Auld Lang Syne

Reading Michael Keller's article The Worst Solitaire Mistake? got me curious about how low the win rates are for Auld Lang Syne and Tam O' Shanter. So I wrote a solver to find out.

I'm a little unclear about whether or not you must make every move to the foundations you can before dealing out the next set of four cards. Intuitively, it seems to me that you should be able to refuse a play in the rare instances when you think you're better off not doing so. But the way I read the rules from several sources, an argument can be made it is implied that you have no choice but to make these moves (perhaps it just didn't occur to the authors that there might be a reason why someone might wish not to play them). So I implemented this as an option ("Must Play"), figuring that it might be interesting anyway, given that most human players will rarely pass up moves in this game intentionally.

Assuming you are playing by rules that allow building foundations regardless of suit, it appears that about 1-in-213 Auld Lang Syne games are winnable. But in practice, it will be much less than that, because you lack the solver's perfect knowledge of the order of cards in the stock. A better way of looking at these results, is that you will definitely lose about 212 out of 213 games in the long run, and while you have a chance at the others, you will probably lose most of them as well. To start with, if you make all the moves you can before dealing the next set of four cards (which I assume is typical), then you are certain to lose about 1,216 out of 1,217 games (and even then, you will lose most of the remainder as well).

Increasing the number of piles does increase the percentage of games which are winnable, but it also increases the number of choices. So even though a higher percentage of these games are technically winnable, in practice you won't match the win rates shown below:

And don't even think about winning if you are building foundations by suit! Even triping the number of piles does virtually no good, although the solver did manage to win one game with eight piles.

In order to give yourself a reasonable chance of winning Auld Lang Syne, do not build the foundations by suit, and consider using at least eight piles (perhaps even twelve), or permit redeals.

Tam O' Shanter

Not surprisingly, the lack of pre-founded Aces makes the win rates even lower in Tam O' Shanter. In the long run, you are guaranteed to lose 1,189 out of 1,190 games, or 9,345 out of 9,346 if you make all the moves you can before dealing each new set of four cards (which I assume is typical). Either way, you will probably lose most of the remaining deals as well.

If the rules you learned for this game (or Auld Lang Syne) include building the foundations by suit, it is a lethal situation whenever a card in any pile gets covered by another card of the same suit with a higher rank. Therefore, increasing the number of piles will not help by as much as you might expect. Even with thirteen piles and perfect knowledge of the stock, the solver won only 24 games out of ten million Tam O' Shanter deals when building the foundations by suit. Even with a ridiculous 26 piles, the win rate doesn't go much above one percent!

In order to give yourself a reasonable chance of winning Tam O' Shanter, do not build the foundations by suit, and consider using thirteen piles, or permit redeals.

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Last modified May 28, 2022

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