If I remember correctly, somewhere in Mnemonica, there are directions on how to get from the Tamariz stack to ndo. I see the instructions on how to get from the stack to staystack (page 19). I also see the instructions for getting from staystack to ndo (page 35), but it requires an anti faro. Is there any way of accomplishing this second step without the antifaro.

Okay--I figured it out--now I have a better question. While I figured out how to do the antifaro--I also figured out that you can also get to ndo by just doing 4 faros. Anyone have a theory on why Tamariz suggested an antifaro as opposed to 4 faros as the way back to ndo?

Cesar, read more carefully. Tamariz gives you both methods. Antifaro is for those who can't, or choose not to, faro.

Piqsirpoq,will do thanks!

On page 322 of Mnemonica, Juan Tamariz describes a table method of accomplishing the Out-AntiFaro-4. This is also the same as four faros.

The key thing about four faros is that it brings the cards into a position in which cards 1, 18, 35 and 52 have not moved from their starting positions and all other movements are pairwise position swaps (eg cards in positions 2 and 17 have swapped, 5 and 14 have swapped, etc.) After looking carefully at the permutations involved, this suggested to me another method of doing 4 out faros.

My method involves starting in new deck order, dealing cards into 3 piles face down, as in a 3 player game, then turning cards face up in 5 clumps (one of which is the entire pile 1, and the others are as clumps take from the tops and bottoms of other piles 1 and 2). To finish we pick up cards from 3 face up piles. Because of this final pickup step this is probably not as fast as the method of 16 piles that is described in Mnemonica - but it may have application. We could, for example, start in 4-faroed staystack and after dealing cards out to a game with three players, quickly return to NDO. I think this could be presented as a surprising outcome.

It is hard to believe anything can be new in the world of the faro shuffle. Has anyone seen anything like this before? (I have omitted one detail and not said where to turn over the clumps in case I would be treading on someone's toes.) Hugard and Braue in "Expert Card Technique" have a "Chart of Seventeen", but this is something different. They talk about "The Eighteenth Card" which, as we see above, swaps with the 35th card at each out faro, so both 18 and 35 are unmoved by an even number of faros.

A fun fact about mnemonica stack is that the staystack reached after 4 out faros has 9C-9S kissing at positions 26-27. After performing the rest of the shuffling needed to reach mnemonica order, these two cards are now back in their original NDO positions of 44 and 9 (as is also the AD). Coincidence or design?

Tamariz says (page 318) the he hit upon his stack by trial and error. I had wondered if there was any logic to it. Why reverse 26 cards (not 13 or 20)? Why the step of out-faroing in 18 cards (not 16, or 20)? Why a final cut of 9 cards to the bottom (not 8 or 10)? One thing I have noticed is that out-faroing 18 means cutting under KD, and then moving 9 at the end brings KD to position 26. Can anyone think of any fortuitous things that happen because of Tamariz's particular choices? One is that AS (a popular card) comes to position 7 (a popular number).