Rule Out

My latest video from the 2022 Table Game Protection and Table Games Conference is up. This one is by our very own SphinxOfCups. That said, let's try to be nice.


Direct: https://youtu.be/kaAyp3rMOmE

The question for the poll is would you play Rule Out!

This is a game that uses non-standard decks of cards. It's hard to form an opinion about how much fun this game is without an understanding of the rules and the various decks used in the game.

Is there any online statement of the Rule Out rules?

How many jokers in the deck?

And where can we find information on the composition of the "rules deck?" Is the "rules deck" reshuffled each time?

Also, there are 21 different optional side-bets. Holy Craps! Twenty of these side-bets were not explained in the video.

Quote: gordonm888

Also, there are 21 different optional side-bets. Holy Craps! Twenty of these side-bets were not explained in the video.
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Yes, that is my bad for not asking about them. Hopefully Sphinx will come along to answer all questions.

Hi there, that's me and my game! Very excited to be able to show it to all of you. I definitely learned a lot from this conference so some things have changed slightly, most specifically with the layout design and non-standard card faces.

Quote: gordonm888

This is a game that uses non-standard decks of cards. It's hard to form an opinion about how much fun this game is without an understanding of the rules and the various decks used in the game.

Is there any online statement of the Rule Out rules?

How many jokers in the deck?

And where can we find information on the composition of the "rules deck?" Is the "rules deck" reshuffled each time?
link to original post

It's definitely a unique game, and the non-standard cards can make it feel a bit daunting, but they are only handled by the dealer and are fully public-knowledge, with only 15 different cards, so I try to keep things as simple as possible. The game is really intended to target newer players who don't know a good Poker hand or Basic Strategy, so they still have to learn a new game, but the mechanics and the strategy are approachable and easily identifiable after a hand or two.

We do have a website at www.novelgamesstudios.com, which has the Rack Card, Rules of Play, and a playable demo. I can also give a brief statement here if needed, but to answer some of your direct questions:

The game is played with 2 Jokers per deck. We were playing with a 6-deck shoe at the conference, so we had 12 Jokers total in there. The Jokers are of course technically countable, but a combination of a high house edge on the side bet and a house rule limiting the side bet wager to not-more than the main bet help keep it from being beatable.

The Rule Deck's composition is listed on the table, what you mistook below as optional side bets. All 15 are displayed for the player to be able to make an informed decision about their trade. Although, once you have the strategy down, players don't really need to pay attention to the chart, making Rule Out! great to play with friends as it's easy to hold a conversation while playing.

Each Rule Deck contains exactly 15 cards, 1 of each, and is shuffled every hand. At the conference, we used a shoe of shuffled Rule Decks with cut cards between each deck, so after each hand, the remaining 12 cards of that deck get burned, and they all get discarded together to be shuffled later. However we've found that neither a shoe with cut cards or 1 deck shuffled every hand have a significant advantage when it comes to time between hands.

Quote: gordonm888

Also, there are 21 different optional side-bets. Holy Craps! Twenty of these side-bets were not explained in the video.
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I can see your confusion here, but as explained above there's only the one side bet, on the Joker. The chart on the table was designed to allow for relatively easy legibility so players could feel informed, while offering a wide play space for the players' cards (in the new layout design, not shown here). There's certainly a possibility for the rule squares to become side bets if the game becomes popular, but definitely prioritizing getting the core gameplay out there right now.

Quote: SphinxOfCups

I can see your confusion here, but as explained above there's only the one side bet, on the Joker. The chart on the table was designed to allow for relatively easy legibility so players could feel informed, while offering a wide play space for the players' cards (in the new layout design, not shown here). There's certainly a possibility for the rule squares to become side bets if the game becomes popular, but definitely prioritizing getting the core gameplay out there right now.
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Yes. Now it is coming back to me. I should have made it clear in the video about the unique "rule out" cards and how they were clearly indicated on the layout.

I don't like the rules. They aren't pre-determined. They come out at you from a blind deck of cards. I'd have a better chance at the Squid Game.

Quote: ChumpChange

I don't like the rules. They aren't pre-determined. They come out at you from a blind deck of cards. I'd have a better chance at the Squid Game.
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The cards in your hand aren't predetermined either, so that's an interesting through-line especially for a gambling game, but you're certainly welcome not to like it--no game is for everyone.

As I said in the video, following the optimal trading strategy (which is really easy to identify and doesn't require careful consideration of what all possible rules could come out, far from it), the house edge comes down to about 1-1.5%. No spoilers for Squid Game but it seems to me like that is designed to have a 99% house edge. Take your pick.

If you can tell red from black, you can play this game at the smallest possible edge.

Quote: ChumpChange

I don't like the rules. They aren't pre-determined. They come out at you from a blind deck of cards. I'd have a better chance at the Squid Game.
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The rules are quantified. I know the video didn't state the composition of the dealer deck, but Sphinx said it is disclosed at the table.

Quote: Wizard

...The rules are quantified...

Their site has a document ( https://www.novelgamesstudios.com/wp-content/uploads/2022/05/Rule-Out-Rules-of-Play.pdf ) with most of the details.

Is there any other game where winning a side bet means you lose the primary wager?.

Deck composition and number of decks? Number of jokers?

How do the highest, middle, and lowest work? I presume it is highest and lowest value including case where you have one card. What about middle? Middle position? Middlest value? How about when there are two cards?

Does trading actually benefit the player while jokers still exist in deck? The number of cards returned would be less than one by some amount when you have option to get a joker?

I do have some questions about unusual hands.

Your hand is 8c-8c-8d. The rules are lowest, red and diamonds. Is this 1 or 2 cards remaining? I.e., can the 8d be considered to be lowest?

With an originally-dealt hand of Joker-Joker-Joker and no Joker sidebet, this hand appears to pay 6-1 all the time. Correct? Without a joker sidebet, is an (original) Joker never eliminated by any rule?
**************************************
For a hand with three cards of the same rank and suit, such as 8c-8c-8c, I get an EV = 0.46812. Of course, such a hand will occur relatively rarely.

This hand pays 6 to 1 (for 3 cards remaining) with a frequency of 0.123076923, and pays 2-1 (2 cards remaining) with a frequency of 0.184615385. It pushes (with one remaining card) with a frequency of 0.052747253.

The Hi/Lo/Med is defined when there are Jokers present, essentially the Jokers sometimes take the hit.

Yes there are some games which allow you to bet when the exception will happen, sometimes though the main hand is a standoff. Examples are Freebet Blackjack (Dealer=22), Insurance at Trente et Quarante, EZ Pai Gow Poker etc.

(edit) The suits of cards do help determine the order, however only one is removed for a "Lo", "Med" or "Hi" rule.

When analyzing this game you can do both suit-folding and rank-folding.

Rank folding is possible, because certain ranks are interchangeable and interchanging them will not affect the EV of the hand as integrated over all possible combinations of rules.

The folded ranks may be defined as

Joker
Face (J, Q, K)
Ten
Odd medium (7, 9)
Even Medium (6, 8 )
Odd low (3, 5 )
Even Low (2, 4)
Aces

Easier to analyze with 8 folded ranks as opposed to 14 ranks!

Hoo boy, give me a sec here all!

Quote: itsmejeff

Is there any other game where winning a side bet means you lose the primary wager?.

Deck composition and number of decks? Number of jokers?

How do the highest, middle, and lowest work? I presume it is highest and lowest value including case where you have one card. What about middle? Middle position? Middlest value? How about when there are two cards?

Does trading actually benefit the player while jokers still exist in deck? The number of cards returned would be less than one by some amount when you have option to get a joker?
link to original post

Note that winning the side bet doesn't make you lose the main bet here, it just puts you at a disadvantaged. I do believe it is uncommon, perhaps even novel, but this was done to encourage the side bet, obviously with the expectation that smarter gamblers will avoid the side bet altogether anyway.

Poker decks are standard 52+2 jokers for each. Can be a single deck or shoe, here it's a 6-deck shoe, so containing 12 Jokers. The Rule Deck is 15 different cards, shuffled every hand, so each has the same odds of being dealt. This list can be found printed on the layout or online/on the rack card at https://www.novelgamesstudios.com/

Highest, Lowest, and Middle consider value, yes. So the Middle Rule eliminates the player's middle-value card, where Aces are low. Jokers don't count towards these, they're neither high or low, and a hand with one Joker doesn't have a middle-value card to get eliminated. In the event there are two cards of the same value but different suits, the suit hierarchy is lowest-to-highest Clubs, Diamonds, Hearts, Spades, and this is printed on the layout. In the case of two cards of identical suit and rank against a Highest, Lowest, or Middle rule, only and exactly once of those cards is eliminated, not both.

