{"id":8,"date":"2016-09-06T04:25:06","date_gmt":"2016-09-06T04:25:06","guid":{"rendered":"http:\/\/jonlyons.net\/blog\/?p=8"},"modified":"2017-08-06T01:22:45","modified_gmt":"2017-08-06T01:22:45","slug":"how-to-be-a-winner-at-the-game-of-life","status":"publish","type":"post","link":"http:\/\/jonlyons.net\/blog\/2016\/09\/06\/how-to-be-a-winner-at-the-game-of-life\/","title":{"rendered":"How to be a Winner at the Game of Life"},"content":{"rendered":"<p>Sorry, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Conway%27s_Game_of_Life\">Conway<\/a> fans, this one isn\u2019t for you.\u00a0 This is for everyone who grew up playing\u00a0Milton Bradley\u2019s board game The Game of Life.\u00a0 The game puts you in control of your own destiny as you drive your car through the decades and into retirement.\u00a0 On the way, your fate is forged by choices you make and the spin of a clicky wheel.\u00a0 While luck is clearly a big part of the game, I\u2019ve always wondered how important those few choices really are.\u00a0 To answer that question, I wrote a <a href=\"https:\/\/github.com\/JonMLyons\/GameOfLifeSimulator\">small program to simulate the game<\/a>.\u00a0 Armed with the ability to simulate over 50,000 games per second, I confirmed what we probably all already knew were the best choices to make when playing the game.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/usedphotosna\/42937718_614.jpg\" alt=\"The Game of Life\" width=\"386\" height=\"290\" \/><\/p>\n<h1>Strategy<\/h1>\n<p>Game of Life\u00a0players only have a few decisions to make.\u00a0 I simulated the effect of each decision in 1 million simulated head-to-head matchups.<\/p>\n<table style=\"height: 341px;\" width=\"584\" align=\"Center\">\n<tbody>\n<tr>\n<td width=\"27%\"><\/td>\n<td style=\"text-align: center;\" width=\"25%\"><strong>Losing Strategy<br \/>\nWin Percentage<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"25%\"><strong>Winning Strategy<br \/>\nWin Percentage<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"23%\"><strong>Difference<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Buy Stock<\/strong><\/td>\n<td style=\"text-align: center;\">25.7%<\/td>\n<td style=\"text-align: center;\">74.2%<\/td>\n<td style=\"text-align: center;\">48.5<\/td>\n<\/tr>\n<tr>\n<td><strong>Buy Life Insurance<\/strong><\/td>\n<td style=\"text-align: center;\">35.7%<\/td>\n<td style=\"text-align: center;\">64.3%<\/td>\n<td style=\"text-align: center;\">28.6<\/td>\n<\/tr>\n<tr>\n<td><strong>Go to College<\/strong><\/td>\n<td style=\"text-align: center;\">39.8%<\/td>\n<td style=\"text-align: center;\">60.2%<\/td>\n<td style=\"text-align: center;\">20.4<\/td>\n<\/tr>\n<tr>\n<td><strong>Play the Market<\/strong><\/td>\n<td style=\"text-align: center;\">46.8%<\/td>\n<td style=\"text-align: center;\">53.2%<\/td>\n<td style=\"text-align: center;\">6.3<\/td>\n<\/tr>\n<tr>\n<td><strong>Play Lucky Days<\/strong><\/td>\n<td style=\"text-align: center;\">48.0%<\/td>\n<td style=\"text-align: center;\">52.0%<\/td>\n<td style=\"text-align: center;\">4.0<\/td>\n<\/tr>\n<tr>\n<td><strong>Buy Fire Insurance<\/strong><\/td>\n<td style=\"text-align: center;\">49.5%<\/td>\n<td style=\"text-align: center;\">50.5%<\/td>\n<td style=\"text-align: center;\">1.1<\/td>\n<\/tr>\n<tr>\n<td><strong>Buy Auto Insurance<\/strong><\/td>\n<td style=\"text-align: center;\">49.8%<\/td>\n<td style=\"text-align: center;\">50.1%<\/td>\n<td style=\"text-align: center;\">0.3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><\/h2>\n<h2>Buy Stock (74.2% wins)<\/h2>\n<p>This is <strong><em>the<\/em><\/strong> most important choice you can make in Life.\u00a0 A player who buys stock will win the game 74.2% of the time vs. a player who does not.\u00a0 Stock allows you to play the market (more on this later) and also reveals a number of bonus tiles along the board.\u00a0 Not to mention, even if you do nothing with your stock certificate, it\u2019s worth $120,000 at the end of the game.\u00a0 Just buy it!<\/p>\n<h2>Buy Life Insurance (64.3% wins)<\/h2>\n<p>Does anyone really realize how important life insurance is in this game?\u00a0 It\u2019s the second most important factor after buying stock.\u00a0 A player with Life Insurance will win head-to-head 64.3% of the time against a player who does not.<\/p>\n<h2>Pick the University track (60.2% wins)<\/h2>\n<p>We all knew this one, right?\u00a0 Early on, the game asks you to decide whether to go on the University track or the faster Business track.