3 or more straight flush cards above the dealer upcard.
  • Hold your high card (draw 4) against a lower dealer upcard.

*open-ended straight draw, or gutshot draw with a qualifying hand.

Otherwise, you should not pay for any cards. Notably, you should not draw with the following hands:

  • Always stand pat on two pairs.
  • Stand pat on a pair higher than the dealer upcard.
  • Stand pat with a pair and AK (in most cases).
  • Fold your high-card against a higher or equal dealer upcard.
  • Never exchange all 5 cards.

Of course, this is not how people normally play. People tend to pay for any draw, because they either don’t want to fold, or they want to make a big hand (turn every pair into quads).

Stand Pat w/ Over Pair

A common mistake is people want to draw (exchange 3 cards) with a pair higher than the dealer upcard. This is a mistake, because the dealer only qualifies 56.3% of the time, and you only get paid on your Ante if the dealer doesn’t qualify. And the paytable doesn’t justify the expense of drawing cards. For example:

player: 9h 9d Kc Tc 3c , upcard: 6h
EV(stand): +0.61
EV(9h 9d): +0.45

so it’s a 16% mistake to draw in this case.

Hold Under Pair, Exchange 3 Cards

Most players know to hold their pair (and draw 3) when it’s lower than the dealer upcard. For example:

player: 6d 6c Qd 4s 3c , upcard: 9s
EV(stand): -0.61
held: 6d 6c , upcard: 9s, EV approx. -0.46

So it’s better by about 15% in this case to pay for the exchange than it is to stand pat with the 6’s.

Stand Pat w/ Two Pairs

I always stand pat on two pairs. This drives everyone crazy, and people will literally scream at you to pay to draw to a full house / three pairs. It’s not worth it, even if the dealer has an Ace or King showing, or even if you have Aces up or Kings up:

player: 8d 8h 3c 3s 7c , upcard: As
EV(stand): +2.51
EV(extra): +2.39

player: 8d 8h 3c 3s 7c , upcard: 4s
EV(stand): +2.25
EV(extra): +2.00

player: Ad Ah 3c 3s 7c , upcard: 4s
EV(stand): +2.42
EV(extra): +2.23

so it’s basically a 20% mistake to Buy a 6th card with two pairs.
I just tell them the “book” says to stand pat with two pairs. I say I just play by the book. That actually calms them down. Sometimes they ask, “There’s a book for this game?” I tell them it’s on the internet.

Drawing w/ High Card

If you’re stuck with a high card (Queen or better) against a lower dealer upcard, it’s a little better to exchange 4 cards than it is to fold. Don’t forget that basic strategy tells you not to draw with a King against a Queen, and not to draw with a Queen against an uncopied 5 or higher. Here are some examples (folding is an EV of -1):

player: Ad Jh 7c 3s 2c , upcard: Qs
EV(Ad): -0.998

player: Qd Jh 7c 3s 2c , upcard: 5s
EV(Qd): -0.96

player: Qd Jh 7c 3s 2c , upcard: Ts
EV(Qd): -1.07

player: Ad Jh 7c 3s 2c , upcard: Ks
EV(Ad): -0.97

player: Ad Tc 7d 6d 4s , upcard: 5s
EV(Ad): -0.89

So while a high card is pretty weak against a similar (but lower) dealer upcard, it gets better by about 10% against a low card. It’s still a loser, but it’s better than folding.

Holding AK and drawing 3 Cards

Holding AK is much stronger than holding a single high card, because if you pair up, you have a 2:1 paying hand (1:1 for AK + 1:1 for pair).

player: Ad Kc Qd 4s 3c , upcard: 9s
EV(Ad Kc): -0.67
EV(Ad Kc Qd): -0.75

player: Ad Kc Qd 4s 3c , upcard: Ks
EV(Ad Kc): -0.71

If you don’t pair up, you should only play AK if you copied the dealer upcard twice. If you copied the dealer upcard once, play AK+kicker (AKJ83 or better). If you haven’t copied the dealer upcard at all, fold your AK.