The potential to get a Joker in trade is certainly present, however GLI's findings seemed to indicate that it only substantially affects the decision to trade (and therefore house edge) in a single-deck game. In shoe games, the change to house edge is negligible.

Quote: gordonm888

I do have some questions about unusual hands.

Your hand is 8c-8c-8d. The rules are lowest, red and diamonds. Is this 1 or 2 cards remaining? I.e., can the 8d be considered to be lowest?

With an originally-dealt hand of Joker-Joker-Joker and no Joker sidebet, this hand appears to pay 6-1 all the time. Correct? Without a joker sidebet, is an (original) Joker never eliminated by any rule?
**************************************
For a hand with three cards of the same rank and suit, such as 8c-8c-8c, I get an EV = 0.46812. Of course, such a hand will occur relatively rarely.

This hand pays 6 to 1 (for 3 cards remaining) with a frequency of 0.123076923, and pays 2-1 (2 cards remaining) with a frequency of 0.184615385. It pushes (with one remaining card) with a frequency of 0.052747253.
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You bet. So as described above, the clubs are considered low for suit heirarchy, but in the case of two identical ranked-and-suited cards against Lowest, only one is eliminated. Note that Highest, Lowest, and Middle technically consider your whole hand, not just what hasn't yet been eliminated, which is why the dealer would typically use a peek mirror after dealing all three rules face-down, to flip those rules first--for convenience and clarity for player and dealer. So, with those three rules, Lowest eliminates one 8c,8d is eliminated by Red and Diamonds, so 1 card is left surviving.

Incorrect, Jokers are always eliminated for the main bet, whether or not you placed a side bet. 3 Jokers is a losing hand on the main bet. 3 Jokers in a shoe game would only pay 250:1 on a side bet wager.

Your math may be slightly off if you didn't take into account the Highest/Lowest/Middle's effect on identical cards, but yes the hypothetical best hand is three identical cards of any kind. All cards have the same number of Rules that could eliminate them (4) ignoring the Highest/Lowest/Middle, so any 3-of-a-kind is a very strong hand.

Quote: charliepatrick

The Hi/Lo/Med is defined when there are Jokers present, essentially the Jokers sometimes take the hit.

Yes there are some games which allow you to bet when the exception will happen, sometimes though the main hand is a standoff. Examples are Freebet Blackjack (Dealer=22), Insurance at Trente et Quarante, EZ Pai Gow Poker etc.

(edit) The suits of cards do help determine the order, however only one is removed for a "Lo", "Med" or "Hi" rule.
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Hi/Lo/Med rules do not consider any present Jokers, Jokers act basically as if they aren't in-hand at all for resolving Rule Cards.

Quote: gordonm888

When analyzing this game you can do both suit-folding and rank-folding.

Rank folding is possible, because certain ranks are interchangeable and interchanging them will not affect the EV of the hand as integrated over all possible combinations of rules.

The folded ranks may be defined as

Joker
Face (J, Q, K)
Ten
Odd medium (7, 9)
Even Medium (6, 8 )
Odd low (3, 5 )
Even Low (2, 4)
Aces

Easier to analyze with 8 folded ranks as opposed to 14 ranks!
link to original post

Not sure if you took this into account but remember Aces are odd as well as low!

Quote: itsmejeff

Is there any other game where winning a side bet means you lose the primary wager?
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Insurance in blackjack. Perhaps the most widespread and longest lasting side bet.

My first look at this is totally ignoring Jokers (hoping to add the logic later) and single deck. When looking at what might happen, with no jokers in hand, the details of Lo/Med/Hi doesn't matter, essentially one of them gets rid of the first card, one the second card, and one the third card. Together the average effect is to remove one of the cards with an equal probability. Similarly for two rules. All three rules together clearly get rid of all the cards. Thus logically I replaced them with First card/Second card/Third Card.

btw ignoring Jokers gives a player edge, so I imagine that's why they were added in.

EDIT: I had a small error in one of the rules, so without Jokers it seems there is a very small House Edge. The check that found it was that each card (except the Hi/Med/Lo rule) should have four rules that apply to them. You can see there are 28 different kinds of cards from the rule point of view, e.g. 5s and 3s are low odd (Black) Spades.

I do not think that the rules are intuitive in some places. I assumed the remaining cards in play would be evaluated for each action card, not the hand as a whole. in my mind, flipping a card over means it no longer exists. The rules consider the eliminated cards in some places.
i assumed ace was outside the rules for odd even as well. cause it is a letter and letters are not odd or even.
Why do suits need ranks? How does evaluation from left to right affect the odds?

Quote: unJon

Quote: itsmejeff

Is there any other game where winning a side bet means you lose the primary wager?
link to original post

Insurance in blackjack. Perhaps the most widespread and longest lasting side bet.
link to original post

maybe, though that is different wager from the game itself.

Quote: itsmejeff

I do not think that the rules are intuitive in some places. I assumed the remaining cards in play would be evaluated for each action card, not the hand as a whole. in my mind, flipping a card over means it no longer exists. The rules consider the remaining cards in some places.

i assumed ace was outside the rules for odd even as well. cause it is a letter and letters are not odd or even.
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Definitely understandable but these are tension areas that get resolved after the first time a player experiences them.

And, things have been made more intuitive to accommodate. For example, yes technically the Hi/Low/Mid rules consider the entire hand, but you're correct that's not intuitive, so instead those rules just always get revealed/resolved first of they're among the three. It's important the rules are clear on that, but on practice, there's never a situation that a player would have to guess or try to understand that relationship.

Also, newer versions of the rule deck have a corner indicator for the dealer to check with a peek mirror before flipping face-up.

And once you recognize Ace as low, it's not a far stretch to understand why it's also Odd--its just a One. People at the conference repeatedly finished my sentence when I would go to clarify that.

The concept of the game is not bad. Frequency seems like it would be pretty high, which players like. The payout schedule is not what players are looking for. Players want an opportunity to win 10, 20 100, 300 times their side/optional bet. Table Game Directors look for the side bet to increase hold by 2% or more. The base House Advantage is good, but I don't think the side bet edge is going to help get the hold up a few percent.

Have you thought about making it a 5 card game? You should be able to have much higher payouts for the side bet then.

Can you put 2 side bets on a table? Most non BJ table games have 2, many times 3 (including a progressive) side bets.

Do you have a progressive jackpot for it?

Most of the top games ever can be explained by the dealer to a player in 5 to 10 seconds for basic gameplay and 30 seconds for side bets and other details.. They cant understand or just stop listening past that. Do you have a 10 second pitch? You might need it to start of a sales presentation.


ZCore13

Quote: Zcore13

The concept of the game is not bad. Frequency seems like it would be pretty high, which players like. The payout schedule is not what players are looking for. Players want an opportunity to win 10, 20 100, 300 times their side/optional bet. Table Game Directors look for the side bet to increase hold by 2% or more. The base House Advantage is good, but I don't think the side bet edge is going to help get the hold up a few percent.

Have you thought about making it a 5 card game? You should be able to have much higher payouts for the side bet then.

Can you put 2 side bets on a table? Most non BJ table games have 2, many times 3 (including a progressive) side bets.

Do you have a progressive jackpot for it?

Most of the top games ever can be explained by the dealer to a player in 5 to 10 seconds for basic gameplay and 30 seconds for side bets and other details.. They cant understand or just stop listening past that. Do you have a 10 second pitch? You might need it to start of a sales presentation.


ZCore13
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Some good observations. The game definitely has lots of room to grow. The payout schedule may not be what every player is looking for, but the push frequency is comparable to Pai Gow, so there's some market for a faster-hand game that lets you stay at the table for longer.

I think the 3-card variation is the simplest and fastest, however I have every intent to explore 4-5 card variations down the line should the game see play. I wanted to prioritize pushing the game in its simplest form, fully aware that it is so different from any other, and on top requires a non-standard deck. This is also why there's only one side bet. Several games at the conference had several side bets and were getting regular comments regarding too many player decisions. If that's happening to Poker-style games, I want to avoid that for something so unusual at Rule Out!, until it becomes more familiar.

I don't currently have a progressive for it, been thinking quite hard on that and even other individuals at the convention that asked about it, after thinking on it a moment, determined it just may not be a game that can have a convenient progressive. The first thought that comes to everyone's mind is a progressive for Poker hands, but not only is that antithetical to the game's target audience, it also puts the progressive at odds with the main bet gameplay, creating a weird dissonance with player decision.