\u00a0 It\u2019s pretty clear that slow-but-steady wins the race and University is the way to go.\u00a0 The simulator confirms it with 60.2% of University players winning in a head-to-head over Business players.\u00a0 I think the only surprising thing here is that the game tells us that going to college is <strong>less important than buying life insurance<\/strong>.<\/p>\n<h2>Play the Market if you Own stock (53.2% wins)<\/h2>\n<p>If you bought stock (and per above, you should!), you\u2019re often given the option to play the market.\u00a0 Just do it!\u00a0 Each time, there is a 30% chance you\u2019ll lose $60,000 and a 40% chance you\u2019ll make $120,000.\u00a0 That\u2019s an expected value of $30,000 each time.\u00a0 Bet on the odds and go for it.\u00a0 The simulator shows that those who do will win 53.2% of the time over those who don\u2019t.<\/p>\n<h2>Bet on Lucky Days (52.0% wins)<\/h2>\n<p>When you land on a Lucky Day space you are given two $10,000 bills.\u00a0 You can keep them, or put each one on a different number of the wheel.\u00a0 If the wheel hits your number, you win $300,000.\u00a0 If not, you lose your original $20,000.\u00a0 That\u2019s an expected value of $44,000.\u00a0 This comes up less frequently in the game than playing the market, so even though it\u2019s a bigger expected value, this strategy has slightly less impact than playing the market.\u00a0 Those who bet on Lucky Days will win 52.0% of the time vs. those who don\u2019t.<\/p>\n<h2>Buy Fire Insurance (50.5% wins)<\/h2>\n<p>We\u2019re getting into diminishing returns here.\u00a0 Fire insurance owners will win 50.5% of the time vs. those who don\u2019t have it.<\/p>\n<h2>Buy Auto Insurance (50.1% wins)<\/h2>\n<p>Buy auto insurance if you want to play optimally.\u00a0 Skip it if you want to impress your friends with your brazen strategy.\u00a0 Those with auto insurance will win 50.1% of the time vs. an opponent without it.\u00a0 It\u2019s almost even odds.<\/p>\n<h2>Combined Optimal Strategies vs. Combined Losing Strategies<\/h2>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone aligncenter\" src=\"https:\/\/s-media-cache-ak0.pinimg.com\/736x\/0d\/7b\/1f\/0d7b1fef781675391fcf381aafd50f59.jpg\" width=\"292\" height=\"219\" \/><\/p>\n<p>If you compare a player who plays optimally in each strategy defined above with a player who plays all of the opposite losing strategies, the optimal player will win the game 93.3% of the time.<\/p>\n<h1>Player Order<\/h1>\n<p>Going first in the Game of Life gets you a small but noticeable advantage.\u00a0 There\u2019s ultimately still some fairness here since order is determined by spinning the wheel.\u00a0 Here are your odds of winning a game based on the order in which you start.<\/p>\n<table width=\"827\" align=\"Center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"100\">\u00a0<strong>Number of Players<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"101\"><strong>Player 1<br \/>\nWin %\u00a0<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"72\"><strong>Player 2<br \/>\nWin %<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"72\"><strong>Player 3<br \/>\nWin %\u00a0<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"88\"><strong>Player 4<br \/>\nWin %\u00a0<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"72\"><strong>Player 5<br \/>\nWin %\u00a0<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"72\"><strong>Player 6<br \/>\nWin %\u00a0<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"72\"><strong>Player 7<br \/>\nWin %\u00a0<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"72\"><strong>Player 8<br \/>\nWin %<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>2<\/strong><\/td>\n<td style=\"text-align: center;\">50.8%<\/td>\n<td style=\"text-align: center;\">49.2%<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>3<\/strong><\/td>\n<td style=\"text-align: center;\">34.1%<\/td>\n<td style=\"text-align: center;\">33.3%<\/td>\n<td style=\"text-align: center;\">32.5%<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>4<\/strong><\/td>\n<td style=\"text-align: center;\">25.7%<\/td>\n<td style=\"text-align: center;\">25.1%<\/td>\n<td style=\"text-align: center;\">24.7%<\/td>\n<td style=\"text-align: center;\">24.4%<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>5<\/strong><\/td>\n<td style=\"text-align: center;\">20.7%<\/td>\n<td style=\"text-align: center;\">20.3%<\/td>\n<td