(Message Deleted by Poster)
and thanks to ETF since he was able to shed the proper amount of light on the issue. If you track unidentified objects then their resulting location is of no more value than untracked objects.
If you are able to make use of information gained by observing the previous shoe with these machines then you have already done something impressive. But questions such as Maverick's indicate that it may not be clear as to just what you are retracting. Is there any greater tendency for a non-volatile shoe to follow a non-volatile shoe with these machines than with a hand shuffle?
Thanks to all who participated in this thread.
The �Evenness� theory was clearly well thought out and genuinely and sincerely held by alienated.
Particular thanks to ET Fan for giving his time and smarts to work through alienated�s rationale.
Congatualtions, alienated for being both an original thinker and a thorough gentleman.
Student
For my sim, I didn't actually play out the Blackjack hands. Instead, I constructed 8-deck shoes where each 32-card segment had exactly 4 cards from each of the previous shoe's decks, as per alienated "evenness" definition, and simply examined the running count in each segment.
Specifically, the sim sets the running count to 0 at the beginning of each segment, records the running count at the middle of the segment, and for each midpoint running count, accumulates the average change in the running count by the end of the segment.
Setting the running count to 0 at the beginning of the segment is justified because, presumably, the order of the segments does not have any affect, so any segment might have been first one in the shoe. (Or, equivalently, we might have come into the shoe late and not seen the earlier segments. We can still calculate a true count based on the cards we see, starting a running count at that point, but any inference drawn from that true count applies to all unseen cards.)
The True Count Theorem provides a means of calculating the running-count changes that we would expect to see with a random shuffle. For example, if the running count is +3 after 16 cards in the first segment, then the true count would be 3 / (400 / 52) = 0.39. The True Count Theorem says that the true count is still expected to be 0.39 at the end of the 32-card segment. For that to be the case, the running count would need to be 0.39 * (384 / 53) = 2.88. In my sim, therefore, if the "evenness effect" does not exist then for a running count of +3 at the midpoint, the average change in the running count by the end of the segment should be -0.12. A similar calculation predicts a change of -0.20 for a midpoint running count of +5. (This is for the first segment of the shoe, but as noted above, if we reset the running count to 0 for each segment, we can pretend that it's the first segment of the shoe. To check this logic, I also have an option in the sim to only count the first segment, and the results are indeed the same as when all segments are counted.)
However, alienated's "even but non-random" hypothesis predicts that the changes will be greater than those numbers (because the average count of each segment will be 0), and that this greater change is an effect that could be exploited.
I tried several variations, which are now options in the sim: taking either 1 card from each deck in sequence or taking 4 cards at a time from each deck; randomly shuffling each 32-card segment within itself after construction; randomly reshuffing the entire shoe periodically to remove any cyclic effects of constructing the segments with positionally-fixed rules; and counting only the first segment. However, all produced similar results (except that not shuffling the segments and also not periodically reshuffling the entire shoe produced irregular results, different from one run to the next, due to recycling the same sets of segments).
Following are two runs: one where all 13 segments were counted in each shoe, and one where only the first segment was counted. In each of these, 4 cards were taken from each of the previous decks, sequentially. The segments were not shuffled within themselves, but the entire shoe was reshuffled every 13 shoes. However, as noted above, so far I have gotten similar results running with different options. These runs were for a half-million shoes each, which appears to be enough to give consistent results at least for the lower running counts.
In both these sims, the average change from a midpoint running count of +3 was -0.12 as predicted by the True Count Theorem. For +5, the change was -0.20 in the first sim, as predicted by the TCT, and -0.21 in the second (which had fewer samples for that count, so it's less precise). I didn't exhaustively check all the counts, but they seem to be in line with the results for +3 and +5. From this experiment, I conclude that the "evenness effect" when nothing is known about the previous shoe (unfortunately) cannot be exploited.
