{"id":3206,"date":"2016-03-23T21:36:12","date_gmt":"2016-03-24T04:36:12","guid":{"rendered":"http:\/\/www.dresan.com\/blog\/?p=3206"},"modified":"2017-03-26T14:48:08","modified_gmt":"2017-03-26T21:48:08","slug":"all-the-transitions-of-tic-tac-toe-redux","status":"publish","type":"post","link":"https:\/\/dresan.com\/blog\/2016\/03\/23\/all-the-transitions-of-tic-tac-toe-redux\/","title":{"rendered":"All the Transitions of Tic-Tac-Toe, Redux"},"content":{"rendered":"

\"\"<\/a><\/p>\n

What was supposed to be a quick exercise to help me visualize a reinforcement learning problem has turned into a much larger project, one which I’m reluctantly calling a temporary halt to: a visualization of all the states of Tic-Tac-Toe.<\/p>\n

\"\"<\/a><\/p>\n

What I found is that it’s surprisingly hard to make this work: all the states want to pile on top of each other, and there are a few subtleties to representing it correctly. To make it work, I had to separately represent board positions<\/em> – the typical X’es and Oh’s used in play – from game states<\/em>, such as Start, X Wins, O Wins, and Stalemate.<\/p>\n

\"\"<\/a><\/p>\n

The Mathematica for this is gnarly and a total hack; it probably could be made more efficient to process all 17,000+ transitions of the game, and I definitely need to think of a way to make each state appear in its own, non-overlapping position. But that will require more thought than my crude jitter function above, the time it takes to run each render is way too long to quickly iterate, and I have a novel to finish. I don’t want to get stuck in a grind against a game known for its stalemate.<\/p>\n

\"\"<\/a><\/p>\n

Ugh. You can see the jumble there; it’s hard to see which transitions lead to X’s or O’s victory and which lead to stalemate. I have ideas on how to fix this, but I want my novel done more and first, dag nab it. So let me give you all the transitions of Tic-Tac-Toe in their full glory (22.8mb<\/a>). I could say more about this problem – or I can say what I have, call it victory, and move on.<\/p>\n

\"\"<\/a><\/p>\n

On to the novel. It’s going well.<\/p>\n

-the Centaur<\/p>\n","protected":false},"excerpt":{"rendered":"

What was supposed to be a quick exercise to help me visualize a reinforcement learning problem has turned into a much larger project, one which I’m reluctantly calling a temporary…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[67,8],"class_list":["post-3206","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-gaslights-and-rayguns","tag-intelligence","ratio-2-1","entry"],"_links":{"self":[{"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/posts\/3206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/comments?post=3206"}],"version-history":[{"count":15,"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/posts\/3206\/revisions"}],"predecessor-version":[{"id":3223,"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/posts\/3206\/revisions\/3223"}],"wp:attachment":[{"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/media?parent=3206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/categories?post=3206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dresan.com\/blog\/wp-json\/wp\/v2\/tags?post=3206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}