Are all Pyramid Solitaire games winnable?

No. Pyramid is one of the less forgiving solitaires. You remove pairs of cards that add up to 13, and once the open cards stop pairing, many deals lock up with no way to finish.

We measured this directly by dealing 500 seeded games with the same engine the site runs on and solving every legal line of play. At least 60.6% of them, 303 of 500, turned out to be winnable. A few were proven impossible, and the rest ran past our search limit before finishing, which is why we report 60.6% as a floor rather than an exact figure. The true rate is somewhat higher, but well short of every deal. We never screen deals to be solvable first.