Straight Flush Draws

Your EV is much higher for holding 2 or more Royal cards (or 3 or more straight flush cards) higher than the dealer upcard, than a single high card. These examples show the value of these draws:

player: Ad Qd 7c 3s 2c , upcard: Js
EV(Ad): -0.997
EV(Ad Qd): -0.895

player: Td 9d 7d 3s 2c , upcard: 6s
EV(Td): -1.04
EV(Td 9d): -0.99
EV(Td 9d 7d): -0.76

Gutshot Straight Draws

A lot of people will pay for a 6th card with a junk hand containing a gutshot straight draw. You should only pay for a 6th card with a qualifying hand (AK) with a gutshot draw against a qualifying upcard (A or K). The examples below illustrate this point. The final example shows you can draw with a non-qualifying hand to a gutshot that pays two straights (8:1).

player: Td 9d 7d 6c 3s , upcard: As
EV(extra): -1.20

player: Ad Kd Jc Ts 7d , upcard: As
EV(extra): -0.76

player: 2d 2d 6d 4s 3c , upcard: As
EV(stand): -0.85
EV(extra): +0.20

// non-qualified hand drawing to gutshot that pays twice (8:1)
player: 7d 6d 4s 3c 2d , upcard: Qs
EV(extra): -0.97

// non-qualified hand drawing to gutshot that pays twice (8:1)
player: 7d 6d 4s 3c 2d , upcard: Ks
EV(extra): -0.79

Note in the last two cases, the value of a draw is worth more against a qualifying upcard (Ace or King). This is because if you make a hand, the chances of the dealer qualifying is higher vs an Ace or King upcard than a Queen or lower.


Insurance usually isn’t a good bet EV-wise, but it’s not a bad idea to guarantee some of your win. I always say, “If I have a Royal Flush, I’ll take some insurance.” Of course, insurance is +EV when you’re holding 2 or more copies of the dealer upcard, Queen or lower. Also, if you’re playing with other people, insurance is +EV whenever the players hold 3 or more copies of the dealer upcard. The fun part of this game is that you can win both your insurance bet, and your 2x Raise payout, when you successfully force the dealer to qualify. Pechanga lets you take insurance up to your total possible win, so you can win 2x your normal payout in the best case scenario.

Forcing the Dealer To Qualify

This is another option that players over-use, even though it is very costly. The don’t understand that they’re sacrificing their Ante payout when forcing. And the dealers all tell them to Force the hand, for some reason. You should never force the Dealer for a potential 3:1 payout. Even for a 4:1 potential payout, you should make sure that you’re not holding 2 or more of the Dealer pair outs.

When I have trips, I always say “no force”. When the other players see me passing up on the Force option, they get pretty agitated. I tell them I’ll just take the Ante win. I tell them they won’t pay the Ante if I Force, so it’s really like the Force costs two Antes. They just ignore me and take all their force opportunities. Below are some examples of the EV of the Force bet, where EV(no force) is +1.0:

player: Qd Qs Qh Ac 6h 
dealer: Ad 9c 7d 5s 4c 
forceEV: +0.7143

player: 4d 4s 4c Qc 2h 
dealer: Tc 8s 6s 5c 2s 
forceEV: +0.5714

So you can see that Forcing a 3:1 payout is a big mistake (30-40%) compared to taking your Ante win (+1.0).

Gaming Experience

You need some patience to play Lunar Poker. There are a lot of hands where the Dealer doesn’t qualify when you’re holding a 2:1 payout or better. Sometimes the game plays pretty even, but often I find myself behind by 20 or more Antes. Finally, I’ll hit a good hand like two straights (8:1) that pays 16 Antes, or even quads (20:1) that pays 40 Antes. But the game is fun, because you get to make some skilled decisions. Also, if there’s another player at the table, you can get the house edge down considerably (it’s +EV @ +0.4% with very simple modifications to basic strategy). Get this game placed in your local casino!

