Forty Hidden Pieces
Ars Technica reports that an AI called Ataraxos has beaten Pim Niemeijer, perhaps the best Stratego player ever, 15 games to one with four draws. One of its tricks was a second network that guesses what the hidden pieces are. Below is the dumbest possible version of that guess, counting alone, on a hidden army you can poke at.
What the selected piece might be
The odds come from counting, with a uniformly random setup as the prior. A piece that has moved is equally likely to be any of the movable pieces still unaccounted for. An unmoved piece is weighted a little towards bombs and the flag, because the moved pieces have used up some of the movable ones. Real players hide the flag in the back row and plant bombs round it, so a real belief model starts from how people actually set up and learns from how each piece moves. This one only counts.
The numbers in the article
| Ars Technica | Check | |
|---|---|---|
| Texas Hold'em: two hidden cards, "just 1,326 possible hands" | 52 × 51 ÷ 2 = 1,326 | right |
| Stratego: "more than a decillion possible setups" | 40! ÷ (6! 8! 5! 4! 4! 4! 3! 2!) for 6 bombs, 8 scouts, 5 miners, 4 each of sergeants, lieutenants and captains, 3 majors, 2 colonels, and one each of the rest: 1,411,873,643,675,199,617,616,832,128,000,000, or 1.4 × 1033. A decillion is 1033. | right |
| 40 pieces each, marshal down to spy, plus bombs and a flag | Wikipedia, Stratego: the counts above add up to 40 | right |
Also from the article: 163 million self-play games; 16 GPUs against DeepNash's 1,024 chips; 38 wins in 40 games against players at the 2025 world championship; and a habit of hiding its flag in a corner behind just two bombs.