How to mash shuffle honestly and straight-forwardly

To mash shuffle a deck of cards is to divide the deck in two halves and mash the two halves together.

Topologically it’s the same as a traditional “riffle shuffle” but instead of riffling through the cards, you just mash them together.

Setting aside how bad card sleeves are for the environment, card sleeves make it harder to riffle shuffle but easier to mash shuffle.

Here is how to mash shuffle in an honest and random way.

• Have the cards at an angle or even horizontal so that you can keep the face sides of the cards angled away from you.
• Do not have the cards vertical so that they fan out so that you can see the faces.
• Ideally practice enough so that you can mash shuffle while looking in a completely different direction.

• Interleave the cards.
• Repeat the mash shuffle at least seven times (for a sixty-card deck; more for a bigger deck).
• Ideally, there should be 50% chance of one card and 50% of two cards in the interleaving. If you are always putting in exactly one card between each other card, you’re not doing it right. Erring in the opposite direction, putting too many cards in between the other cards, you can compensate for by mashing it even more times.
• The goal of shuffling a full deck is to make all permutations equally likely, and for all cards to have equal chance to be at the top of the deck. Clumps of a particular color or card type is very normal in true randomness. A perfect weave (such as Hearts, Spades, Diamonds, Clubs alternating perfectly) is not particularly random.
• After every mash, a card from the middle of the pack should be the new top card. If you keep mashing but the top card keeps staying the same card, you are messing up. After each mash there should be a new top card and a new bottom card.

For example, let’s say you have this permutation:

A A A A A b b b b b

You take the bottom half and mash it together with a tiny offset so that the new top card of the combined pile came from the middle:

b b A b A b b A A A

The offset should be minimal. If you make the offset too big, mash more than seven times to compensate.

The “more random part” is the middle part of the deck.

In this example, the B B at the top isn’t particularly mashed up, nor is the A A A at the bottom.

Then, you repeat:

B B A B A b b a a a →
b b B a B a A a B A

B B B A B a a a b a →
a a B a B b B a A B

etc.

All the entropy and randomness lives in that middle, mashed up, part. So everytime you re-mash, the top of the deck should come from the middle, mashed-up part. The sum of the two less random “offsets” at the top and bottom need to be much smaller than the random “elevator” in the middle. The “elevator” has the randomness that you want to spread into the rest of the deck as much as possible. Sort of like when stirring cinnamon into a dough.

If you have shuffled your opponent’s deck (which means you’re the last person who’ll get to shuffle it) also cut the deck.