I have seen two different common versions of Vertical. Some sources have seven columns of six cards each, with ten cards in the reserve. Other sources have the middle column with a seventh card, and only nine cards in the reserve (as pictured above).

It was easy to modify my Nestor solver to allow playing either version of Vertical. If the cards are dealt with rectification (so that no two cards of the same rank are in any of the columns), the win rate is 93.2% when playing with a 10-card reserve, or 86.7% when playing with a 9-card reserve and an extra card in the middle column. Without rectification, the win rate drops down to 39.0% for the 10-card reserve, or 29.4% with the 9-card reserve and an extra card in the middle column. Either way, in about 3 out of 7 losses, the game is blocked due to having three cards of the same rank in a single column (these losses are easy to detect).

It may not seem like it matters very much whether you play with a reserve size of 9 cards or 10, but it actually does make a bigger difference in the win rate than you might expect!

Vertical solver results,
one million deals each
Rate %

See the article Nestor and Double Nestor -- Rank Pair Discarding Games at Solitaire laboratory for more discussion of Nestor and its variants (including Vertical).

Any comments are welcome, please send to Mark Masten at:

Last modified January 2, 2022

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