Pro21 said:
In 2 riffles there should be 3 cards between the key card and ace.
Stophon, I suggest you get some decks and start dealing yourself some hands. Also, the shuffle data in Wong's book is nothing like the data we gathered. Do your own shuffling and deal yourself some hands.
In 2 perfect riffles! Most dealers drop lots of 2 card clumps and a couple 3's, this really skews that data. However if you are dealing with a fine riffle I agree that 3 cards should be the mean. Once you get to a third riffle this mean tends to flatten out over a range of cards I find.
What data did you gather? How does it differ? PM if you don't want to say.
I have shuffled decks myself and seen how many cards I am likely to interleave. My own riffle isn't far off from most studies I have seen.
Wong's data is slightly different than the data generated by curtis's study but not too far off. Epstein conducted a larger study which points towards a finer riffle. I believe his results are a result of dealers being extra careful when shuffling b/c they are being tested but if you believe you are dealing with a very fine riffler you can use his results. I believe most riffles drop one card around 3/4 of the time, 2 cards around 1/5 and 3 cards most of the rest of the time. I computed that wong's dealer probably dropped 1 card around 71% of the time, 2 cards 16%, 3 cards 6%, 4 cards 4% and 5 cards 3%. That data generates numbers very close to wong's. Why is that shuffle unusual?
Code:
same sim details as before except
using epstein shuffle data (drop 1 card - 80%, 2 cards - 18% and 3 cards - 2%)
riffle-riffle
cards separating ace and key
0 3.34%
1 12.98%
2 19.87%
3 32.10%
4 16.86%
5 8.60%
6 3.90%
7 1.48%
8 0.53%
9 0.18%
10 0.04%
11 0.01%
12 0.00%
There is 2 fine riffles and while the mean is 3 cards it is far from what will occur the majority of the time!