Knockout 52

On May 17, Knockout 52 will begin a field trial at the Strat. Here is how I briefly introduce the game at WoO.

Knockout 52 is a unique card game that will premier at the Strat casino in Las Vegas on May 17, 2024. There is no other game it can be easily compared to. Briefly, there is a layout on the table with the 13 ranks in a deck. The dealer will deal one card at a time to each position on the layout. Play stops when a card from the deck matches the rank on the next spot on the layout. If the player goes 13, 26, or 39 cards without a match, then he starts over at the first position. The object is to correctly predict how long it will take for a match to be formed or no match at all.

This game won the best new table game award at the 2024 Global Table Games and Game Protection Conference. I made a video of the game at the show, which should be up before the big launch.

For all the rules and analysis, please see my new page at WoO on Knockout 52. I welcome all comments and questions.

The question for the poll is would you play Knockout 52?

when are we going to see YOUR game? and is this a very low house edge or am i just not good at reading your tables?

Quote: heatmap

when are we going to see YOUR game? and is this a very low house edge or am i just not good at reading your tables?
link to original post

Which is my game? Lowest house edge of 3.54% doesn't seem so low to me.

I thought the edge was lower on the round 1 bet at the show (somewhere between 2-3%), but my guess is that was with an 8 deck shoe not a single deck. I am curious if that is why the Strat is using a 1 deck version w/ shuffler.

You may remember the Wiz shared a video from last year for Match 52:
https://youtu.be/BrrQjMYewdg?si=9xJ5F5-XONR4RJlP

Similar concept and from the same inventor, but Knockout 52 is far simpler.

Easier to explain, easier to play and easier to deal.

When I first saw Match 52 I thought there was no way that would see the light of day in a casino.

When I saw Knockout 52 in March at the gaming conference, I knew it was a winner!

——

Hey Wiz! Where’s the poll choice reminder of the next eclipse? 🤪

Quote: Wizard

On May 17, Knockout 52 will begin a field trial at the Strat.
link to original post

If you can’t wait until then, and you’re in the area, it’s launching on 5/3 at Firekeepers in Battle Creek MI.

Quote: Wizard

Quote: heatmap

when are we going to see YOUR game? and is this a very low house edge or am i just not good at reading your tables?
link to original post

Which is my game? Lowest house edge of 3.54% doesn't seem so low to me.
link to original post

a game you invent

Is it hand shuffled?

Why is the probability for a round 1 knockout not just 1-(12/13)^13
I ran the simulation and it shows that your result is correct. I must be getting worse at math...

Quote: Codingforest

Why is the probability for a round 1 knockout not just 1-(12/13)^13
I ran the simulation and it shows that your result is correct. I must be getting worse at math...
link to original post

Let's look at the case of no match is the first two cards.

The exact probability is 1-(11/13)*(47/51) - (1/13)*(48/51) = 0.147813

Your approximation would give 1-(12/13)^2 = 0.147929

My simple explanation is if the first card was not an ace, then the remaining cards are ace rich for the second card. That makes it less likely a 2 is the second card.

Much for the same reason the first two cards dealt from a deck are more likely to be opposite in color than the same.

I thought of a game which in deals was similar in that there was a possibility the entire deck could be dealt before a game concluded.

I haven't pursued this game because I figured no casino would want to have a game that takes so long to conclude. They always want quick deal games.

How long on average does this game take for a single deal and do you see this as being prohibitive and if no, why not?

Quote: darkoz

I thought of a game which in deals was similar in that there was a possibility the entire deck could be dealt before a game concluded.

I haven't pursued this game because I figured no casino would want to have a game that takes so long to conclude. They always want quick deal games.

How long on average does this game take for a single deal and do you see this as being prohibitive and if no, why not?
link to original post

I think the average round deals 13.5 cards, it plays quick since there are no decisions beyond the initial bet.

Quote: Codingforest

Why is the probability for a round 1 knockout not just 1-(12/13)^13
I ran the simulation and it shows that your result is correct. I must be getting worse at math...
link to original post

It would be 1 - (12/13)^13 if they shuffled the cards back into the deck immediately after they are drawn.

