Adam N. Subtractum
Well-Known Member
I recently spoke to Stanford Wong about an error I discovered in his "Single Deck Shuffle Study", pages 224-231. He assured me the error would be corrected in the next edition of PBJ, but for those who have current editions, the error is disclosed here.
Stanford states on page 230:
"In a completely random shuffle the probability of three initially-adjacent cards finishing up in that order with no more than one card separating them is .8 per ten decks; _this study got one, which is not significantly different from expectation._"
Note the underlined statement. Extensive analysis of Tables 87 & 88, found on pages 226 & 227, reveals that the figure given here (1 per 10 decks) is incorrect, and in fact, this sequence occurs 5 times per 10 decks, over 6 times the expectation for a random shuffle!
Here are the "tags" of the 5 three card sequences maintained in order with only one card separating after the shuffle:
shuffle 3: 8,9,10
shuffle 4: 42,43,44
shuffle 5: 36,37,38
shuffle 7: 5,6,7
shuffle 7: 47,48,49
I explained to Stanford the magnitude of this, in that I believe even this fairly thorough shuffle (R,R,S,R) can be exploitable by sequencing techniques, and that this data tends to support that notion.
ANS
Stanford states on page 230:
"In a completely random shuffle the probability of three initially-adjacent cards finishing up in that order with no more than one card separating them is .8 per ten decks; _this study got one, which is not significantly different from expectation._"
Note the underlined statement. Extensive analysis of Tables 87 & 88, found on pages 226 & 227, reveals that the figure given here (1 per 10 decks) is incorrect, and in fact, this sequence occurs 5 times per 10 decks, over 6 times the expectation for a random shuffle!
Here are the "tags" of the 5 three card sequences maintained in order with only one card separating after the shuffle:
shuffle 3: 8,9,10
shuffle 4: 42,43,44
shuffle 5: 36,37,38
shuffle 7: 5,6,7
shuffle 7: 47,48,49
I explained to Stanford the magnitude of this, in that I believe even this fairly thorough shuffle (R,R,S,R) can be exploitable by sequencing techniques, and that this data tends to support that notion.
ANS