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.

[Iwantmoney]

If you investigate to such detail you must be capable of figuring it out yourself.

However anyways it seems the logic is The first hand will not necessarily be out the next. Hence for the first hand, when there are small cards out there can be many small cards. However if big cards are out there is a limit. Hence you see the small cards will not be out next hand and this is why the skew towards the big cards

[peterlee]

As Don said :"There is NO tendency for the true count to change as cards are dealt!"
So for CSM game, all 13 ranks of cards, A~K, should be dealt out equally by chance, and should not be bias on any kind of cards.
My question is, from the figures in the page, "Distribution of Ranks in CSM Game", Why more high cards are dealt?

[davethebuilder]

There was a discussion about this in the subscriber section some time ago. The article is confusing, however, a random shuffle has been simulated, not a CSM algorithm. The large figure for the 10 value cards is because most rounds end with a high card. Given the same number of decks and rule set the CSM game has a slightly lower house edge for the Basic Strategy player than a Cut Card game as the Cut Card Effect does not exist in a CSM.

[peterlee]

There was a discussion about this in the subscriber section some time ago. The article is confusing, however, a random shuffle has been simulated, not a CSM algorithm. The large figure for the 10 value cards is because most rounds end with a high card. Given the same number of decks and rule set the CSM game has a slightly lower house edge for the Basic Strategy player than a Cut Card game as the Cut Card Effect does not exist in a CSM.

So the simulation is the same as I guessed, only play one hand after each shuffle. ..CSM does not work that way.

Have Mike confirmed about this?

However, the simulation shows the first round use more high cards.

BTW, any conclusion from the discussion in the subscriber section?

[davethebuilder]

CSM output is not random and to simulate one of these machines requires knowledge of the algorithm the machine uses. From the information in the article it's not clear what is being measured so I wrote to Mike for an explanation but I didn't receive a reply.

[peterlee]

CSM output is not random and to simulate one of these machines requires knowledge of the algorithm the machine uses. From the information in the article it's not clear what is being measured so I wrote to Mike for an explanation but I didn't receive a reply.

I had the machine before, and I have my own program to simulate the input/output of the cards, trying my best to minic the machine.
It is not fully random shuffle, but random enough to deal out equal chances for the 13 ranks of cards, not bias to more high cards out...I think.

[Gronbog]

It's not the dealing of the cards that is biased. It is the tendency for the dealer's hand to finish with a ten and, to a lesser extent, the tendency for hands played using basic strategy to end with a ten which cause the first hand of the shoe to tend toward a negative running count. The difference is subtle.

[peterlee]

It's not the dealing of the cards that is biased. It is the tendency for the dealer's hand to finish with a ten and, to a lesser extent, the tendency for hands played using basic strategy to end with a ten which cause the first hand of the shoe to tend toward a negative running count. The difference is subtle.

[The difference is subtle.], Yes it is.

For a CSM game, only once "first hand" and no cut card effect(or only once), for totally 1116434123 cards are dealt.
The figures of more high cards are dealt, my guess is the simulation did it as a one round per shoe.
I think a real CSM game will not produce this kind of figures.
So the simulation results cannot reflect the reality.

[Gronbog]

I think a real CSM game will not produce this kind of figures.

It does. This bias is a property of the algorithm used by the players and the dealer when taking cards and not the source of the card stream.

[Iwantmoney]

In the link he wrote “ the effect of shuffling after every hand and use of a CSM are the same”

So to solve this puzzle we can just simulate the first round and see if it matches the results on the page

So the simulation is the same as I guessed, only play one hand after each shuffle. ..CSM does not work that way.

Have Mike confirmed about this?

However, the simulation shows the first round use more high cards.

BTW, any conclusion from the discussion in the subscriber section?

[peterlee]

It does. This bias is a property of the algorithm used by the players and the dealer when taking cards and not the source of the card stream.

At a angle of the ratio of 13 ranks of cards dealt out, a CSM game would be quite the same as a shoe of infinity decks of cards. I cannot think of a reason to make the high cards come out more than the low cards.
The only difference is the CSM game can only deal a rank of cards to limit number in a row(or some kind of combination), while the infinity decks shoe has no limit.

So for a CSM game, no matter how you play, blackjack game of not, how you rearrange the cards after dealt out, and put back to the machine, the ratio of the ranks of cards dealt should be close to 1/13. Just like a shoe of infinity decks, you name a number large enough, and count that number of cards, the ratio of the ranks of cards should be close to 1/13.

[peterlee]

In the link he wrote “ the effect of shuffling after every hand and use of a CSM are the same”

So to solve this puzzle we can just simulate the first round and see if it matches the results on the page

Yes!