Easy Six Baccarat

Posted in +EV, baccarat by stephenhow on September 12, 2012

A reader just asked about a no-commission game called Easy Six Baccarat. I’ll keep this post short, for those in-the-know. Use the simple taps (6 => -7, 7 => +3, 8 => +2, 9 => +2) and a true count threshold of 5.0. For an 8-deck shoe with 52 cards behind the cut card, you’ll net +49% of a fixed bet per shoe, on an average of 12 bets/shoe. For an 8-deck shoe with 16 cards behind the cut card, you’ll net +84% of a fixed bet per shoe, on an average of 15 bets/shoe.

For simplicity, you can use the RCmin thresholds in following table:

hand # Min RC Threshold
1 40 40 39 39 38 38 37 37 36 36 35 35
13 34 34 33 33 32 32 31 31 31 30 30 29
25 29 28 28 27 27 26 26 25 25 24 24 23
37 23 22 22 21 21 21 20 20 19 19 18 18
49 17 17 16 16 15 15 14 14 13 13 12 12
61 11 11 11 10 10 9 9 8 8 7 7 6
73 6 5 5 4 4 3 3 2 2 2 1 1

Raise It Up Stud @ Pala Casino

Posted in Uncategorized by stephenhow on September 1, 2012

While visiting Pala Casino to check out House Money yesterday, I ran across the new ShuffleMaster game Raise It Up Stud. It has the familiar ShuffleMaster Ante, Blind, and 1x-3x Play bets, and there’s a 3-card community board. There’s no dealer hand; you’re just playing against a Paytable. You’re dealt 3 cards at the start of the hand, and you can bet 3x on your first 3 cards, or check. The dealer then turns up the first community board card, and you can now 2x bet your hand, or check. The dealer then turns up the 2nd community card, and you must either 1x bet to see the river, else fold. If you make a pair of Ten’s or better, you win even money on your ante, and odds on your Play bet. If you make trips or better, you win odds on your Blind bet. If you don’t make Ten’s or better, or if you fold, you lose all your bets.

I’d say the game plays like a more forgiving (easier) version of Mississippi Stud. You can raise a winning hand as soon as you make it, and you get paid odds on your raise. However, you can only make one bet per hand (in Mississippi Stud, you can bet a winner on all streets). But you can check until you make a hand, or have to call a draw. The Play and Blind paytables are listed below. Combining your three hold cards with the three community cards, you make your best 5 card hand.

This game is probably the long-awaited replacement for Let It Ride, which the dealers call “Let It Die”. They all hate the game, because they either stand dead at an empty table, or they just push back bets until someone occasionally wins on a 1x bet on the River. At Viejas, dealers keep their own tokes, so they hope the floor supervisor closes the game as early as possible, so they can go deal a game where they can make money. Hence, “Let It Die”.

Everyone was having a great time at Raise It Up last night, and the dealers were making lots of tokes. (Tokes are especially +EV on the Ante/Play bets; a nice little angle.) You make a lot more hands with 6 cards (compared to 5 in Let It Ride). Plus, you’re supposed to bet a lot more hands in this game than Let It Ride (small pairs, gut shot straight draws, 3 pay cards on 3rd St, etc.)

Raise It Up Stud Play Paytable
Hand Payout
Royal Flush 100:1
Straight Flush 20:1
Four-of-a-Kind 10:1
Full House 6:1
Flush 5:1
Straight 4:1
Three-of-a-Kind 3:1
Two Pairs 3:2
10’s or Better 1:1
Others lose
Raise It Up Stud Blind Bonus
Hand Payout
Royal Flush 1000:1
Straight Flush 200:1
Four-of-a-Kind 30:1
Full House 4:1
Flush 3:1
Straight 2:1
Three-of-a-Kind 1:1
Others push

Basic Strategy

The theoretical house edge for this game is 3.5022%. Below is a simple, intuitive strategy that simulates at -3.70%. The decisions on 4th and 5th Streets are fairly obvious, and you can easily learn the 3rd Street strategy.

