After writing the Nestor Solver, I modified it to solve deals of Open (face-up) Doublets as well. The rules of Open Doublets can be found at Pretty Good Solitaire.
When using rectified deals (so that no column contains more than one of the same rank), my solver won over 99.8% of the time! Without rectification (as the game is normally played), the win rate dropped to under 85% (when you do lose, 80% of the time you are blocked due to having three cards of the same rank in one of the columns). With careful play, you should be able to win at least 2/3 of the time (the human simulator won 69.3%).
It turns out that having reserve cards fill in empty columns one at a time, rather than being immediately available (as in Nestor) does not lower the win rate by much. I tested Doublets using a Nestor-like reserve, and the win rate increased by less than 2% (to 86.8%).
When played face-down, Doublets has a lower win rate than these results would suggest. Soon, I plan to simulate playing the face-down version, in order to more closely simulate the regular (non-open) game.
| Rectified? | Reserve | Games Won | Win Rate % |
|---|---|---|---|
| No | Doublets | 84,919,413 | 84.9 |
| No | Nestor | 86,797,366 | 86.8 |
| Yes | Doublets | 99,843,916 | 99.8 |
| Yes | Nestor | 99,999,554 | 99.9996 |
| Rectified? | Reserve | Games Won | Win Rate % |
|---|---|---|---|
| No | Doublets | 69,281,442 | 69.3 |
See the article Nestor and Double Nestor -- Rank Pair Discarding Games at Solitaire Laboratory for more discussion of Nestor and variations, including Doublets.
Any comments are welcome, please send to Mark Masten at:
Last modified January 4, 2022
Copyright ©2022 by Mark Masten. All rights reserved.