Obviously I do have a 10-15 second hook (I prefer this to pitch, I think it's more accurate to the intent) and a 30 second explanation, that's what I was using all at the conference and what is in the video. "The player is dealt three cards face-up, then three 'Rules' are randomly chosen to try and eliminate cards from the players hand. Players win and lose based on the number of cards surviving." The side bet takes even less time and can be done offhandedly. "The side bet pays out if you're dealt a Joker in your first three cards."

Duplicate post. Sorry!

Quote: Zcore13

Most of the top games ever can be explained by the dealer to a player in 5 to 10 seconds for basic gameplay and 30 seconds for side bets and other details.. They cant understand or just stop listening past that. Do you have a 10 second pitch? You might need it to start of a sales presentation.
link to original post

As I recall, I caught on pretty quickly at the show. It's a bit difficult to explain it in writing, but I think players would catch on quickly at the table.

Quote: Wizard

Quote: Zcore13

Most of the top games ever can be explained by the dealer to a player in 5 to 10 seconds for basic gameplay and 30 seconds for side bets and other details.. They cant understand or just stop listening past that. Do you have a 10 second pitch? You might need it to start of a sales presentation.
link to original post

As I recall, I caught on pretty quickly at the show. It's a bit difficult to explain it in writing, but I think players would catch on quickly at the table.
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That's true, one can even tell in the video that you're playing faster than I can explain the decisions!

The hardest thing to do when teaching people at the show was to get them to stop thinking in terms of Poker hands, which only a few people got a bit stumped with. For everyone else, I was able to reassure with "If you can tell Red from Black, you're already playing the game well."

Using 52 cards+Jokers, I'm getting different RTPs for single deck to those quoted. I'm hoping to look at the deck as 29 different cards (with multiple copies of some) and see whether this gets a different result.

Can some explain the difference between what "RTP" means (as normally it would mean using the optimum strategy) and the "Optimal RTP".
I can see a slight difference in strategy depending on whether there are Two Jokers or Not. e.g. As Ts 9c Stand -0.046154 Hit -0.038439 Hit2J -0.053825. (With As Ts 9-2c without Jokers you would play for odd/even as appropriate A9,T8,A7 etc.; but with Jokers you would stand). I've yet to fully check these EVs so there may be a bug in my code!

Quote: charliepatrick

Using 52 cards+Jokers, I'm getting different RTPs for single deck to those quoted. I'm hoping to look at the deck as 29 different cards (with multiple copies of some) and see whether this gets a different result.

Can some explain the difference between what "RTP" means (as normally it would mean using the optimum strategy) and the "Optimal RTP".

# of Decks  2 Surviving  3 Surviving  RTP      Optimal RTP
Single Deck    2            7         95.11%   99.08%
Four Decks     2            6         94.85%   98.45%
Six Decks      2            6         94.91%   98.55%

I can see a slight difference in strategy depending on whether there are Two Jokers or Not. e.g. As Ts 9c Stand -0.046154 Hit -0.038439 Hit2J -0.053825. (With As Ts 9-2c without Jokers you would play for odd/even as appropriate A9,T8,A7 etc.; but with Jokers you would stand). I've yet to fully check these EVs so there may be a bug in my code!
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Here RTP means without any strategy, so no trades at all, and Optimal RTP is with optimal strategy.

They very well may be a slightly better strategy one could use in a single-deck game--GLI's Optimal Strategy for the single deck differed from my independent mathematician's, as I mentioned earlier.

Thanks for the update, I now agree with both your figures for a single deck with two Jokers, I had a mistake with hands with two from "Hi", "Mid", "Lo" rules. RTP by standing on your intiial cards = 95.1122%; Optional RTP = 99.0768%.
Here's the list of hands you DO swap cards - note this assumes you can work out identical hands (e.g. the first line covers AsKsTh, AsQsTh, AsJs,Th, AsKsTd... but not AsKsTc; also AhKhTs etc.).
On some occasions it's worth swapping a card even though you have a Joker ("?x"), sometimes it doesn't matter, other times it does!
P: 3s Ah ?x a: -1.000000000 b: -0.414522732 c: -0.415513898 St: -0.428571429 (3s/?x) -0.414522732

Sorry for the big table, I'm sure it can be simplified, e.g. As Ts h draw to (As Ts); however it's late here now!