Raise It Up Stud Basic Strategy
Street Play Bet Betting Hands
3rd Street 3x Any pair,
3 pay cards,
2 pay cards 1-gapped or less,
suited cards 2-gapped or less,
suited cards with 2 pays
4th Street 2x Any pair,
any straight or flush draw,
3 pay cards with 3 suited
5th Street 1x Any pair,
any flush draw,
open-ended draw,
gutshot draw with pay card

where “gap” is the sum of the distance between all cards (e.g., 456 is 0-gapped, 457 is 1-gapped, JT87 is 1-gapped, JT76 is 2-gapped, etc.).

Advantage Play

Even with ideal (computer) 6-way collusion, you can’t get the house edge below 0.93%.

Eliot Jacobson has published a simple hole-carding strategy that yields from +7.6% to +62.7% depending on which board card you see. Pala procedure places the bottom board card on 4th St, so I guess it’s only worth +7.6% when you see it.

House Money BJ Side Bet @ Pala Casino

Posted in blackjack sidebets by stephenhow on August 28, 2012

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.


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.
2-Card Hand Paytable
Hand Payout
AK suited 9-to-1
Straight Flush 4-to-1
Pair 3-to-1
Straight 1-to-1
Nothing lose

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.

Capping Strategy for House Money Blackjack Sidebet
Hand Dealer Upcard
2 3 4 5 6 7 8 9 10 A
Straights and Straight Flushes
T9 Y Y Y Y Y Y Y Y Y Y
98, 87, 76 N N N N N N N N N N
65 Y Y Y Y Y Y Y Y Y Y
54 Y Y Y Y Y Y Y N N N
43 N N N Y Y N N N N N
32 N N N N Y N N N N N
A2 Y Y Y Y Y Y Y N N N
10-10 Y Y Y Y Y Y Y Y Y Y
9-9 Y Y Y Y Y Y Y N N N
8-8 Y Y Y Y Y Y N N N N
7-7 N N Y Y Y N N N N N
6-6 N N Y Y Y N N N N N
5-5 Y Y Y Y Y Y Y Y Y Y
4-4 N Y Y Y Y Y N N N N
3-3 N N Y Y Y N N N N N
2-2 N N Y Y Y Y N N N N


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.

Lunar Poker @ Pechanga Casino

Posted in +EV, collusion, lunar poker by stephenhow on August 24, 2012

Well, someone is finally bringing the infamous Lunar Poker (aka Russian Poker) to the US, starting at my nearby Pechanga Casino. The game is a very interesting version of the old Caribbean Stud Poker, with a lot more options like drawing cards, buying an extra card, buying insurance, and forcing the dealer to draw (all for a price).

The game has been infamous, because the many player options result in an incalculable number of possible hand combinations (6.27x 10^20 according to the WoOs), and because of the absence of a published strategy. It sounds like people have played this game by the seat of their pants for years in Europe and Asia. But a lot of us won’t play a game without first knowing the basic strategy and house edge. So I grinded out the analysis, just in case you run across this game.


The rules follow the basic structure of Caribbean Stud Poker. You place an Ante before the hand starts, and the players and dealer each receive five cards. The dealer exposes one of his cards. You eventually decide to either Raise 2x, or fold your Ante. The dealer turns up his hand, and needs Ace-King or better to qualify. If the dealer doesn’t qualify, then the remaining Antes are paid even-money, and the Raise bets push. If the dealer qualifies, then the Antes push, and the Raise bets are paid according to a paytable.

So far, these rules are just like Caribbean Stud, except here, the Ante only pays when the dealer doesn’t qualify.

Now, Lunar Poker offers the following player options before the Player makes his 2x Raise decision:

  • The player may either receive an extra (6th) card, or may replace 2-5 of his cards, for the cost of 1x the Ante.
  • With three-of-a-kind or better, the player may take even-money insurance against the Dealer not qualifying (up to 1/2 the amount of the winning payout).

