Why I doubt about the results of the CSM simulation

[peterlee]

https://wizardofodds.com/games/black...t-card-effect/

CSM reduction in House Edge
Number Reduction
of Decks
1 0.113%
2 0.063%
4 0.034%
5 0.028%
6 0.020%
8 0.014%

The next two tables show the distribution of each rank in both types of games, both using a single deck.

Distribution of Ranks in Cut Card Game

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

[Distribution of Ranks in Cut Card Game]
In this section, Distribution of Ranks is quite close to the EXPECTED, means each rank appears about 1/13 of chance, even with the cut card effect.

[Distribution of Ranks in CSM Game]
In this section, without the cut card effect, our(or just me?) simple logic is each rank should appear more close to 1/13 of chance than "in the cut card game".
But from the figures, the differences are much larger. And the trend is, high cards appear much more frequently. Why?

Look back to the introduction, it said "The continuous shuffling machine is a device that randomly inserts discards back in the deck. With one in use it is like playing against a freshly shuffled shoe every hand."
Did Mike use this assumption to code his simulation program, and played only the first hand to assume this is the same as how a CSM works?
Hope someone could tell me the true story.
If this is the case, the figures show us that the first hand accually uses more high card. And the CSM EV in the page may not be accuracy.

I might misread the contents or the figures in the page, please correct me.