Let's work on the probability that it is not a first-round knockout. 13 things have to happen:
1. The first card is not an Ace; the probability is 12/13, or 48/52.
2. The second card is not a 2; there are 51 cards left in the deck, of which 47 are not 2s, so the probability is 47/51.
3. The third card is not a 3; there are 50 cards left in the deck, of which 46 are not 3s, so the probability is 46/50.
4. The fourth card is not a 4; there are 49 cards left in the deck, of which 45 are not 4s, so the probability is 45/49
...
13. The 13th card is not a King; there are 40 cards left in the deck, of which 36 are not Kings, so the probability is 36/40.
The probability of not getting a first-round knockout is (48 x 47 x 46 x ... x 36) / (52 x 51 x 50 x ... x 40) = (39 x 38 x 37 x 36) / (52 x 51 x 50 x 49) = 6327 / 20,825.
The probability of a first-round knockout = 1 - 6327 / 20,825 = 14,498 / 20,825, or about 0.69618.
Note that 1 - (12/13)^13 = about 0.64674.

Quote: DJTeddyBear

Quote: Wizard

On May 17, Knockout 52 will begin a field trial at the Strat.
link to original post

If you can’t wait until then, and you’re in the area, it’s launching on 5/3 at Firekeepers in Battle Creek MI.
link to original post

I just added a table for eight decks to my page at WoO.

Quote: zbrownson

I think the average round deals 13.5 cards, it plays quick since there are no decisions beyond the initial bet.
link to original post

I show the average cards dealt is 12.906 with one deck and 12.825 with eight decks.

So what happened with the issue years ago that patents were being denied for new strictly card based games?

Something about they needed some mechanical features otherwise they were being rejected.

Is that no longer the case?

Quote: darkoz

So what happened with the issue years ago that patents were being denied for new strictly card based games?

Something about they needed some mechanical features otherwise they were being rejected.

Is that no longer the case?
link to original post

]]

You can still create a game without a patent. Some patents have gone through for card games in the last few years, however they are usually written to be played in electronic format then add an embodiment where they could be played on a physical table. I can't speak to what percentage might get approved this way, but I know some have, at the end of the day it still doesn't answer the question of if it is enforceable, but people will take the risk.

Quote: Wizard

Quote: zbrownson

I think the average round deals 13.5 cards, it plays quick since there are no decisions beyond the initial bet.
link to original post

I show the average cards dealt is 12.906 with one deck and 12.825 with eight decks.
link to original post

I assume that is calculated off the top of the shoe. If you start a new game when the shoe contains nothing but aces, the probability for matching in round #1 goes to 100%. I am guessing any shoe that has depleted some ranks unevenly favors the player.

I spoke to the lovely dealer / model, Angela today to ask her a detail she was mentioning at the show: “What was the hands per hour that you were stating?”

She said, 60. Frankly, when she mentioned it at the show, I thought there was no way that could be true. But at ~13 cards to get resolution, maybe 60 hands per hour is possible.

Oh. Who is Angela? She’s in this photo. Figure it out. 🤪

Quote: Mental

Quote: Wizard

Quote: zbrownson

I think the average round deals 13.5 cards, it plays quick since there are no decisions beyond the initial bet.
link to original post

I show the average cards dealt is 12.906 with one deck and 12.825 with eight decks.
link to original post

I assume that is calculated off the top of the shoe. If you start a new game when the shoe contains nothing but aces, the probability for matching in round #1 goes to 100%. I am guessing any shoe that has depleted some ranks unevenly favors the player.
link to original post

I wrote a sim for the game. I deal consecutive games through the shoe with no burn card between games. The first table is a sanity check. There should be almost no difference between dealing Game #0 from the top of the shoe or dealing Game #30. I don't think the shoe composition is biased much depending on whether it is a new shoe or whether many games have been dealt from it.

Game	Rnd 1	Rnd 2	Rnd 3	Rnd 4	No Match	Sum Prob
0	0.64623028	0.22848800	0.08097850	0.02864830	0.01565490	1.00000000
10	0.64639378	0.22841150	0.08090430	0.02865410	0.01563630	1.00000000
20	0.64634281	0.22848921	0.08085300	0.02863160	0.01568340	1.00000000

Then I define a concept of a ragged shoe. I count the ranks remaining in a shoe. The shoe is ragged if the max rank count is at least twice the min rank count. For example, assume there are 130 cards remaining in the shoe. There might be 15 sixes and only 7 kings. This qualifies as a ragged shoe. (Obviously, the new shoe is never ragged.) The biggest difference that I see is that 'No Match' is more probable for a ragged shoe. This isn't what I expected.