AAs KJs 10h	(As/Ks)
AAs KJs 97h	(As/Ks)
AAs KJs 86h	(As/Ks)
AAs KJs 53h	(As/Ks)
AAs KJs 42h	(As/Ks)
AAs KJs 86c	(As/Ks)
AAs KJs 42c	(As/Ks)
AAs 10s AAh	(As/Ts)
AAs 10s KJh	(As/Ts)
AAs 10s 10h	(As/Ts)
AAs 10s 97h	(As/Ts)
AAs 10s 86h	(As/Ts)
AAs 10s 53h	(As/Ts)
AAs 10s 42h	(As/Ts)
AAs 97s 10h	(As/9s)
AAs 97s 53h	(As/9s)
AAs 97s 42h	(As/9s)
AAs 97s 10c	(As/9s)
AAs 86s 10h	(As/8s)
AAs 97s 42c	(As/9s)
AAs 86s 53h	(As/8s)
AAs 86s 42h	(As/8s)
AAs 53s KJh	(As/5s)
AAs 53s 10h	(As/5s)
AAs 53s 97h	(As/5s)
AAs 53s 86h	(As/5s)
AAs 53s 42h	(As/5s)
AAs 53s 10c	(As/5s)
AAs 53s 86c	(As/5s)
AAs 42s 10h	(As/4s)
AAs 42s 53h	(As/4s)
AAs 42s 42h	(4s/4h)
AAs AAh 10h	(Ah/Th)
AAs AAh 86h	(Ah/8h)
AAs AAh 42h	(Ah/4h)
AAs AAh 10d	(As/Ah)
AAs AAh 86d	(As/Ah)
AAs AAh 42d	(As/Ah)
AAs AAh 10c	(As/Ah)
AAs AAh 86c	(As/Ah)
AAs KJh 10h	(Kh/Th)
AAs AAh 42c	(As/Ah)
AAs KJh 53h	(Kh/5h)
AAs KJh 42h	(Kh/4h)
AAs KJh KJd	(Kh/Kd)
AAs KJh 10d	(Kh/Td)
AAs KJh 97d	(Kh/9d)
AAs KJh 86d	(Kh/8d)
AAs KJh 53d	(Kh/5d)
AAs KJh 42d	(Kh/4d)
AAs KJh AAc	(As/Ac)
AAs KJh 10c	(As/Tc)
AAs KJh 97c	(As/9c)
AAs KJh 86c	(As/8c)
AAs KJh 53c	(As/5c)
AAs KJh 42c	(As/4c)
AAs KJh JKR	(As/?x)
AAs 10h 97h	(Th/9h)
AAs 10h 86h	(Th/8h)
AAs 10h 53h	(Th/5h)
AAs 10h 42h	(Th/4h)
AAs 10h AAd	(As/Ad)
AAs 10h KJd	(Th/Kd)
AAs 10h 10d	(Th/Td)
AAs 10h 97d	(Th/9d)
AAs 10h 86d	(Th/8d)
AAs 10h 53d	(Th/5d)
AAs 10h 42d	(Th/4d)
AAs 10h AAc	(As/Ac)
AAs 10h KJc	(As/Kc)
AAs 10h 10c	(Th/Tc)
AAs 10h 97c	(As/9c)
AAs 10h 86c	(As/8c)
AAs 10h 53c	(As/5c)
AAs 10h 42c	(As/4c)
AAs 97h 53h	(9h/5h)
AAs 97h 42h	(9h/4h)
AAs 10h JKR	(As/?x]
AAs 97h KJd	(9h/Kd)
AAs 97h 10d	(9h/Td)
AAs 97h 97d	(9h/9d)
AAs 97h 86d	(9h/8d)
AAs 97h 53d	(9h/5d)
AAs 97h 42d	(9h/4d)
AAs 97h AAc	(As/Ac)
AAs 97h KJc	(As/Kc)
AAs 97h 10c	(As/Tc)
AAs 97h 86c	(9h/8c)
AAs 97h 53c	(As/5c)
AAs 97h 42c	(As/4c)
AAs 86h 53h	(8h/5h)
AAs 86h 42h	(8h/4h)
AAs 97h JKR	(9h/?x)
AAs 86h AAd	(As/Ad)
AAs 86h KJd	(8h/Kd)
AAs 86h 10d	(8h/Td)
AAs 86h 97d	(8h/9d)
AAs 86h 86d	(8h/8d)
AAs 86h 53d	(8h/5d)
AAs 86h 42d	(8h/4d)
AAs 86h AAc	(As/Ac)
AAs 86h KJc	(As/Kc)
AAs 86h 10c	(As/Tc)
AAs 86h 97c	(As/9c)
AAs 86h 86c	(8h/8c)
AAs 86h 53c	(As/5c)
AAs 86h 42c	(8h/4c)
AAs 86h JKR	(8h/?x)
AAs 53h 53h	(5h/3h)
AAs 53h 42h	(5h/4h)
AAs 53h KJd	(5h/Kd)
AAs 53h 10d	(5h/Td)
AAs 53h 97d	(5h/9d)
AAs 53h 86d	(5h/8d)
AAs 53h 53d	(5h/5d)
AAs 53h 42d	(5h/4d)
AAs 53h AAc	(As/Ac)
AAs 53h KJc	(As/Kc)
AAs 53h 10c	(As/Tc)
AAs 53h 97c	(As/9c)
AAs 53h 86c	(As/8c)
AAs 53h 42c	(5h/4c)
AAs 42h 53h	(4h/3h)
AAs 42h 42h	(4h/2h)
AAs 53h JKR	(5h/?x)
AAs 42h AAd	(As/Ad)
AAs 42h KJd	(4h/Kd)
AAs 42h 10d	(4h/Td)
AAs 42h 97d	(4h/9d)
AAs 42h 86d	(4h/8d)
AAs 42h 53d	(4h/5d)
AAs 42h 42d	(4h/4d)
AAs 42h AAc	(As/Ac)
AAs 42h KJc	(As/Kc)
AAs 42h 10c	(As/Tc)
AAs 42h 97c	(As/9c)
AAs 42h 86c	(4h/8c)
AAs 42h 53c	(As/5c)
AAs 42h 42c	(4h/4c)
AAs 42h JKR	(4h/?x)
KJs KJs 10h	(Ks/Qs)
KJs KJs 53h	(Ks/Qs)
KJs KJs 42h	(Ks/Qs)
KJs 10s AAh	(Ks/Ts)
KJs 10s 97h	(Ks/Ts)
KJs 10s 86h	(Ks/Ts)
KJs 10s 53h	(Ks/Ts)
KJs 10s 42h	(Ks/Ts)
KJs 10s 97c	(Ks/Ts)
KJs 97s 10h	(Ks/9s)
KJs 10s 53c	(Ks/Ts)
KJs 97s 53h	(Ks/9s)
KJs 97s 42h	(Ks/9s)
KJs 86s 10h	(Ks/8s)
KJs 86s 53h	(Ks/8s)
KJs 86s 42h	(Ks/8s)
KJs 53s AAh	(Ks/5s)
KJs 53s KJh	(Ks/5s)
KJs 53s 10h	(Ks/5s)
KJs 53s 97h	(Ks/5s)
KJs 53s 86h	(Ks/5s)
KJs 53s 53h	(5s/5h)
KJs 53s 42h	(Ks/5s)
KJs 42s 10h	(Ks/4s)
KJs 42s 53h	(Ks/4s)
KJs 42s 42h	(4s/4h)
KJs AAh 10h	(Ah/Th)
KJs AAh 97h	(Ah/9h)
KJs AAh 86h	(Ah/8h)
KJs AAh 53h	(Ah/5h)
KJs AAh 42h	(Ah/4h)
KJs AAh AAd	(Ah/Ad)
KJs AAh 10d	(Ah/Td)
KJs AAh 97d	(Ah/9d)
KJs AAh 86d	(Ah/8d)
KJs AAh 53d	(Ah/5d)
KJs AAh 42d	(Ah/4d)
KJs AAh KJc	(Ks/Kc)
KJs AAh 10c	(Ks/Tc)
AAs 10c 86c	(Tc/8c)
AAs 10c 42c	(Tc/4c)
KJs KJh 53h	(Kh/5h)
KJs KJh 42h	(Kh/4h)
AAs 10c JKR	(As/?x]
KJs KJh 97d	(Ks/Kh)
KJs KJh 86d	(Ks/Kh)
KJs KJh 53d	(Ks/Kh)
KJs KJh 42d	(Ks/Kh)
AAs 86c 86c	(8c/6c)
AAs 86c 42c	(8c/4c)
AAs 86c JKR	(8c/?x)
KJs 10h 97h	(Th/9h)
KJs 10h 86h	(Th/8h)
KJs 10h 53h	(Th/5h)
KJs 10h 42h	(Th/4h)
KJs 10h AAd	(Th/Ad)
KJs 10h 10d	(Th/Td)
KJs 10h 97d	(Th/9d)
KJs 10h 86d	(Th/8d)
KJs 10h 53d	(Th/5d)
KJs 10h 42d	(Th/4d)
KJs 10h AAc	(Ks/Ac)
KJs 10h KJc	(Ks/Kc)
KJs 10h 97c	(Ks/9c)
KJs 10h 86c	(Ks/8c)
KJs 10h 53c	(Ks/5c)
KJs 10h 42c	(Ks/4c)
KJs 97h 53h	(9h/5h)
KJs 97h 42h	(9h/4h)
KJs 10h JKR	(Th/?x)
KJs 97h AAd	(9h/Ad)
KJs 97h KJd	(Ks/Kd)
KJs 97h 10d	(9h/Td)
KJs 97h 97d	(9h/9d)
KJs 97h 86d	(9h/8d)
KJs 97h 53d	(9h/5d)
KJs 97h 42d	(9h/4d)
KJs 97h AAc	(Ks/Ac)
KJs 97h KJc	(Ks/Kc)
KJs 97h 10c	(Ks/Tc)
KJs 97h 97c	(9h/9c)
KJs 97h 86c	(9h/8c)
KJs 86h 53h	(8h/5h)
KJs 86h 42h	(8h/4h)
KJs 86h AAd	(8h/Ad)
