Carpet

Rules for this game can be found here. Some sources say to use prefounded Aces while others do not, so I tested both ways.

Filling Spaces Immediately

I assume that many players probably fill in any spaces in the carpet (from the waste pile) as soon as they become available, so I wrote a program to determine the corresponding win rates:

So, you can win Carpet 4 games out of 9, or about 5 in 9 if prefounding the Aces.

Allowing Spaces to Remain Unfilled

At first, it might seem like there is no skill in Carpet. But there actually is a little, if you don't insist upon filling the empty spaces immediately. Then, whenever there is an empty space, you need to decide whether to fill it, or keep it open to save a potentially more desirable card later. By making smart choices, you can beat the win rates mentioned above.

It occurred to me that Carpet can be described using the JSON rules format used by the Solvitaire general purpose solver, so I did so, and it generated the following results using these custom rules (no inconclusives):

Carpet can be won 7 deals out of 8 without prefounding Aces, or 19 out of 20 with prefounded Aces.

These results show the percentage of games that are "winnable", but in practice you will win less often (especially if you don't peek ahead). Soon, I plan to enhance my program to simulate a human player (who plays imperfectly, and doesn't know the order of the remaining cards), to generate a more realistic win rate estimate.

Aisleriot's Implementation

In Aisleriot (shown in the screenshot on top), available spaces in the carpet are filled automatically. Therefore, you might expect to win 55.4% of the time, the win rate for prefounding Aces (as Aisleriot does) when always filling spaces. However, Aisleriot's suggested strategy of "Just put anything you can on the foundation" is not optimal! It takes some getting used to, but by strategically waiting to play cards from the carpet to the foundation until you get a card on top of the waste pile you wish to keep, you can get equivalent results as if playing cards from the carpet to the foundations immediately, but not necessarily filling the spaces.

Carpet with a Redeal

Normally, there is no redeal in Carpet, which is fine since the game is won often enough that a redeal really isn't necessary. However, there is a redeal in the version I first learned. If you don't win on the first pass, you flip the waste pile over to form the new stock. But on the second pass, you may not play cards from the waste pile to the carpet (only from the waste pile to the foundations, or from the carpet to the foundations). This version results in the following win rates (if always filling spaces):

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

Last modified May 15, 2022

Main page

Copyright ©2022 by Mark Masten. All rights reserved.