style=\"text-align: center;\">19.9%<\/td>\n<td style=\"text-align: center;\">19.7%<\/td>\n<td style=\"text-align: center;\">19.4%<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>6<\/strong><\/td>\n<td style=\"text-align: center;\">17.3%<\/td>\n<td style=\"text-align: center;\">16.9%<\/td>\n<td style=\"text-align: center;\">16.7%<\/td>\n<td style=\"text-align: center;\">16.5%<\/td>\n<td style=\"text-align: center;\">16.4%<\/td>\n<td style=\"text-align: center;\">16.1%<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>7<\/strong><\/td>\n<td style=\"text-align: center;\">14.7%<\/td>\n<td style=\"text-align: center;\">14.5%<\/td>\n<td style=\"text-align: center;\">14.5%<\/td>\n<td style=\"text-align: center;\">14.2%<\/td>\n<td style=\"text-align: center;\">14.1%<\/td>\n<td style=\"text-align: center;\">14.0%<\/td>\n<td style=\"text-align: center;\">13.8%<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>8<\/strong><\/td>\n<td style=\"text-align: center;\">13.0%<\/td>\n<td style=\"text-align: center;\">12.8%<\/td>\n<td style=\"text-align: center;\">12.6%<\/td>\n<td style=\"text-align: center;\">12.5%<\/td>\n<td style=\"text-align: center;\">12.4%<\/td>\n<td style=\"text-align: center;\">12.3%<\/td>\n<td style=\"text-align: center;\">12.2%<\/td>\n<td style=\"text-align: center;\">12.0%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h1>Career<\/h1>\n<p>While you can\u2019t control your Career (aside from choosing Business vs. University), it is one of the most important factors in the game.\u00a0 Career determines your salary which is strongly correlated with how much money you will have at the end of the game.<\/p>\n<table style=\"height: 307px;\" width=\"544\" align=\"Center\">\n<tbody>\n<tr>\n<td width=\"116\"><\/td>\n<td style=\"text-align: center;\" width=\"100\"><strong>Chances of Getting this Career<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"100\"><strong>Salary<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"100\"><strong>Average Wealth<br \/>\n<\/strong><strong>at End of Game<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Doctor<\/strong><\/td>\n<td style=\"text-align: center;\">21.4%<\/td>\n<td style=\"text-align: center;\">$50,000<\/td>\n<td style=\"text-align: center;\">$1,985,690<\/td>\n<\/tr>\n<tr>\n<td><strong>Lawyer<\/strong><\/td>\n<td style=\"text-align: center;\">11.4%<\/td>\n<td style=\"text-align: center;\">$50,000<\/td>\n<td style=\"text-align: center;\">$1,972,915<\/td>\n<\/tr>\n<tr>\n<td><strong>Physicist<\/strong><\/td>\n<td style=\"text-align: center;\">9.3%<\/td>\n<td style=\"text-align: center;\">$30,000<\/td>\n<td style=\"text-align: center;\">$1,646,089<\/td>\n<\/tr>\n<tr>\n<td><strong>Journalist<\/strong><\/td>\n<td style=\"text-align: center;\">21.4%<\/td>\n<td style=\"text-align: center;\">$24,000<\/td>\n<td style=\"text-align: center;\">$1,567,040<\/td>\n<\/tr>\n<tr>\n<td><strong>Teacher<\/strong><\/td>\n<td style=\"text-align: center;\">10.4%<\/td>\n<td style=\"text-align: center;\">$20,000<\/td>\n<td style=\"text-align: center;\">$1,489,827<\/td>\n<\/tr>\n<tr>\n<td><strong>University<\/strong><\/td>\n<td style=\"text-align: center;\">26.0%<\/td>\n<td style=\"text-align: center;\">$16,000<\/td>\n<td style=\"text-align: center;\">$1,446,165<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>Most games are won by a player with the highest salary.<\/p>\n<table style=\"height: 389px;\" width=\"472\" align=\"Center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"30%\"><strong>\u00a0Number of Players<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"70%\"><strong>Percent of Games Where Winner has the Highest Salary<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>2<\/strong><\/td>\n<td style=\"text-align: center;\">72.6%<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>3<\/strong><\/td>\n<td style=\"text-align: center;\">63.0%<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>4<\/strong><\/td>\n<td style=\"text-align: center;\">59.5%<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>5<\/strong><\/td>\n<td style=\"text-align: center;\">58.2%<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>6<\/strong><\/td>\n<td style=\"text-align: center;\">58.0%<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>7<\/strong><\/td>\n<td style=\"text-align: center;\">58.0%<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>8<\/strong><\/td>\n<td style=\"text-align: center;\">58.6%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Methodology<\/h1>\n<p>All statistics were produced using a custom game simulator written in C# and <a href=\"http:\/\/jonlyons.net\/blog\/wp-admin\/post.php?post=8&amp;action=edit\">available as open source on GitHub<\/a>.