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Cut Card Effect

Introduction

Cut Card Effect

This appendix will address how the introduction of a continuous shuffling machine (CSM) influences the house edge. The CSM is designed to continuously mix discarded cards back into the main deck, making it feel like every hand is played with a freshly shuffled shoe. It's important to differentiate this technology from automatic shufflers, which only shuffle a complete deck or shoe.

While many players criticize the CSM, it actually tends to reduce the house edge. To demonstrate this, I conducted extensive simulations both with and without a cut card under standard rules. The results show how significantly the house edge is minimized with the presence of a continuous shuffling machine compared to a game using a cut card. blackjack The subsequent two tables illustrate how different ranks are distributed in both game types, each using a single deck.

CSM reduction in House Edge

Number
of Decks
Reduction
1 0.113%
2 0.063%
4 0.034%
5 0.028%
6 0.020%
8 0.014%

Distribution of Ranks in a Game with a Cut Card

In the CSM game, observe how the distribution favors high-value cards, contrasting the more even distribution seen in cut card gameplay. The Chi-Squared statistic measures the degree of deviation from expected results, revealing a value of under 3 for the cut card game and an astonishing 1250 for the CSM variant in the bottom right cell of each respective table.

Rank Number Expected Difference Chi-Squared
Ace 85905301 85908934 -3633 0.15
2 85907560 85908934 -1374 0.02
3 85911516 85908934 2582 0.08
4 85901000 85908934 -7934 0.73
5 85902875 85908934 -6059 0.43
6 85906345 85908934 -2589 0.08
7 85904400 85908934 -4534 0.24
8 85912242 85908934 3308 0.13
9 85911202 85908934 2268 0.06
10 343653697 343635735 17962 0.94
total 1116816138 1116816138 0 2.86

Distribution of Ranks in CSM Game

Rank Number Expected Difference Chi-Squared
Ace 85906480 85879548 26932 8.45
2 85707548 85879548 -172000 344.48
3 85737570 85879548 -141978 234.72
4 85785213 85879548 -94335 103.62
5 85819356 85879548 -60192 42.19
6 85846280 85879548 -33268 12.89
7 85875012 85879548 -4536 0.24
8 85908944 85879548 29396 10.06
9 85930794 85879548 51246 30.58
10 343916926 343518192 398734 462.83
Total 1116434123 1116434123 0 1250.05

I have been asked about the timing of small cards appearing in a cut card game. There is no specific moment they can be expected; the odds remain consistent throughout the last hand compared to the full shoe. However, if the dealer deals significantly more hands than average, the final hands can be particularly disadvantageous for players. This often happens because previous hands resulted in little action, leading to a surplus of large cards and leaving an abundance of small cards later in the shoe.

It’s also crucial to understand that the CSM allows the dealer to keep dealing without interruption, thereby increasing the hourly number of hands played. For those utilizing basic strategy, this can lead to higher expected losses within each hour. In real casinos, I often observe the use of these machines in shoe games; however, the effects are comparable in online contexts, where games are frequently shuffled after each hand, regardless of the number of decks. The impact of shuffling after every hand aligns closely with that of a CSM.

Splitting Strategies for Players Wagering from the Back

Internal Links

External Links

  • There is an informative discussion regarding the cut card effect found here BlackjackInColor.com .
  • Mathematically sound strategies and data available for various casino games, including blackjack, craps, roulette, and many more. Casino Verite .