Game	Rnd 1	Rnd 2	Rnd 3	Rnd 4	No Match	Sum Prob
10	0.61687106	0.21595275	0.10837787	0.03768794	0.02111039	1.00000000
20	0.63427502	0.22440833	0.08931462	0.03201239	0.01998965	1.00000000
30	0.63892955	0.22897851	0.07681894	0.03143449	0.02383850	1.00000000

I push this concept further and use (max >= (3*min)) as the cutoff. Now I am seeing bigger differences. Maybe there are not enough super ragged shoes after only 10 games and my sample size is too small. It still seems that ragged shoes favor 'No Match'.

Game	Rnd 1	Rnd 2	Rnd 3	Rnd 4	No Match	Sum Prob
10	0.60032892	0.20814575	0.12181880	0.04429191	0.02541463	1.00000000
20	0.63117778	0.22217239	0.08940069	0.03357313	0.02367602	1.00000000
30	0.63924652	0.22851303	0.07460260	0.03235944	0.02527841	1.00000000

I repeated the calculations for a smooth shoe. (max <= (1.5*min))

Game	Rnd 1	Rnd 2	Rnd 3	Rnd 4	No Match	Sum Prob
0	0.64637232	0.22856776	0.08085106	0.02856392	0.01564496	1.00000000
10	0.63850844	0.22876911	0.08577770	0.03034509	0.01659963	1.00000000
20	0.63874590	0.23098660	0.08429455	0.02970863	0.01626430	1.00000000
30	0.63557017	0.23737301	0.08079363	0.02995183	0.01631135	1.00000000

Note that I am using number of games dealt as a proxy for penetration. Maybe I should be using number of decks dealt instead.

I did this all in less than 2 hours, so there could be coding errors. Still, I am only changing the definition of ragged/smooth and the probabilities seem to be affected.

Question? Comments? Can anyone corroborate my results?

EDIT: I am disavowing much of what I wrote above. Because I was using number of games as a proxy for penetration, I often ran out of cards in the simulations above. There are usually enough cards to do thirty games from one 8-deck shoe. But sometimes, all 416 cards will be used up during game #30. This corrupted my results. I switched to using the number of decks to measure penetration in my new version, so I will never run out of cards in the shoe. I will write a new post later.

Here are my results from my updated study. The first column is penetration measured in numbers of decks. The last column is the percent of shoes that are very ragged at the start of the first game after the penetration mark is achieved. Very ragged means (max >= (min*3) where max is the most frequent rank left in the shoe and min is the least frequent rank. The first two rows have a very small percentage of ragged shoes, so the results are not very precise (and probably not meaningful).

The last row is included for a reference point. It is calculated for zero penetration and using every shoe.

Pen	Rnd 1	Rnd 2	Rnd 3	Rnd 4	No Match	Ragged%
2.5	0.64109	0.22847	0.08450	0.02754	0.01840	0.008%
3.5	0.64597	0.22939	0.08065	0.02834	0.01565	0.422%
4.5	0.64628	0.22858	0.08095	0.02867	0.01550	6.361%
5.5	0.64667	0.22835	0.08083	0.02852	0.01559	36.609%
6.5	0.64646	0.22845	0.08084	0.02859	0.01564	75.545%
0.0	0.64637	0.22852	0.08089	0.02855	0.01566	0.000%

You need a lot of penetration to get to high percentages of ragged shoes. Playing from a raggedy unbalanced shoe does not seem to change the probabilities for any of the bets to any significant degree. This means the game is probably not countable. The penetration can never exceed 7 of 8 decks because you need 52 cards to play a game.

Quote: Mental

Here are my results from my updated study. The first column is penetration measured in numbers of decks. The last column is the percent of shoes that are very ragged at the start of the first game after the penetration mark is achieved. Very ragged means (max >= (min*3) where max is the most frequent rank left in the shoe and min is the least frequent rank. The first two rows have a very small percentage of ragged shoes, so the results are not very precise (and probably not meaningful).

The last row is included for a reference point. It is calculated for zero penetration and using every shoe.

Pen	Rnd 1	Rnd 2	Rnd 3	Rnd 4	No Match	Ragged%
2.5	0.64109	0.22847	0.08450	0.02754	0.01840	0.008%
3.5	0.64597	0.22939	0.08065	0.02834	0.01565	0.422%
4.5	0.64628	0.22858	0.08095	0.02867	0.01550	6.361%
5.5	0.64667	0.22835	0.08083	0.02852	0.01559	36.609%
6.5	0.64646	0.22845	0.08084	0.02859	0.01564	75.545%
0.0	0.64637	0.22852	0.08089	0.02855	0.01566	0.000%

You need a lot of penetration to get to high percentages of ragged shoes. Playing from a raggedy unbalanced shoe does not seem to change the probabilities for any of the bets to any significant degree. This means the game is probably not countable. The penetration can never exceed 7 of 8 decks because you need 52 cards to play a game.
link to original post

It seems like a naturally balancing game, because you have to play through all 13 ranks each round it seems to eliminate that key card effect.

