Dale Yu: Preview of 21X


  • Designer: Leo Samson
  • Publisher: Naylor Games
  • Players: 1-6
  • Age: 10+
  • Time: 15 min
  • Played with preview copy provided by publisher

21X is one of those quirky games that based on the description – immediately caught my eye, and honestly, I thought it was one of the games brought home from one of James Nathan’s Japan trips.   However, this one was sent to me from the UK, and as soon as it arrived, we were playing the game “21X: Blackjack for Math Lovers”.

The game is made up of a 54 card deck, each with a mini-formula on the card where X is a whole number chosen by the player and N is the number of cards that the player currently has.  There are 3 levels of cards in the game, and as you would suspect, there is an increasing amount of complexity in the cards as you progress through the levels.

Level 1 – addition, subtraction, multiplication

Level 2 – division, brackets, exponents

Level 3 – even more complex stuff

Once you set up the deck, each player is dealt two cards facedown.  The player aids, which would also be helpful for a junior high math student, remind you of BIDMAS – the order of operations that you may need.

When everyone is ready, the cards are revealed, and each player tries to set a value for X to get them to 21 exactly, or at least as close as possible without going over.  X must be a whole non-zero number, though it can be positive or negative.  It is the same for all cards in the player’s hand.  

If someone thinks they can score 21, they yell out “21” and try to prove their math skills.  If they are right, they win the round.  If they are wrong, they are eliminated and all of their friends summarily make fun of their error.

If no one can get to 21, there are two options:

A] Twisting – at any time, you can say “twist” and draw another card and add it to your hand.  You may never have more than 5 cards.  Note that each time you add a card to your hand, this will change the N value


B] Sticking – if you think you can’t make 21, you can decide to “stick”.  You call out your hand’s value (as well as your chosen X value).  All other players now have a minute to finish (either get to 21 or as close as possible).  Once you have stuck on a number, you can’t change your mind.  You can stick on a fraction, and you may not stick on exactly 20.  

If someone makes exactly 21 in this final minute, they win the round.  Otherwise, at the end of the minute, the player who is closest to 21 without going over (and NOT exactly 20) wins.  The reason you can’t win with 20 is because the way the cards are set up, it’s too easy to get 20 – so the designer has just taken that option away from you!

Play however many rounds you like and whoever reaches the predetermined number of round wins first is the overall winner.

My thoughts on the game

This is one of those games that you’re either going to love or hate.  Well, at least that is the experience that I’ve seen when I’ve introduced it to people.  It certainly requires a requisite amount of mental mathematical ability, or a scientific calculator app on your phone.  

For me, I love playing with the numbers in my head, trying to figure out how each additional card will increment my “n” value, and then what “x” values will work with those changes.  With the low and medium difficulty cards, I can easily do everything in my head. When the most complex cards are added in- things can get a bit spicy when trying to work this all out in your head.

For me, I’m fine just trying to work things out in my head, and not use a calculator until I’ve decided on values and have chosen to stick.  This, admittedly, is not a super successful strategy, and the number of times I have ended up quite far away from 21 is high.  The non-mathematically inclined have had a more difficult time with the game, and I can easily see why.   The fun is in the wacky formulae that you have to work through in your head, and the complicated cards give you this in spades; however, they are the same cards that can melt non-STEM brains.

The only other thing about the game is that there isn’t much you can do if you don’t see a fairly easy path from your first two or three cards.  Each time you add a card, the math involved to figure things out increases to the point where you end up not having enough time to figure things out before someone else triggers the end of the round.

There is definitely an interesting game going on here, and one that I enjoy trying to play from time to time; but it’s commendable more for its intent than the fun it delivers.  Maybe I’ll have a better time with it when I next head to Boston for the MIT puzzle hunt; that might be my best chance of getting a game full of people who can do the math.  But as long as there is a risk of a liberal arts person in my game group, this one is best viewed as a curiosity.

If you know who Ramanujan or Erdős is (without having to look it up), I would strongly recommend this one.  If you’re more into Hemingway or Austen; try it once before buying!

Thoughts from other Opinionated Gamers

Joe Huber (1 play): I think I enjoyed 21x more than anyone else at the table – all of whom gave up after two hands, and I suspect only played a second hand at my urging.  The issue with 21x as a game was actually summed up beautifully by the two hands.  On the second hand, I was able to trivially get to 21.  On the first hand, I was initially dealt:

4n/x and 4

Since x must be an integer, and n was 2 at that point, I wasn’t going to get closer to 21 than 12.  So I drew another card:

– (n-1)

That doesn’t help.  Maybe the next one would:


There is a limit of five cards, but the set I had was useless, so I drew my final card:


This would have, just, been enough for me to win the point; with x=44, the sum is approximately 20.65, which would have been enough to win the point.  But there’s only a minute, after someone decides they’re done, to find a solution; when time ran out I knew the best value for x was greater than 37 but smaller than 50, but I hadn’t reached the best answer.  Even if trying to solve quadratic equations in your head with non-integral solutions is your idea of a good time, you may well be frustrated by the vast differences in the level of challenge provided.

Dan B. (1 play): I like the idea a lot, but the implementation has issues. Joe’s explanation covers most of what I would say about those; I would just note that there’s no guarantee that you can get anywhere close to 21 with random cards. 

The game might work better if everyone were given one red and one black card at the start and then could draw either type at will; I think this would make it more likely that everyone can get reasonably close to 21 (but I haven’t inspected the cards closely let alone tried this, so no promises). Even so, I think there’s a more fundamental problem which is that finding a solution to your puzzle can be done by guesswork, but checking it is difficult; the only way to make the actual solution-finding difficult is to do as Joe implies and combine your cards into a single equation in your head, which you then solve. To me this seems rather different from other puzzle games such as Ricochet Robot, where finding the solution is interesting.

Until your next appointment

The Gaming Doctor

About Dale Yu

Dale Yu is the Editor of the Opinionated Gamers. He can occasionally be found working as a volunteer administrator for BoardGameGeek, and he previously wrote for BoardGame News.
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