KJs 86h KJd	(Ks/Kd)
KJs 86h 10d	(8h/Td)
KJs 86h 97d	(8h/9d)
KJs 86h 86d	(8h/8d)
KJs 86h 53d	(8h/5d)
KJs 86h 42d	(8h/4d)
KJs 86h AAc	(Ks/Ac)
KJs 86h KJc	(Ks/Kc)
KJs 86h 10c	(Ks/Tc)
KJs 86h 97c	(8h/9c)
KJs 86h 86c	(8h/8c)
AAs 42c 42c	(4c/2c)
AAs 42c JKR	(4c/?x)
KJs 53h 53h	(5h/3h)
KJs 53h 42h	(5h/4h)
KJs 53h AAd	(5h/Ad)
KJs 53h KJd	(Ks/Kd)
KJs 53h 10d	(5h/Td)
KJs 53h 97d	(5h/9d)
KJs 53h 86d	(5h/8d)
KJs 53h 53d	(5h/5d)
KJs 53h 42d	(5h/4d)
KJs 53h AAc	(Ks/Ac)
KJs 53h KJc	(Ks/Kc)
KJs 53h 10c	(Ks/Tc)
KJs 53h 97c	(5h/9c)
KJs 53h 86c	(Ks/8c)
KJs 53h 53c	(5h/5c)
KJs 53h 42c	(5h/4c)
KJs 42h 53h	(4h/3h)
KJs 42h 42h	(4h/2h)
KJs 53h JKR	(5h/?x)
KJs 42h AAd	(4h/Ad)
KJs 42h KJd	(Ks/Kd)
KJs 42h 10d	(4h/Td)
KJs 42h 97d	(4h/9d)
KJs 42h 86d	(4h/8d)
KJs 42h 53d	(4h/5d)
KJs 42h 42d	(4h/4d)
KJs 42h AAc	(Ks/Ac)
KJs 42h KJc	(Ks/Kc)
KJs 42h 10c	(Ks/Tc)
KJs 42h 97c	(Ks/9c)
KJs 42h 86c	(4h/8c)
KJs 42h 53c	(4h/5c)
KJs 42h 42c	(4h/4c)
KJs 42h JKR	(4h/?x)
KJs 97c 97c	(9c/7c)
KJs 97c 86c	(9c/8c)
KJs 97c 53c	(9c/5c)
KJs 97c 42c	(9c/4c)
KJs 97c JKR	(9c/?x)
KJs 86c 97c	(8c/7c)
KJs 86c 86c	(8c/6c)
KJs 86c 53c	(8c/5c)
KJs 86c 42c	(8c/4c)
KJs 86c JKR	(8c/?x)
KJs 53c 53c	(5c/3c)
KJs 53c 42c	(5c/4c)
KJs 53c JKR	(5c/?x)
KJs 42c 53c	(4c/3c)
KJs 42c 42c	(4c/2c)
KJs 42c JKR	(4c/?x)
10s 97s AAh	(Ts/9s)
10s 97s KJh	(Ts/9s)
10s 97s 10h	(Ts/9s)
10s 97s 97h	(9s/9h)
10s 97s 86h	(Ts/9s)
10s 97s 53h	(Ts/9s)
10s 97s 42h	(Ts/9s)
10s 86s 53h	(Ts/8s)
10s 86s 42h	(Ts/8s)
10s 86s AAc	(Ts/8s)
10s 86s 53c	(Ts/8s)
10s 53s AAh	(Ts/5s)
10s 53s KJh	(Ts/5s)
10s 53s 10h	(Ts/5s)
10s 53s 97h	(Ts/5s)
10s 53s 86h	(Ts/5s)
10s 53s 53h	(5s/5h)
10s 53s 42h	(Ts/5s)
10s 42s 53h	(Ts/4s)
10s 42s AAc	(Ts/4s)
10s 42s 97c	(Ts/4s)
10s AAh KJh	(Ah/Kh)
10s AAh 10h	(Ah/Th)
10s AAh 97h	(Ah/9h)
10s AAh 86h	(Ah/8h)
10s AAh 53h	(Ah/5h)
10s AAh 42h	(Ah/4h)
10s AAh AAd	(Ah/Ad)
10s AAh KJd	(Ah/Kd)
10s AAh 10d	(Ts/Td)
10s AAh 97d	(Ah/9d)
10s AAh 86d	(Ah/8d)
10s AAh 53d	(Ah/5d)
10s AAh 42d	(Ah/4d)
10s AAh AAc	(Ah/Ac)
10s AAh KJc	(Ts/Kc)
10s AAh 10c	(Ts/Tc)
10s AAh 97c	(Ts/9c)
10s AAh 86c	(Ts/8c)
10s AAh 53c	(Ts/5c)
10s AAh 42c	(Ts/4c)
10s KJh 53h	(Kh/5h)
10s KJh 42h	(Kh/4h)
10s AAh JKR	(Ah/?x)
10s KJh AAd	(Kh/Ad)
10s KJh KJd	(Kh/Kd)
10s KJh 97d	(Kh/9d)
10s KJh 86d	(Kh/8d)
10s KJh 53d	(Kh/5d)
10s KJh 42d	(Kh/4d)
10s KJh AAc	(Ts/Ac)
10s KJh 10c	(Ts/Tc)
10s KJh 97c	(Ts/9c)
10s KJh 86c	(Ts/8c)
10s KJh 53c	(Ts/5c)
10s KJh 42c	(Ts/4c)
10s KJh JKR	(Ts/?x)
10s 10h 97h	(Th/9h)
10s 10h 53h	(Th/5h)
10s 10h AAd	(Ts/Th)
10s 10h 97d	(Ts/Th)
10s 10h 53d	(Ts/Th)
10s 10h AAc	(Ts/Th)
10s 10h 97c	(Ts/Th)
10s 10h 53c	(Ts/Th)
10s 97h 53h	(9h/5h)
10s 97h 42h	(9h/4h)
10s 97h AAd	(9h/Ad)
10s 97h KJd	(9h/Kd)
10s 97h 10d	(Ts/Td)
10s 97h 97d	(9h/9d)
10s 97h 86d	(9h/8d)
10s 97h 53d	(9h/5d)
10s 97h 42d	(9h/4d)
10s 97h AAc	(Ts/Ac)
10s 97h KJc	(Ts/Kc)
10s 97h 10c	(Ts/Tc)
10s 97h 97c	(9h/9c)
10s 97h 86c	(Ts/8c)
10s 97h 53c	(9h/5c)
10s 97h 42c	(Ts/4c)
10s 86h 53h	(8h/5h)
10s 86h 42h	(8h/4h)
10s 97h JKR	(9h/?x)
10s 86h AAd	(8h/Ad)
10s 86h KJd	(8h/Kd)
10s 86h 97d	(8h/9d)
10s 86h 86d	(8h/8d)
10s 86h 53d	(8h/5d)
10s 86h 42d	(8h/4d)
10s 86h AAc	(Ts/Ac)
10s 86h KJc	(Ts/Kc)
10s 86h 10c	(Ts/Tc)
10s 86h 97c	(8h/9c)
10s 86h 53c	(Ts/5c)
10s 86h 42c	(Ts/4c)
10s 86h JKR	(8h/?x)
10s 53h 53h	(5h/3h)
10s 53h 42h	(5h/4h)
10s 53h AAd	(5h/Ad)
10s 53h KJd	(5h/Kd)
10s 53h 10d	(Ts/Td)
10s 53h 97d	(5h/9d)
10s 53h 86d	(5h/8d)
10s 53h 53d	(5h/5d)
10s 53h 42d	(5h/4d)
10s 53h AAc	(Ts/Ac)
10s 53h KJc	(Ts/Kc)
10s 53h 10c	(Ts/Tc)
10s 53h 97c	(5h/9c)
10s 53h 86c	(Ts/8c)
10s 53h 53c	(5h/5c)
10s 53h 42c	(Ts/4c)
10s 42h 53h	(4h/3h)
10s 42h 42h	(4h/2h)
10s 53h JKR	(5h/?x)
10s 42h AAd	(4h/Ad)
10s 42h KJd	(4h/Kd)
10s 42h 97d	(4h/9d)
10s 42h 86d	(4h/8d)
10s 42h 53d	(4h/5d)
10s 42h 42d	(4h/4d)
10s 42h AAc	(Ts/Ac)
10s 42h KJc	(Ts/Kc)
10s 42h 10c	(Ts/Tc)
10s 42h 97c	(Ts/9c)
10s 42h 86c	(Ts/8c)
10s 42h 53c	(4h/5c)
10s 42h JKR	(4h/?x)
97s 97s AAh	(9s/7s)
97s 97s KJh	(9s/7s)
97s 97s 10h	(9s/7s)
97s 97s 86h	(9s/7s)
97s 97s 53h	(9s/7s)
97s 97s 42h	(9s/7s)
97s 86s 10h	(9s/8s)
97s 86s 53h	(9s/8s)
97s 86s 42h	(9s/8s)
97s 53s AAh	(9s/5s)
97s 53s KJh	(9s/5s)
97s 53s 10h	(9s/5s)
97s 53s 86h	(9s/5s)
97s 53s 42h	(9s/5s)
10s AAc 97c	(Ac/9c)
97s 42s 10h	(9s/4s)
10s AAc 53c	(Ac/5c)
97s 42s 53h	(9s/4s)
97s 42s 42h	(9s/4s)
10s AAc JKR	(Ac/?x)
97s AAh KJh	(Ah/Kh)
97s AAh 10h	(Ah/Th)
97s AAh 86h	(Ah/8h)
97s AAh 53h	(Ah/5h)
97s AAh 42h	(Ah/4h)
97s AAh AAd	(Ah/Ad)
97s AAh KJd	(Ah/Kd)
97s AAh 10d	(Ah/Td)
97s AAh 86d	(9s/8d)
97s AAh 53d	(Ah/5d)
97s AAh 42d	(Ah/4d)
97s AAh KJc	(9s/Kc)
97s AAh 10c	(9s/Tc)