Quote: zbrownson

Quote: Mental

You need a lot of penetration to get to high percentages of ragged shoes. Playing from a raggedy unbalanced shoe does not seem to change the probabilities for any of the bets to any significant degree. This means the game is probably not countable. The penetration can never exceed 7 of 8 decks because you need 52 cards to play a game.
link to original post

It seems like a naturally balancing game, because you have to play through all 13 ranks each round it seems to eliminate that key card effect.
link to original post

Yes, the game inventors were probably aware of this naturally balancing effect. The 8-deck shoe cannot become seriously unbalanced by random depletion of ranks. However, I can force the shoe to be extremely unbalanced, and then all the probabilities go out of whack.

Imagine I have a stack of cards with 32 aces on top, 32 deuces just below, 32 threes below that, ..., and 32 kings on the bottom. Now, I pick a number, Num, of cards off the top of the stack and shuffle just those cards and put them in the shoe. For example, if Num=128, then the shoe only contains ranks ace through four.

Num	Rnd 1	Rnd 2	Rnd 3	Rnd 4	No Match
32	1.00000	0.00000	0.00000	0.00000	0.00000
64	0.74605	0.18942	0.04813	0.01220	0.00420
96	0.70137	0.20939	0.06263	0.01866	0.00795
128	0.68205	0.21679	0.06893	0.02197	0.01026
160	0.67102	0.22078	0.07260	0.02389	0.01171
192	0.66380	0.22320	0.07502	0.02521	0.01277
224	0.65914	0.22476	0.07661	0.02603	0.01346
256	0.65527	0.22585	0.07795	0.02682	0.01412
288	0.65311	0.22651	0.07852	0.02730	0.01455
320	0.65072	0.22718	0.07943	0.02778	0.01489
352	0.64910	0.22770	0.08005	0.02799	0.01517
384	0.64752	0.22820	0.08051	0.02835	0.01543
416	0.64622	0.22858	0.08096	0.02856	0.01568

For Num=32, the game always ends after one card is dealt, so the game always ends in Round 1. If Num=64, then the game has an approximately 75% chance of ending in round 1. There is roughly a 25% chance each that the two cards off the top of the shoe are AA, A2, 22, or 2A. The game only goes to round 2 in the latter case.

The game is naturally balancing, but extreme random fluctuations will change the probabilities slighty. These extreme situations are so unlikely that they would have no significant effect on the game. This is true even with penetration of 7 out of 8 decks.

I was playing around with the online game on the developer's website. A couple fo times I won with an ace dealt on the first round. I then thought that maybe there is a possibility of some side bets on betting which position wins the hand. For example, if I bet on round 1 to win, with an ace round 1 wins with a dealt ace, then I would win the round bet as well as the side bet on which card. Maybe even a range of winners, like one bet for cards A-7, and another bet of 8-K. I leave the mathematics to those smarter on such topics than I am. With a table layout of 6 spaces, the side bet layout could get unwieldy, I suppose.

Quote: GenoDRPh

I was playing around with the online game on the developer's website. A couple fo times I won with an ace dealt on the first round. I then thought that maybe there is a possibility of some side bets on betting which position wins the hand. For example, if I bet on round 1 to win, with an ace round 1 wins with a dealt ace, then I would win the round bet as well as the side bet on which card. Maybe even a range of winners, like one bet for cards A-7, and another bet of 8-K. I leave the mathematics to those smarter on such topics than I am. With a table layout of 6 spaces, the side bet layout could get unwieldy, I suppose.
link to original post

So if you lookup a game called "Match 52" it was this game with a million side bets (for every single position), had to be played on a craps or roulette table and was a mess. So this was the much better version of it. I could still see some form of a progressive added based on a single position, or streak of cards, or something.

When looking at the game dealt out of an 8 deck shoe, I also came to the same hypothesis as you that the game may be beatable with computer perfect play. However, after some brief simulations, it doesn't come up often enough to make the game profitable.

I did only analyze round 1 betting to hit the 3% house edge. After some thinking... there may be something to do with no match.

My one-deck numbers are based on a shuffle after every game. For eight decks, I assumed a cut card after seven decks.

I just added a table for the probability of a match after any given number of cards to my page at WoO.