Wonderland is full of games that are immensely unfair and illogical. Take the croquet game, which is played on an uneven turf and uses live creatures for balls and mallets.  Carroll explains through Alice’s point of view:

     Alice thought she had never seen such a curious croquet-ground in her life: it was all ridges and furrows: the croquet balls were live hedgehogs, and the mallets live flamingoes, and the soldiers had to double themselves up and stand on their hands and feet, to make the arches.

The live creatures make it a game of random chance rather than skill.  They also make it wonderfully loopy and fun and imaginative.  Could Carroll be mocking here a Victorian game that is a bit staid and stuffy?  He wants rules that are fair and that work, but he also loves defying rules and logic.​
​     Alice says to the Cheshire Cat:

 “I don’t think they play at all fairly,” Alice began, in rather a complaining tone, “and they all quarrel so dreadfully one ca’n’t hear oneself speak—and they don’t seem to have any rules in particular: at least, if there are, nobody attends to them—and you’ve no idea how confusing it is all the things being alive: for instance, there’s the arch I’ve got to go through next walking about at the other end of the ground—and I should have croqueted the Queen’s hedgehog just now, only it ran away when it saw mine coming.”

​    On the one hand, I hear in Alice’s petulance  Lewis Carroll’s frustration with a world that does not work logically.  He was, after all, a logician.  On the other hand, how much more fun and wondrous is a game with live creatures than a game with plain wooden sticks and wire wickets?  Just look at this picture of a real Victorian croquet game.  It is not at all inspiring.

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  ​      I am  indebted to Alice Medinger for reminding me of the Caucus Race and its connection to American politics in her beautifully illustrated blog post:  https://medinger.wordpress.com/2016/01/26/lewis-carrolls-caucus-race/.   
​The caucus race is another illogical and unfair game. Again, the course is uneven and the rules are unclear.
     First it [the Dodo] marked out a race-course, in a sort of circle, (“the exact shape doesn’t matter,” it said,) and then all the party were placed along the course, here and there.  There was no “One, two three, and away!” but they began running when they liked, so that it was not easy to know when the race was over.​​
     What on earth would Carroll have made of this year’s Iowa caucuses?  In Alice in Wonderland, when everyone asks the Dodo who has won the caucus race, he says: “Everybody has won, and all must have prizes.”  What if the election in Iowa doesn’t eliminate any candidates?  What if everyone wins and keeps running around in “a sort of circle” endlessly?  It feels as though this has already happened. Carroll was eerily prescient.

​http://www.nytimes.com/2015/10/12/opinion/the-importance-of-recreational-math.html?_r=0
      It’s funny for me to be writing a blog post in response to an article about recreational math.  I am after all the most mathematically challenged person in the universe.  My children realized by about fourth grade that they had already surpassed me.  When students ask what they need to make on a test to get an A in my class, I tell them they will have to do that math themselves. 
      But enough about my math challenges.  I was surprised to see in the article the name Martin Gardner and to discover that he was famous in the math world for creating elaborate puzzles.  I, of course, know Martin Gardner as the editor of the annotated Alice in Wonderland.  

       And it makes perfect sense that as a mathematician, Martin Gardner would be interested in Lewis Carroll.  Lewis Carroll taught mathematics and logic at Oxford. 
       But the more important connection between Gardner and Carroll is their love of puzzles and play, their belief that learning should be fun.  Perhaps if I had played more mathematical games, I would have less trouble now adding up my students’ grades.  And I certainly hope, as the article suggests, that recreational mathematics will find a place in the Common Core.

            Supervised by her governess, Miss Prickett, and shuffled between lessons and fittings by her ambitious mother, Alice could only pretend to be a child of nature.

            Of course it is deeply problematic to idealize and prettify childhood poverty, but Dodgson was on to something in opposing the overly structured lives of middle and upper class Victorian children.   In a letter to May Forshall, one of his child friends, he wrote: “Do you ever play at games?  Or is your idea of life “breakfast, lessons, dinner, lessons, tea, lessons, bed, lessons, breakfast, lessons,” and so on?  It is a very neat plan of life and almost as interesting as being a sewing machine or a coffee grinder.”  Just the word coffee grinder evokes images of Dickens’ Mr. Gradgrind stuffing facts down little childrens’ throats and destroying their imaginations.

            When he asks Miss Forshall if she plays at “games,” Dodgson does not mean exclusive, organized sports like cricket, which he associates with wealth and privilege.

                  Ill fares the place, to luxury a prey,

                  Where wealth accumulates, and minds decay;

                  Athletic sports may flourish or may fade,

                  Fashion may make them, even as it has made;

                  But the broad Parks, the city’s joy and pride,

                 When once destroyed can never be supplied!

                  Rather he means the kind of imaginative games that children invent on their own, games without “pavilions” and “scorers’ tents,” games without winners and losers, games without complicated and absurd rules.  

                  Dodgson was obsessed with childhood and children because they represented for him freedom from the oppressive constraints of Victorian life.  They represented freedom from finicky indoor spaces, freedom from ticking wristwatches, freedom from attention to manners and dress, and finally freedom from the burdens of his academic work.