97s KJh 10h	(Kh/Th)
97s KJh 53h	(Kh/5h)
97s KJh 42h	(Kh/4h)
97s KJh AAd	(Kh/Ad)
97s KJh KJd	(Kh/Kd)
97s KJh 10d	(Kh/Td)
97s KJh 97d	(9s/9d)
97s KJh 86d	(9s/8d)
97s KJh 53d	(9s/5d)
97s KJh 42d	(Kh/4d)
97s KJh AAc	(9s/Ac)
97s KJh KJc	(Kh/Kc)
97s KJh 10c	(9s/Tc)
10s 97c 97c	(9c/7c)
10s 97c 53c	(9c/5c)
10s 97c JKR	(9c/?x)
97s 10h 97h	(9s/9h)
97s 10h 86h	(Th/8h)
97s 10h 53h	(Th/5h)
97s 10h 42h	(Th/4h)
97s 10h AAd	(Th/Ad)
97s 10h KJd	(Th/Kd)
97s 10h 10d	(Th/Td)
97s 10h 97d	(9s/9d)
97s 10h 86d	(Th/8d)
97s 10h 53d	(9s/5d)
97s 10h 42d	(Th/4d)
97s 10h AAc	(9s/Ac)
97s 10h KJc	(9s/Kc)
97s 10h 10c	(Th/Tc)
97s 10h 97c	(9s/9c)
97s 10h 86c	(9s/8c)
97s 10h 53c	(9s/5c)
97s 10h 42c	(9s/4c)
97s 97h 42h	(9h/4h)
97s 10h JKR	(9s/?x)
97s 97h KJd	(9s/9h)
97s 97h 10d	(9s/9h)
97s 97h 42d	(9s/9h)
97s 97h KJc	(9s/9h)
97s 97h 10c	(9s/9h)
10s 53c 53c	(5c/3c)
97s 86h 53h	(8h/5h)
97s 86h 42h	(8h/4h)
10s 53c JKR	(5c/?x)
97s 86h AAd	(9s/8h)
97s 86h KJd	(9s/8h)
97s 86h 10d	(8h/Td)
97s 86h 86d	(8h/8d)
97s 86h 53d	(8h/5d)
97s 86h 42d	(8h/4d)
97s 86h AAc	(9s/Ac)
97s 86h KJc	(9s/8h)
97s 86h 10c	(9s/8h)
97s 86h 97c	(9s/9c)
97s 53h 53h	(5h/3h)
97s 53h 42h	(5h/4h)
97s 53h AAd	(5h/Ad)
97s 53h KJd	(9s/5h)
97s 53h 10d	(9s/5h)
97s 53h 86d	(5h/8d)
97s 53h 53d	(5h/5d)
97s 53h 42d	(5h/4d)
97s 53h AAc	(9s/Ac)
97s 53h KJc	(9s/5h)
97s 53h 10c	(9s/5h)
97s 53h 97c	(9s/9c)
97s 53h 86c	(9s/8c)
97s 53h 42c	(9s/4c)
97s 42h 53h	(4h/3h)
97s 42h 42h	(4h/2h)
97s 53h JKR	(9s/?x]
97s 42h AAd	(4h/Ad)
97s 42h KJd	(4h/Kd)
97s 42h 10d	(4h/Td)
97s 42h 97d	(9s/9d)
97s 42h 86d	(4h/8d)
97s 42h 53d	(4h/5d)
97s 42h 42d	(4h/4d)
97s 42h AAc	(9s/Ac)
97s 42h KJc	(9s/Kc)
97s 42h 10c	(9s/Tc)
97s 42h 97c	(9s/9c)
97s 42h 86c	(9s/8c)
97s 42h 53c	(9s/5c)
97s 42h 42c	(4h/4c)
97s 42h JKR	(9s/?x]
86s 97s AAh	(8s/7s)
86s 97s KJh	(8s/7s)
86s 97s 10h	(8s/7s)
86s 97s 53h	(8s/7s)
86s 97s 42h	(8s/7s)
86s 86s 10h	(8s/6s)
86s 86s 53h	(8s/6s)
86s 86s 42h	(8s/6s)
86s 53s AAh	(8s/5s)
86s 53s KJh	(8s/5s)
86s 53s 10h	(8s/5s)
86s 53s 97h	(8s/5s)
86s 53s 86h	(8s/5s)
86s 53s 53h	(8s/5s)
86s 53s 42h	(8s/5s)
86s 42s 10h	(8s/4s)
86s 42s 53h	(8s/4s)
86s 42s AAc	(8s/4s)
97s KJc KJc	(Kc/Qc)
97s KJc 10c	(Kc/Tc)
97s KJc 42c	(Kc/4c)
97s KJc JKR	(9s/?x)
86s AAh KJh	(Ah/Kh)
86s AAh 10h	(Ah/Th)
86s AAh 97h	(Ah/9h)
86s AAh 86h	(8s/8h)
86s AAh 53h	(Ah/5h)
86s AAh 42h	(Ah/4h)
86s AAh AAd	(Ah/Ad)
86s AAh KJd	(Ah/Kd)
86s AAh 10d	(Ah/Td)
86s AAh 97d	(Ah/9d)
86s AAh 86d	(8s/8d)
86s AAh 53d	(Ah/5d)
86s AAh 42d	(8s/4d)
86s AAh AAc	(Ah/Ac)
86s AAh KJc	(8s/Kc)
86s AAh 10c	(8s/Tc)
86s KJh 10h	(Kh/Th)
97s 10c 42c	(Tc/4c)
86s KJh 53h	(Kh/5h)
86s KJh 42h	(Kh/4h)
97s 10c JKR	(9s/?x)
86s KJh AAd	(Kh/Ad)
86s KJh KJd	(Kh/Kd)
86s KJh 10d	(Kh/Td)
86s KJh 97d	(8s/9d)
86s KJh 86d	(8s/8d)
86s KJh 53d	(Kh/5d)
86s KJh 42d	(8s/4d)
86s KJh AAc	(8s/Ac)
86s KJh KJc	(Kh/Kc)
86s KJh 10c	(8s/Tc)
86s 10h 97h	(Th/9h)
86s 10h 53h	(Th/5h)
86s 10h 42h	(Th/4h)
86s 10h AAd	(Th/Ad)
86s 10h KJd	(Th/Kd)
86s 10h 10d	(Th/Td)
86s 10h 97d	(8s/9d)
86s 10h 53d	(Th/5d)
86s 10h 42d	(Th/4d)
86s 10h AAc	(8s/Ac)
86s 10h KJc	(8s/Kc)
86s 10h 97c	(8s/9c)
86s 10h 86c	(8s/8c)
86s 10h 53c	(8s/5c)
86s 10h 42c	(8s/4c)
86s 97h 53h	(9h/5h)
86s 97h 42h	(9h/4h)
86s 10h JKR	(8s/?x)
86s 97h AAd	(9h/Ad)
86s 97h KJd	(8s/9h)
86s 97h 10d	(8s/9h)
86s 97h 97d	(9h/9d)
86s 97h 53d	(9h/5d)
86s 97h 42d	(9h/4d)
86s 97h AAc	(8s/9h)
86s 97h KJc	(8s/9h)
86s 97h 10c	(8s/Tc)
86s 97h 86c	(8s/8c)
86s 86h 53h	(8h/5h)
86s 86h AAd	(8s/8h)
86s 86h KJd	(8s/8h)
86s 86h 53d	(8s/8h)
86s 86h AAc	(8s/8h)
86s 86h KJc	(8s/8h)
97s 42c 42c	(4c/2c)
97s 42c JKR	(4c/?x)
86s 53h 53h	(5h/3h)
86s 53h 42h	(5h/4h)
86s 53h AAd	(5h/Ad)
86s 53h KJd	(5h/Kd)
86s 53h 10d	(5h/Td)
86s 53h 97d	(5h/9d)
86s 53h 86d	(8s/8d)
86s 53h 53d	(5h/5d)
86s 53h 42d	(5h/4d)
86s 53h AAc	(8s/Ac)
86s 53h KJc	(8s/Kc)
86s 53h 10c	(8s/Tc)
86s 53h 97c	(8s/9c)
86s 53h 86c	(8s/8c)
86s 53h 53c	(5h/5c)
86s 53h 42c	(8s/4c)
86s 42h 53h	(4h/3h)
86s 42h 42h	(4h/2h)
86s 53h JKR	(8s/?x]
86s 42h AAd	(8s/4h)
86s 42h KJd	(8s/4h)
86s 42h 10d	(4h/Td)
86s 42h 97d	(4h/9d)
86s 42h 53d	(4h/5d)
86s 42h 42d	(4h/4d)
86s 42h AAc	(8s/4h)
86s 42h KJc	(8s/4h)
86s 42h 10c	(8s/Tc)
86s 42h 97c	(8s/9c)
86s 42h 86c	(8s/8c)
86s 42h 53c	(8s/5c)
86s 42h JKR	(8s/?x]
86s AAc KJc	(Ac/Kc)
86s AAc 53c	(Ac/5c)
86s AAc JKR	(8s/?x)
86s KJc KJc	(Kc/Qc)
86s KJc 53c	(Kc/5c)
86s KJc JKR	(8s/?x)
86s 53c 53c	(5c/3c)
86s 53c JKR	(5c/?x)
53s 53s AAh	(5s/3s)
53s 53s KJh	(5s/3s)
53s 53s 10h	(5s/3s)
53s 53s 97h	(5s/3s)
53s 53s 86h	(5s/3s)
53s 53s 42h	(5s/3s)
53s 42s AAh	(5s/4s)
53s 42s KJh	(5s/4s)
