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Knockout 52

Introduction

Knockout 52 is a unique table that will make it's debut at the FireKeepers casino in Battle Creek, Michigan in May 2024.  Later, on May 17, 2024, it is scheduled to begin a field trial at the Strat 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.

Rules

  1. Any number of decks can be used. The analysis in this report is based on a single 52-card deck is used.
  2. The betting layout shall consist of four rows and 13 columns. The columns shall be labeled ace to king, in that order, from left to right. Each of the four rows shall be referred to as a "round."
  3. After betting is closed, the dealer shall deal the first card to the first round. If this card matches the rank on the layout, in this case an ace, then the round will be over and winning bets will be adjudicated.
  4. Otherwise, if the first card wasn’t an ace, then the second card will be dealt to the first round. If that card matches the rank on the layout, in this case a 2, then the round will be over and winning bets will be adjudicated.
  5. This process of dealing across the first round will continue until a card matches the column heading or none of the 13 cards match their respective column heading.
  6. If there are no matches in the first round, the dealer shall deal the 14th card to the A column in the second round. If that card is not an ace, then the dealer shall continue to deal across the second round until he reaches the end of that round or there is a match.
  7. If there is no match in the first 26 cards, the dealer will deal across the third round Path in the same manner. If there is no match in the third round, then the dealer will go onto the final fourth round.
  8. If the dealer gets through all 52 cards without a match, then there will be said to be “No Match” and bets on No Match will be adjudicated (there can be no other winners in this event).
  9. All bets win or lose according to the row and/or column of the first match or no match at all.
  10. The following types of bets are available:
    • First Round — The first match will be in the first round. Wins pay 1 to 2.
    • Second Round — The first match will be in the second round. Wins pay 3 to 1.
    • Third Round — The first match will be in the third round. Wins pay 10 to 1.
    • Fourth Round — The first match will be in the fourth round. Wins pay 30 to 1.
    • No Match — No matches in all four rounds Wins pay 50 to 1.

 


Knockout 52 layout

Analysis

The following table shows my analysis assuming a single deck of cards. The right column shows the best bet is on round 1 with a house edge of 3.56%.

Single Deck Analysis

Bet Pays Probability House Edge
Round 1 0.5 0.643070 0.035395
Round 2 3 0.229534 0.081865
Round 3 10 0.081924 0.098832
Round 4 30 0.029240 0.093557
No Match 50 0.016232 0.172189

Following is my analysis based on eight decks of cards.

Eight Deck Analysis

Bet Pays Probability House Edge
Round 1 0.5 0.646281 0.030579
Round 2 3 0.228605 0.085579
Round 3 10 0.080858 0.110560
Round 4 30 0.028602 0.113344
No Match 50 0.015654 0.201637

The next table shows the probability of a match after any given number of cards or no match for both one and eight decks.

Detailed Analysis

Cards Dealt One Deck Eight Decks
1 0.076929 0.076927
2 0.070886 0.070991
3 0.065338 0.065518
4 0.060230 0.060465
5 0.055538 0.055805
6 0.051209 0.051513
7 0.047222 0.047543
8 0.043560 0.043882
9 0.040178 0.040502
10 0.037071 0.037382
11 0.034204 0.034504
12 0.031568 0.031849
13 0.029135 0.029399
14 0.027456 0.027209
15 0.025301 0.025108
16 0.023325 0.023177
17 0.021499 0.021388
18 0.019824 0.019743
19 0.018278 0.018220
20 0.016856 0.016815
21 0.015547 0.015522
22 0.014344 0.014330
23 0.013232 0.013223
24 0.012209 0.012204
25 0.011266 0.011266
26 0.010399 0.010399
27 0.009800 0.009622
28 0.009032 0.008883
29 0.008323 0.008197
30 0.007672 0.007565
31 0.007074 0.006982
32 0.006523 0.006444
33 0.006016 0.005948
34 0.005549 0.005489
35 0.005121 0.005067
36 0.004723 0.004678
37 0.004359 0.004318
38 0.004021 0.003985
39 0.003712 0.003679
40 0.003497 0.003404
41 0.003223 0.003142
42 0.002971 0.002899
43 0.002739 0.002677
44 0.002526 0.002469
45 0.002330 0.002280
46 0.002147 0.002103
47 0.001981 0.001941
48 0.001826 0.001793
49 0.001685 0.001655
50 0.001556 0.001528
51 0.001435 0.001410
52 0.001324 0.001302
No Match 0.016232 0.015654
Total 1.000000 1.000000

Methodology

A random simulation was used to analyze this game. For one deck, the simulation included 4,910,000,000 games played. For eight decks, it included 8,899,500,000 games. I feel the probabilities are accurate to five decimal places.

External Links

Discussion about Knockout 52 in my forum at Wizard of Vegas.