The players make their 2x Raise or Fold decision, then the dealer turns up his hand. If the dealer doesn’t qualify, the Antes and Insurance pay even money. If the dealer qualifies, then the player must beat the dealer to win his Raise bet and push his Ante. Else, the player loses his Ante and Raise. Insurance loses if the dealer qualifies and the player wins. If the dealer qualifies and the player loses, Insurance pushes. (Note: Pechanga lets you can take Insurance on up to the full amount your potential win.)

Finally, if the dealer doesn’t qualify, the player has an option to:

  • Pay 1x Ante to force the dealer to replace his highest card with a draw from the deck.

If the dealer qualifies after the draw, then the player’s Ante and Raise resolve as before. If the dealer doesn’t qualify, then the Ante and Raise push. Note: if you decide to Force the dealer to draw, then you forfeit the pay on the Ante you would normally receive. (It is expensive to Force the dealer; you forfeit your win on the Ante, AND you have to pay 1x!)


For winning hands against a qualified dealer hand, the Raise bet pays according to the following paytable. More importantly, you are paid on a second hand from the paytable, when the second hand uses at least one different card from your first payout hand. (Note: “hands” do not include kickers; e.g., a three-of-a-kind hand contains only 3 cards for purposes of the paytable.) I’m not going to provide examples of the second payout, as this is described elsewhere.

Hand Payout
Royal Flush 100-to-1
Straight Flush 50-to-1
Four-of-a-Kind 20-to-1
Full House 7-to-1
Flush 5-to-1
Straight 4-to-1
Three-of-a-Kind 3-to-1
Two Pairs 2-to-1
One Pair 1-to-1
AK 1-to-1

Basic Strategy

I worked out a simple strategy for the game that simulates at a 1.43% house edge. That’s not bad as far as carnival games go, but it looks like their claim of “House Advantage Under 1%!” is false.

Draw Decision

The first decision on what to hold and draw is presented in the table below.

Draw Decision for Lunar Poker
5-Card Hand Decision
Royal Flush
Straight Flush
Always buy 6th card.
Four-of-a-Kind Stand.
Full House Buy 6th card unless dealer upcard copies you.
Three-of-a-Kind Stand if 4-of-a-kind not possible,
else hold trips and exchange 2 cards.
Two Pairs Stand.
One Pair w/ AK Discard 2’s or 3’s (hold AK and exchange 3) against higher upcard, Queen or lower,
else stand.
One Pair Buy 6th card for open-ended, flush draw, or gutshot.
Hold pair and exchange 3 if pair below upcard,
else stand.
AK Buy 6th card for open-ended, flush draw, else
Buy 6th card for perfect gutshot to 6-card straight, else
Buy 6th card for gutshot straight draw against A or K upcard, else
Hold AKs and royal cards higher than dealer upcard, else
Hold AK and exchange 3
Nothing Buy 6th card for open-ended or flush draw, else
Buy 6th card for perfect gutshot to 6-card straight, else
Hold AKs and any Royal cards, else
Hold two or more Royal cards higher than the dealer upcard, else
Hold three straight flush cards higher than the dealer upcard, else
Hold A against K upcard or lower, else
Hold K against J upcard or lower, else
Hold Q against copied J upcard or lower, else
Hold Q against 5 upcard or lower,
Else fold.

where open-ended straight draws include double-gutshot straight draws.


It’s only correct to take insurance in a few cases. Never insure your hand against an Ace or King upcard. Otherwise, take insurance when you copy the dealer upcard 2 or more times. If you only copy the dealer upcard once, then take insurance when you also hold 2 or more Aces or Kings in your hand.

2x Raise / Fold

You should 2x Raise any pair or better. Fold any non-qualifying hand. Otherwise, play AK according to the table below.

2x Raise Decision
Hand Decision
Pair or better Raise 2x.
AK Call with any copies of the dealer upcard, Q or lower, else
Call with AKJ83 or better with any copies of the dealer upcard (including A, K), else
Fold all others.
non-qualifying Fold.