53s 53s 86c	(5s/3s)
53s 42s 10h	(5s/4s)
53s 42s 97h	(5s/4s)
53s 42s 86h	(5s/4s)
53s 42s KJc	(5s/4s)
53s AAh KJh	(Ah/Kh)
53s AAh 10h	(Ah/Th)
53s AAh 97h	(Ah/9h)
53s AAh 86h	(Ah/8h)
53s AAh 42h	(Ah/4h)
53s AAh AAd	(Ah/Ad)
53s AAh KJd	(Ah/Kd)
53s AAh 10d	(Ah/Td)
53s AAh 97d	(Ah/9d)
53s AAh 86d	(Ah/8d)
53s AAh 42d	(5s/4d)
53s AAh KJc	(5s/Kc)
53s AAh 10c	(5s/Tc)
53s AAh 97c	(5s/9c)
53s AAh 86c	(5s/8c)
53s KJh 10h	(Kh/Th)
53s AAh 53c	(5s/5c)
53s AAh 42c	(5s/4c)
53s KJh 53h	(5s/5h)
53s KJh 42h	(Kh/4h)
53s AAh JKR	(5s/?x)
53s KJh AAd	(Kh/Ad)
53s KJh KJd	(Kh/Kd)
53s KJh 10d	(Kh/Td)
53s KJh 97d	(5s/9d)
53s KJh 86d	(Kh/8d)
53s KJh 53d	(5s/5d)
53s KJh 42d	(5s/4d)
53s KJh AAc	(5s/Ac)
53s KJh KJc	(Kh/Kc)
53s KJh 10c	(5s/Tc)
53s KJh 97c	(5s/9c)
53s KJh 86c	(5s/8c)
53s KJh 53c	(5s/5c)
53s KJh 42c	(5s/4c)
53s KJh JKR	(5s/?x)
53s 10h 97h	(Th/9h)
53s 10h 86h	(Th/8h)
53s 10h 53h	(5s/5h)
53s 10h 42h	(Th/4h)
53s 10h AAd	(Th/Ad)
53s 10h KJd	(Th/Kd)
53s 10h 10d	(Th/Td)
53s 10h 97d	(5s/9d)
53s 10h 86d	(Th/8d)
53s 10h 53d	(5s/5d)
53s 10h 42d	(Th/4d)
53s 10h AAc	(5s/Ac)
53s 10h KJc	(5s/Kc)
53s 10h 10c	(Th/Tc)
53s 10h 97c	(5s/9c)
53s 10h 86c	(5s/8c)
53s 10h 53c	(5s/5c)
53s 10h 42c	(5s/4c)
53s 97h 42h	(9h/4h)
53s 10h JKR	(5s/?x)
53s 97h AAd	(9h/Ad)
53s 97h KJd	(5s/9h)
53s 97h 10d	(5s/9h)
53s 97h 97d	(9h/9d)
53s 97h 86d	(9h/8d)
53s 97h 42d	(9h/4d)
53s 97h AAc	(5s/Ac)
53s 97h KJc	(5s/9h)
53s 97h 10c	(5s/9h)
53s 97h 86c	(5s/8c)
53s 97h 53c	(5s/5c)
53s 97h 42c	(5s/4c)
53s 86h 53h	(8h/5h)
53s 86h 42h	(8h/4h)
53s 97h JKR	(5s/?x)
53s 86h AAd	(8h/Ad)
53s 86h KJd	(8h/Kd)
53s 86h 10d	(8h/Td)
53s 86h 97d	(8h/9d)
53s 86h 86d	(8h/8d)
53s 86h 53d	(5s/5d)
53s 86h 42d	(8h/4d)
53s 86h AAc	(5s/Ac)
53s 86h KJc	(5s/Kc)
53s 86h 10c	(5s/Tc)
53s 86h 97c	(5s/9c)
53s 86h 86c	(8h/8c)
53s 86h 53c	(5s/5c)
53s 86h 42c	(5s/4c)
53s 86h JKR	(5s/?x)
53s 53h KJd	(5s/5h)
53s 53h 10d	(5s/5h)
53s 53h 86d	(5s/5h)
53s 53h KJc	(5s/5h)
53s 53h 10c	(5s/5h)
53s 53h 86c	(5s/5h)
53s 42h 42h	(4h/2h)
53s 42h AAd	(5s/4h)
53s 42h KJd	(5s/4h)
53s 42h 10d	(4h/Td)
53s 42h 97d	(4h/9d)
53s 42h 86d	(4h/8d)
53s 42h 42d	(4h/4d)
53s 42h AAc	(5s/Ac)
53s 42h KJc	(5s/4h)
53s 42h 10c	(5s/4h)
53s 42h 97c	(5s/9c)
53s 42h 86c	(5s/8c)
53s 42h 53c	(5s/5c)
53s 42h JKR	(5s/?x)
42s 53s AAh	(4s/3s)
42s 53s KJh	(4s/3s)
42s 53s 10h	(4s/3s)
42s 53s 97h	(4s/3s)
42s 53s 86h	(4s/3s)
42s 42s 10h	(4s/2s)
42s 42s 53h	(4s/2s)
42s 42s AAc	(4s/2s)
53s KJc KJc	(Kc/Qc)
53s KJc 10c	(Kc/Tc)
53s KJc 86c	(Kc/8c)
53s KJc JKR	(5s/?x)
42s AAh KJh	(Ah/Kh)
42s AAh 10h	(Ah/Th)
42s AAh 97h	(Ah/9h)
42s AAh 86h	(Ah/8h)
42s AAh 53h	(Ah/5h)
42s AAh 42h	(4s/4h)
42s AAh AAd	(Ah/Ad)
42s AAh KJd	(Ah/Kd)
42s AAh 10d	(Ah/Td)
42s AAh 97d	(Ah/9d)
42s AAh 86d	(4s/8d)
42s AAh 53d	(Ah/5d)
42s AAh 42d	(4s/4d)
42s AAh AAc	(Ah/Ac)
42s AAh KJc	(4s/Kc)
42s AAh 10c	(4s/Tc)
53s 10c 86c	(Tc/8c)
42s KJh 10h	(Kh/Th)
42s KJh 53h	(Kh/5h)
42s KJh 42h	(4s/4h)
53s 10c JKR	(5s/?x)
42s KJh AAd	(Kh/Ad)
42s KJh KJd	(Kh/Kd)
42s KJh 10d	(Kh/Td)
42s KJh 97d	(Kh/9d)
42s KJh 86d	(4s/8d)
42s KJh 53d	(4s/5d)
42s KJh 42d	(4s/4d)
42s KJh AAc	(4s/Ac)
42s KJh KJc	(Kh/Kc)
42s KJh 10c	(4s/Tc)
53s 86c 86c	(8c/6c)
53s 86c JKR	(5s/?x)
42s 10h 97h	(Th/9h)
42s 10h 86h	(Th/8h)
42s 10h 53h	(Th/5h)
42s 10h AAd	(Th/Ad)
42s 10h KJd	(Th/Kd)
42s 10h 10d	(Th/Td)
42s 10h 97d	(Th/9d)
42s 10h 86d	(Th/8d)
42s 10h 53d	(4s/5d)
42s 10h AAc	(4s/Ac)
42s 10h KJc	(4s/Kc)
42s 10h 97c	(4s/9c)
42s 10h 86c	(4s/8c)
42s 10h 53c	(4s/5c)
42s 10h 42c	(4s/4c)
42s 97h 53h	(9h/5h)
42s 97h 42h	(9h/4h)
42s 10h JKR	(4s/?x)
42s 97h AAd	(9h/Ad)
42s 97h KJd	(9h/Kd)
42s 97h 10d	(9h/Td)
42s 97h 97d	(9h/9d)
42s 97h 86d	(9h/8d)
42s 97h 53d	(9h/5d)
42s 97h 42d	(4s/4d)
42s 97h AAc	(4s/Ac)
42s 97h KJc	(4s/Kc)
42s 97h 10c	(4s/Tc)
42s 97h 97c	(9h/9c)
42s 97h 86c	(4s/8c)
42s 86h 53h	(8h/5h)
42s 86h AAd	(4s/8h)
42s 86h KJd	(4s/8h)
42s 86h 10d	(8h/Td)
42s 86h 97d	(8h/9d)
42s 86h 86d	(8h/8d)
42s 86h 53d	(8h/5d)
42s 86h AAc	(4s/8h)
42s 86h KJc	(4s/8h)
42s 86h 10c	(4s/Tc)
42s 86h 97c	(4s/9c)
42s 53h 53h	(5h/3h)
42s 53h AAd	(5h/Ad)
42s 53h KJd	(4s/5h)
42s 53h 10d	(4s/5h)
42s 53h 97d	(5h/9d)
42s 53h 86d	(5h/8d)
42s 53h 53d	(5h/5d)
42s 53h AAc	(4s/5h)
42s 53h KJc	(4s/5h)
42s 53h 10c	(4s/Tc)
42s 53h 97c	(4s/9c)
42s 53h 86c	(4s/8c)
42s 53h 42c	(4s/4c)
42s 53h JKR	(4s/?x]
42s 42h AAd	(4s/4h)
42s 42h KJd	(4s/4h)
42s 42h 97d	(4s/4h)
42s 42h AAc	(4s/4h)
42s 42h KJc	(4s/4h)
42s 42h 97c	(4s/4h)
42s AAc KJc	(Ac/Kc)
42s AAc 97c	(Ac/9c)
42s AAc JKR	(4s/?x)
42s KJc KJc	(Kc/Qc)
42s KJc 97c	(Kc/9c)
42s KJc JKR	(4s/?x)
42s 97c 97c	(9c/7c)
42s 97c JKR	(4s/?x]

