Decade (Ten-Twenty-Thirty)

In this game, Aces are worth one point, and face cards are worth ten. Sets of cards may be discarded if they add up to 10, 20, or 30. There are many different variations of this game, five of which are described below.

Discarding Triples with Wrapping Allowed

In the version I was first taught, cards are dealt one at a time in a single overlapping line. Exactly three cards are discarded at a time. You can discard either the three rightmost cards, the leftmost card and the two rightmost, or the two leftmost cards and the rightmost card (I assume you can also discard the three leftmost cards if you wish, but this situation rarely happens because you could have discarded them earlier in the game when they were the three rightmost cards). Note that after you make a discard, sometimes it is possible to make additional discards. You win the game if you end up with one card left (which will be a ten-valued card).

Using a face-up stock (or unlimited undo), my solver won 98.4%.

Even with perfect knowledge of the stock, I'm amazed at how high the win rate for this game is. While more than 98 percent of deals may technically be winnable, doing so will often require careful planning and/or multiple attempts, strategically passing up one or more discards during the game.

Including Jokers

I like to play the game similarly as the version described above, but with two jokers, each worth 10. This simplifies keeping track of the mathematical properties of the game, and it means that victory will completely clear off all the cards (rather than leave one 10-valued card behind).

When played this way, the winnability drops just slightly down to 98.1%.

Discarding Triples with Wrapping Not Allowed

In the book 150 Ways to Play Solitaire by Alphonse Moyse, Jr., the description of Decade makes no mention of being able to discard any of the row's leftmost cards. Personally, I find this version to be far less satisfying than when allowing wrapping. There are fewer choices to make (and therefore less skill involved), the discards don't open up opportunities for additional discards, the win rate is very low, and the game often seems hopeless fairly quickly.

I assume many players would probably play this variation of the game by simply removing the rightmost triple whenever possible, which results in a win rate of less than 1 in 500,000!

There are situations when it makes sense to decline to discard a triple (depending upon the particular cards already discarded, and how many cards are left in the stock), so a good player can actually do slightly better than this.

Discarding Triples After Dealing All Cards First

An alternative way of playing when wrapping is not allowed, is to deal out all the cards first in a big long row, and then removing the triples in any order you wish.

This helps a llttle bit, but the odds of winning are still under 1 in 200,000.

Discarding Two or More After Dealing All Cards First

The web site onlinesologames.com offers a version of Decade with all cards dealt out, but instead of being limited to discarding triples, the player may discard sets containing two or more consecutive cards.

This way of playing results in a much higher win rate. The solver found that 86.1% of deals are winnable, but a human player is doing well to win about half of that.

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

Main page

Copyright ©2024 by Mark Masten. All rights reserved.