Force Dealer Bet

Your potential Raise payout and the possible dealer outs determine when you should try to force the dealer to draw. The table below tells you when to pay 1x to replace the highest dealer card with one from the deck. Remember, you’re forfeiting your instant Ante win by Forcing the dealer to draw. Plus, you’re paying 1x for the Force, so you need at least a 4:1 payout to make it profitable (i.e., don’t Force trips-only hands).

Force Draw Strategy
Potential Payout Conditions
or lower
Never force.
4-to-1 Don’t force dealer flush or open-ended draws that beat you unless all dealer pair outs are available, else
Don’t force if you hold 2 or more of the dealer’s pair outs,
else force.
5-to-1 Force unless you hold 4 or more of the dealer’s pair outs.
or higher
Always force.

Simple Two Player Collusion

If you’re friendly with your table-neighbor, you can slightly modify basic strategy to get a +EV return of +0.43% on the Ante. The drawing decision is modified accordingly:

Buy/Exchange Decision for Two Player Collusion
5-Card Hand Decision
Three-of-a-Kind Stand pat if your neighbor holds your quad out, else
hold trips and exchange 2 cards.
One Pair
w/o AK
Buy 6th card for open-ended or flush draw, else
Buy 6th card with over-pair (above dealer upcard) and gutshot if all straight outs remain, else
Buy 6th card with under-pair (below dealer upcard) and gutshot if any straight outs remain, else
Stand pat against dead upcard (3 copies) Q or lower, else
Hold under-pair (below dealer upcard) and draw 3 if all outs remain, else
Stand pat for all others.
AK Buy 6th card for open-ended or flush draw, else
Buy 6th card with 2+ outs to perfect gutshot (6-card straight), else
Buy 6th card with 3+ outs to gutshot against A/K upcard, else
Stand pat against dead upcard (3 copies), Q or lower, else
Hold two or more royal cards, exchange rest, else
Buy 6th card with at least 2 gutshot draws to AKQJT, else
Hold AK and exchange 3 cards.
Nothing Buy 6th card for open-ended or flush draw, else
Buy 6th card with 2+ outs to perfect gutshot (6-card straight), else
Stand pat against dead upcard (3 copies), Q or lower, else
Hold two or more royal cards, exchange rest, else
Hold your highest card, 9 or better, higher than the upcard and not copied by your neighbor, else
Hold 3 straight flush cards higher than the upcard, else
Fold all others.

Only take insurance when you and your neighbor hold 3 total copies of the upcard, Queen or lower. Never insure against an Ace or King upcard.

Finally, modify the 2x Raise decision:

  • Call any 2:1 pay or better, else
  • Fold pair deuces against uncopied upcard 3 thru Q, else
  • Call any other pair, else
  • Call any hand when you and your neighbor hold all 3 copies of the dealer upcard Queen or lower, else
  • Call AKJ83 or better when you and your neighbor hold any copies of the upcard, else
  • Call AK when you and your neighbor hold 2 copies of the dealer upcard Queen or lower, else
  • Fold all others.

Improved Six-Card Poker Collusion Strategy (+EV)

Posted in +EV, six card poker by stephenhow on August 11, 2012

I’ve been playing a lot of Six Card Poker at my local Viejas Casino, which gave me the chance to think about a better collusion strategy. When I first posted about this game, I was disappointed that the theoretical limit for collusion would yield only around +1.2% on the Ante bet. So I didn’t try too hard to make a good collusion strategy.

But it’s a pretty fun game, since the dealer shows half his hand, and with a full table, you’ll know 39 of the 52 cards. You can get the rules of the game from the WoOs.

After thinking it through, I boiled down the 6-way collusion strategy to the following three rules:

  • fold any hand already beat by dealer
  • fold any qualifying hand when there are 4 or more remaining single-card outs that beat you
  • fold any non-qualifying hand when a kicker out remains that beats you, or there are 3 or more remaining pair outs for the dealer

This collusion strategy simulates at +0.43%, which isn’t bad. It’s pretty easy to count remaining dealer outs among the confederates. People just have to chime-in on how many copies of the dealer cards they have. The strategy is extremely simple, and the variance is pretty low given the 1x call, and the help in folding -EV hands.