Assuming your shuffling/picking is random, pick-and-replace is better (higher entropy).

However, I’m skeptical about pick and replace for two reasons.

1. Since many games give some cards higher value than others, I would predict that some cards get handled more or less than others. For example, in 5-card draw, people are likely to keep high-value cards and discard low-value cards. Does this unequal wear pattern make a difference when using that deck to pick single cards at random? Would an attacker be able to make use of such a pattern? It probably doesn’t matter, but it’s something I think about. Using the full deck restricts the scope of unequal-wear-pattern effects.

2. People sometimes undermine their own entropy thinking that they’re helping. For example, using pick-and-replace, chances are ~73%* that you’ll see the same card in two seed words back-to-back. People might think they’re doing themselves a favor by tossing the repeat back and picking another, when in fact they’re introducing bias. Worse, memorable (high value) cards are more likely to be tossed back than less memorable cards. Using the Solitaire method makes it impossible to see duplicates.

I designed the Solitarie method to be easy to do and hard to mess up. As mechanical as possible, to try to avoid user-introduced bias.

* Doing the math:

- Chances of neither card matching a card in the previous tuple: 50/52 * 50/51 = 0.9427

- Chances of no back-to-back repeats: 0.9427^22 = 0.2729

- Chances that you’ll see at least one back-to-back duplicated card: 1 - 0.2729 = 0.7271 = ~73%