Number of Decks (2 - 8)? 8
Take how many cards from each deck, 1 or 4? 4
Reshuffle the shoe every N rounds (0 = don't reshuffle)? 13
Randomly shuffle each segment (N/y)? n
Number of segments to count in each shoe (1 - 13)? 13
Number of shoes to test? 500000
RC Change #Segments
-15 -0.43 7
-14 0.46 65
-13 0.27 310
-12 0.46 1135
-11 0.47 3775
-10 0.42 9924
-9 0.36 23694
-8 0.30 50751
-7 0.27 97397
-6 0.23 169657
-5 0.20 268374
-4 0.17 389361
-3 0.12 516365
-2 0.07 633095
-1 0.04 714168
0 0.00 743418
1 -0.05 713330
2 -0.08 632398
3 -0.11 517287
4 -0.16 389142
5 -0.20 269032
6 -0.25 169521
7 -0.28 97594
8 -0.32 51001
9 -0.32 24148
10 -0.45 9889
11 -0.44 3600
12 -0.51 1195
13 -0.33 298
14 -0.48 65
15 -2.00 4
----------------------------------------------------------
Number of Decks (2 - 8)? 8
Take how many cards from each deck, 1 or 4? 4
Reshuffle the shoe every N rounds (0 = don't reshuffle)? 13
Randomly shuffle each segment (N/y)? n
Number of segments to count in each shoe (1 - 13)? 1
Number of shoes to test? 500000
RC Change #Segments
-14 2.00 3
-13 -0.55 20
-12 0.80 92
-11 0.22 308
-10 0.58 784
-9 0.43 1800
-8 0.31 3852
-7 0.30 7371
-6 0.21 13077
-5 0.21 20731
-4 0.21 29473
-3 0.12 39398
-2 0.05 48774
-1 0.06 54950
0 0.00 57191
1 -0.06 54696
2 -0.07 48915
3 -0.12 39970
4 -0.18 30176
5 -0.21 20852
6 -0.22 12911
7 -0.25 7647
8 -0.36 3940
9 -0.33 1877
10 -0.50 779
11 -0.27 304
12 -0.33 89
13 0.31 16
14 1.50 4
=======================
DIM Tags(10), RCs&(100), Segments&(100), Shoe(520), NewShoe(520)
' Hi-Lo card tags
Tags(1) = -1
Tags(2) = 1
Tags(3) = 1
Tags(4) = 1
Tags(5) = 1
Tags(6) = 1
Tags(7) = 0
Tags(8) = 0
Tags(9) = 0
Tags(10) = -1
' Get user input
WHILE Decks < 2 OR Decks > 8
INPUT "Number of Decks (2 - 8)"; Decks
WEND
Cards = Decks * 52
SegSize = 4 * Decks
HalfSegSize = SegSize / 2
WHILE CardsFromDeck <> 1 AND CardsFromDeck <> 4
INPUT "Take how many cards from each deck, 1 or 4"; CardsFromDeck
WEND
INPUT "Reshuffle the shoe every N rounds (0 = don't reshuffle)"; Reshuffle
INPUT "Randomly shuffle each segment (N/y)"; C$
ShuffleSeg = 0: IF LCASE$(C$) = "y" THEN ShuffleSeg = 1
WHILE CountSegs < 1 OR CountSegs > 13
INPUT "Number of segments to count in each shoe (1 - 13)"; CountSegs
WEND
WHILE NumberShoes& < 1
INPUT "Number of shoes to test"; NumberShoes&
WEND
GOSUB SetupShoe ' Initialize shoe and randomly shuffle
' Run the test
FOR ShoeN = 1 TO NumberShoes&
GOSUB EvenShuffle ' Get new shoe having even distribution of prev decks
FOR SegN = 1 TO CountSegs
RC = 0 ' Reset running count for each segment
BeginSegI = (SegN - 1) * SegSize
MidSegI = BeginSegI + HalfSegSize
EndSegI = BeginSegI + SegSize
FOR ShoeI = BeginSegI + 1 TO EndSegI
RC = RC + Tags(Shoe(ShoeI)) ' Get running count
IF ShoeI = MidSegI THEN MidRC = RC ' Save RC at seg midpoint
NEXT ShoeI
RCI = MidRC + 50 ' Offset MidRC so array index is always positive
RCs&(RCI) = RCs&(RCI) + (RC - MidRC) ' add up RC changes, MidRC to end
Segments&(RCI) = Segments&(RCI) + 1 ' count segs having this MidRC
NEXT SegN
IF Reshuffle > 0 THEN ' Periodically shuffle if specified
IF ShoeN MOD Reshuffle = 0 THEN ' every N rounds
GOSUB RandomShuffle ' do random shuffle