Quote: charliepatrick

Thanks for the update, I now agree with both your figures for a single deck with two Jokers, I had a mistake with hands with two from "Hi", "Mid", "Lo" rules. RTP by standing on your intiial cards = 95.1122%; Optional RTP = 99.0768%.
Here's the list of hands you DO swap cards - note this assumes you can work out identical hands (e.g. the first line covers AsKsTh, AsQsTh, AsJs,Th, AsKsTd... but not AsKsTc; also AhKhTs etc.).
On some occasions it's worth swapping a card even though you have a Joker ("?x"), sometimes it doesn't matter, other times it does!
P: 3s Ah ?x a: -1.000000000 b: -0.414522732 c: -0.415513898 St: -0.428571429 (3s/?x) -0.414522732

Sorry for the big table, I'm sure it can be simplified, e.g. As Ts h draw to (As Ts); however it's late here now!

AAs KJs 10h	(As/Ks)
AAs KJs 97h	(As/Ks)
AAs KJs 86h	(As/Ks)

link to original post

I stared at this for awhile before I realized you were using the rank folding strategy I mentioned. So the first column has three folded "cards" entered, where the double entries in the cards are fungible alternatives, and the third folded card category is the identity of the drawn card? And the second column is the effective/representative two card hand after the draw decision has been made.

So, what you are showing is optimal strategy for the draw as a function of the first two cards. Correct?
Edit: and JKR = joker and not Jack -King.

Hey Charlie, what are payout frequencies for one of the cases, say 6 deck? In other words how frequent are the payouts:

Quote: gordonm888

Hey Charlie, what are payout frequencies for one of the cases, say 6 deck? In other words how frequent are the payouts:

6 or 7

2

0

-1

link to original post

I can answer this. Here's the hit frequencies for each outcome represented by number of surviving cards in a 6-deck game.

3 Surviving: 1.62%

2 Surviving: 16.00%

1 Surviving: 39.76%

0 Surviving: 43.62%

As you can see less than half of hands are losing hands, and the push frequency is comparable to Pai Gow.

Quote: gordonm888

Quote: charliepatrick

...

AAs KJs 10h	(As/Ks)
AAs KJs 97h	(As/Ks)
AAs KJs 86h	(As/Ks)

...

I stared at this for awhile before I realized you were using the rank folding strategy I mentioned. So the first column has three folded "cards" entered, where the double entries in the cards are fungible alternatives, and the third folded card category is the identity of the drawn card? And the second column is the effective/representative two card hand after the draw decision has been made.

So, what you are showing is optimal strategy for the draw as a function of the first two cards. Correct?
Edit: and JKR = joker and not Jack -King.
link to original post

No the hands are listed by their original three cards and show those where you keep two and swap one. In the example you cite if you had As Ks Th then you would hold AsKs and swap the Th. Similarly for AsKs 9-6h. Due to folding the same logic applies to AsQsTh and AsJsTh. Yes JKR combines "JK" and "R" for Joker.

There are probably many more simplifications e.g. I list As 3h xx which is the same as 3s Ah xx. So I don't need any hands where the Heart is higher rank than the Spade. The problem with this approach is someone needs to realise their 3s 2s Ah is the same as As 3c 2c. Perhaps I need to create a list of logically unique hands!

The game needs more. You only get one shot to pitch it and on the rare chance you get an install, a few months for it to do well.

It needs higher payouts.

The 3 cards should be dealt to the player to allow them to hold the cards, look at them and choose a discard before placing their cards in the play box to play. Players like to hold and reveal their own cards.

It would be nice to have a community feature. Either an "Envy" style bonus where everyone wins when one person wins or a community pot where highest player hand wins the community side bet. Maybe even a 0 house edge, but require the other side bet to play it.

Keep making it better.


ZCore13

Quote: Zcore13

The game needs more. You only get one shot to pitch it and on the rare chance you get an install, a few months for it to do well.

It needs higher payouts.

The 3 cards should be dealt to the player to allow them to hold the cards, look at them and choose a discard before placing their cards in the play box to play. Players like to hold and reveal their own cards.

It would be nice to have a community feature. Either an "Envy" style bonus where everyone wins when one person wins or a community pot where highest player hand wins the community side bet. Maybe even a 0 house edge, but require the other side bet to play it.

Keep making it better.


ZCore13
link to original post

Appreciate the input.

Right now I am intentionally avoiding feature bloat. The game is already an uphill battle due to the new gameplay mechanics, I don't need to make it harder to pitch and to learn for players or dealers by adding more until the base gameplay is sound. I've got a good backlog of ideas for additions, including additional individual and community side bets, but I got the very strong impression from those I spoke to at the show that much more added right now would be a detriment to an already fun, but unfamiliar game.

I also can't think of any non-poker shoe game where players hold their cards, nor can I think of a reason why casinos would be willing to allow holding cards with this game. The main bet isn't countable, but the side bet is; marked cards make it beatable. This, in addition to preventing false reporting of eliminated cards (even though the player mistakenly eliminating the wrong card from their hand can pretty much only be to their detriment) are why the dealer is expected to see and eliminate all players' cards.

Definitely will continue to improve, but there is intent behind the decisions made thus far, and marketability plays a big role in that.

I understand your thought process and intent. Much of it inexperienced I would guess. My thoughts and suggestions come from 16 years of experience, being a former Table Games Director, trialing a dozen new games including past winners of the Table Games competition, being a panelist at two National gaming conventions on Table Games, consulting on multiple new games and discovering High Card Flush while it had one Table being trialed in Laughlin and urging Galaxy Gaming to buy it quick (which they did).

As to one of your comments, of course a casino and/or regulatory would allow touching of the cards. I had a 6 deck shoe poker games for many years (Texas Shootout) where players touch and discarded cards. It adds to the enjoyment of the game.


ZCore13

Quote: Zcore13

I understand your thought process and intent. Much of it inexperienced I would guess. My thoughts and suggestions come from 16 years of experience, being a former Table Games Director, trialing a dozen new games including past winners of the Table Games competition, being a panelist at two National gaming conventions on Table Games, consulting on multiple new games and discovering High Card Flush while it had one Table being trialed in Laughlin and urging Galaxy Gaming to buy it quick (which they did).

As to one of your comments, of course a casino and/or regulatory would allow touching of the cards. I had a 6 deck shoe poker games for many years (Texas Shootout) where players touch and discarded cards. It adds to the enjoyment of the game.


ZCore13
link to original post

As I said, non-poker shoe game.

Not discounting your experience and as I said, appreciate the input. Certainly a long way for the game to go but I have to be conscious of the impact my decisions will have on marketability in both directions. Adding a new side bet means nothing to the games ability to stand up to scrutiny if it's only there to meet a quota and doesn't improve the gameplay. Not saying your very broad suggestions don't, but it warrants more thought than one person's opinion, experienced or no. Research and math have to follow.