\u00a0 A simulated game contains 2-8 players, each with its own \u201cpersonality\u201d.\u00a0 Each simulated player takes turns spinning the \u201cwheel\u201d and moves tile-to-tile like in a real game.\u00a0 Certain tiles require special actions that are coded into the simulation (e.g., stop to get married).\u00a0 Some tiles also allow players to make one of the decisions described above (e.g., buy stock, play the market, etc.).\u00a0 The simulated player\u2019s \u201cpersonality\u201d determines which decision it will make.\u00a0 The statistics above were all generated using 1 million sequential games.\u00a0 Player order was randomized, except in the case where I was deliberately measuring the effect of player order.<\/p>\n<p>For the head-to-head strategy comparisons, each strategy option (e.g., buying stock) was evaluated against a player who made the opposite decision for that strategy (e.g., not buying stock), but otherwise played \u201coptimally\u201d.<\/p>\n<h1>Future Improvements<\/h1>\n<p>There are a few things I didn\u2019t account for in the simulation.\u00a0 The code is all available online, and contributions to improve these or other factors are welcome!<\/p>\n<ol>\n<li><strong>Revenge tiles<\/strong> in the real game allow you to take $200,000 from any player or to send any player back 10 spaces. I didn\u2019t simulate that perfectly or even pick a great strategy.\u00a0 A simulated player who lands on Revenge picks an opposing player at random and steals $200,000 or all the money that person has, whichever is less.<\/li>\n<li><strong>Share the Wealth cards<\/strong> are given to players in the real game when they land in a Pay Day space by an exact count. You can then play the card later for benefits throughout the game.\u00a0 Growing up, we never played with these cards.\u00a0 I didn\u2019t simulate them either.<\/li>\n<li><strong>Borrowing from the Bank<\/strong> becomes necessary when you run out of money. In the real game, you need to do this in discrete $20,000 increments.\u00a0 For simplicity, I ignored that detail and allow players to go into the red by any amount.\u00a0 I do properly simulate 5% interest on that amount.<\/li>\n<li>Betting on the wheel is allowed in the real game, but it\u2019s basically straight odds. It could be useful if you know you\u2019re behind, but I ignored it in the simulation.<\/li>\n<li>At the end of a real game, a player can try to become a <strong>Millionaire Tycoon<\/strong>. This is a 1\/10 shot of winning the game immediately.\u00a0 If the player fails, he or she loses everything.\u00a0 It\u2019s actually not a bad option for players who know they\u2019re far behind on wealth and have no other shot.\u00a0 I didn\u2019t simulate Millionaire Tycoons.\u00a0 Winners are determined solely by their wealth at the end of the game.<\/li>\n<\/ol>\n<h1>Summary<\/h1>\n<p>Want to be a winner at the Game of Life?\u00a0 Play it exactly how your parents would have told you to play it.<\/p>\n<p align=\"center\"><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/IWXghSfJStc\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sorry, Conway fans, this one isn\u2019t for you.\u00a0 This is for everyone who grew up playing\u00a0Milton Bradley\u2019s board game The Game of Life.\u00a0 The game puts you in control of your own destiny as you drive your car through the decades and into retirement.\u00a0 On the way, your fate is forged by choices you make [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false},"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/posts\/8"}],"collection":[{"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/comments?post=8"}],"version-history":[{"count":9,"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/posts\/8\/revisions"}],"predecessor-version":[{"id":21,"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/posts\/8\/revisions\/21"}],"wp:attachment":[{"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/media?parent=8"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/categories?post=8"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jonlyons.net\/blog\/wp-json\/wp\/v2\/tags?post=8"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}