END IF
END IF
NEXT ShoeN
PRINT ' Results
PRINT " RC Change #Segments"
FOR I = 1 TO 100
IF Segments&(I) > 0 THEN ' Show data for any RCs counted
PRINT USING "### ###.## #########"; I - 50; (RCs&(I) / Segments&(I)); Segments&(I)
END IF
NEXT I
' PRINT: GOSUB ShoeCheck ' (Remove comment mark to check shoe for lost cards)
END
EvenShuffle: ' Build new shoe having even distribution from previous decks
ShoeI = 1
IF CardsFromDeck = 1 THEN ' Get 1 card from each deck
FOR I = 1 TO 52
FOR J = 0 TO Decks - 1
NewShoe(ShoeI) = Shoe((J * 52) + I)
ShoeI = ShoeI + 1
NEXT J
NEXT I
ELSE ' Or get 4 cards from each deck
FOR I = 0 TO 12
FOR J = 0 TO Decks - 1
FOR K = 1 TO 4
NewShoe(ShoeI) = Shoe((J * 52) + (I * 4) + K)
ShoeI = ShoeI + 1
NEXT K
NEXT J
NEXT I
END IF
FOR ShoeI = 1 TO Cards ' Move cards back to shoe
Shoe(ShoeI) = NewShoe(ShoeI)
NEXT ShoeI
IF ShuffleSeg = 1 THEN ' Randomly shuffle each segment separately
FOR SegN = 0 TO 12
FOR ShoeI = 1 TO SegSize STEP 1
SWAP Shoe((J * SegSize) + ShoeI), Shoe(INT(RND(1) * SegSize) + (J * SegSize) + 1)
NEXT ShoeI
NEXT SegN
END IF
RETURN
SetupShoe: ' Initialize the shoe
ShoeI = 1
FOR I = 1 TO Decks
FOR Suit = 1 TO 4
FOR Rank = 1 TO 9
Shoe(ShoeI) = Rank
ShoeI = ShoeI + 1
NEXT Rank
FOR Rank = 10 TO 13
Shoe(ShoeI) = 10
ShoeI = ShoeI + 1
NEXT Rank
NEXT Suit
NEXT I
FOR I = 1 TO 10 ' Random shuffle 10 times
GOSUB RandomShuffle
NEXT I
RETURN
RandomShuffle: ' Shuffle the full shoe by random swapping
FOR ShoeI = 1 TO Cards
SWAP Shoe(ShoeI), Shoe(INT(RND(1) * Cards) + 1)
NEXT ShoeI
RETURN
ShoeCheck: ' Check the shoe by counting ranks
FOR I = 1 TO 10 ' (to insure no cards got lost in the shuffle)
ShoeChk(I) = 0 ' Zero the rank count array
NEXT I
FOR I = 1 TO Cards ' Count number of each rank
ShoeChk(Shoe(I)) = ShoeChk(Shoe(I)) + 1
NEXT I
PRINT "Shoe check: "; ' Show count of each rank
FOR I = 1 TO 10
PRINT ShoeChk(I);
NEXT I
RETURN
They are so fat.
Can you share any tips or tricks on easily detecting a shuffle master machine that is 'tuned' correctly to give the complete shuffle that you are looking for?
I assume there is considerable variation from individual machine to machine.
Before we even had a chance to say "alienated has made a mistake" he forces us to say "alienated has shown us how to gracefully admit he made a mistake." I'm curious about noncontinuous multideck Shuffle Masters, but you're wise not to reveal details on an open board. If you have time, send me an email.
ETF
but were confussed by criticisms and knee-jerk responses to your original FLAWED examples. I can only take credit for seeing other possibilities in work that you still have to be credited with pioneering here.
It is unfortunate that you were then misslead by those responses to some targetlike claims about shoe volutility. Whatever blame you have there has to be shared with those trying to make their points so rudely in that thread; which tend to be those for whoom Hazlit's broken window example of never seeing the opportunities that are destroyed should be considered. I do have to put Don and ETF in that catagory, in that thread!
Now wouldn't it be special to put such million dollar details out for free?
