{"id":10191,"date":"2024-08-21T04:00:00","date_gmt":"2024-08-21T10:00:00","guid":{"rendered":"https:\/\/milesearnandburn.com\/?p=10191"},"modified":"2024-08-21T14:44:49","modified_gmt":"2024-08-21T20:44:49","slug":"wednesday-wisdom-the-kelly-criterion-for-resellers","status":"publish","type":"post","link":"https:\/\/milesearnandburn.com\/index.php\/2024\/08\/21\/wednesday-wisdom-the-kelly-criterion-for-resellers\/","title":{"rendered":"Wednesday Wisdom: The Kelly Criterion for Resellers"},"content":{"rendered":"\n<p><em>EDITOR&#8217;S NOTE: If the math formula doesn&#8217;t render correctly in your reader, <a href=\"https:\/\/milesearnandburn.com\/index.php\/2024\/08\/21\/wednesday-wisdom-the-kelly-criterion-for-resellers\/\">check the website at this link<\/a>.<\/em><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Introduction<\/h4>\n\n\n\n<p>In advantage play (gambling with an edge over the house), the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Kelly_criterion\">Kelly Criterion or Kelly Formula<\/a> gives a simple calculation for the best amount to bet to maximize earnings. We can draw an analog for resellers, whether it&#8217;s the buyer&#8217;s group kind or the gift card arbitrage kind. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\">The Propeller Head Part<\/h4>\n\n\n\n<p>The generalized Kelly formula, rewriting a bit to express terms familiar to resellers, is:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\%_{float} = \\frac{(1-p_{loss})}{\\%_{loss}} - \\frac{p_{loss}}{\\%_{gain}}<\/pre><\/div>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>%<sub>float<\/sub><\/em> = The percentage of your budget to float<\/li>\n\n\n\n<li><em>p<sub>loss<\/sub><\/em> = The probability that you&#8217;re going to lose your profit<\/li>\n\n\n\n<li><em>%<sub>loss<\/sub><\/em> = The percentage you&#8217;ll lose if a loss happens<\/li>\n\n\n\n<li><em>%<sub>gain<\/sub><\/em>= The percentage you&#8217;ll gain if you don&#8217;t lose<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">A Simple and Specific Example<\/h4>\n\n\n\n<p>Let&#8217;s look at Pepper, <a href=\"https:\/\/gcgalore.com\/why-im-cautious-about-pepper-rewards-deals\/\">which may or may not pull the rug out from under you at any point in the next year<\/a>. With Pepper, you&#8217;re probably earning about 3.9% from your credit card (4x Membership Rewards,  worth 4.4% cash back, times 90% due to Pepper&#8217;s convoluted redemption). Assuming your buy rate equals your sell rate after rewards are paid out (buy at 90%, sell at 90%), then we&#8217;ve got a simple calculation:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>p<sub>loss<\/sub><\/em> = 10% (pick your own number here, but let&#8217;s say there&#8217;s a 1 out of 10 chance of Pepper failure)<\/li>\n\n\n\n<li><em>%<sub>loss<\/sub><\/em> = 10% (worst case you lose all of the discount Pepper gives) <\/li>\n\n\n\n<li><em>%<sub>gain<\/sub><\/em>= 3.9% (the percentage you&#8217;ll gain if you don&#8217;t lose, in this case Membership Rewards)<\/li>\n<\/ul>\n\n\n\n<p>Then run the numbers and get:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>%<sub>float<\/sub><\/em> = <em>(1-0.10)\/0.10 &#8211; 0.10\/0.039<\/em> <em>= 644%<\/em> (when probability of loss = 10%)<\/li>\n<\/ul>\n\n\n\n<p>What the hell, you might ask? Why is that number over 100%, and how do I invest that much? Well, the answer is either (1) you should float all of your bank roll to maximize profit because you&#8217;re much more likely to win than lose, or (2) you need 5.44 other players to help you.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Increasing the Chance of Failure<\/h4>\n\n\n\n<p>What if you think there&#8217;s a 30% chance of Pepper failure though? The calculation is again simple:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>%<sub>float<\/sub> = (1-0.30)\/0.10 &#8211; 0.30\/0.039 = -692%<\/em> (when probability of loss = 30%)<\/li>\n<\/ul>\n\n\n\n<p>What the double hell, you might ask? Why is that number over 100% <em>and<\/em> also negative? The formula is telling you that if you think Pepper&#8217;s got a 30% chance of failure in the next 30 days, you shouldn&#8217;t invest anything; &#8220;kill it with fire&#8221; says the formula.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Finding the Middle Ground<\/h4>\n\n\n\n<p>So, what&#8217;s the cut-off at which the formula switches from <em>LFG<\/em> to <em>hells-to-the-no<\/em>? I&#8217;ll spare you the algebra, but it&#8217;s easy to find by setting <em>%<sub>float<\/sub>=0<\/em> and solving for <em>p<sub>loss<\/sub><\/em>. Doing that gives:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>p<sub>loss<\/sub> (cutoff point) = 0.2806 = 28.06%<\/em><\/li>\n<\/ul>\n\n\n\n<p>In other words, if you think Pepper is &lt; 28% likely to fail before you can cash out your rewards, you&#8217;ll maximize your profits by playing the resell game. If you think Pepper is \u2265 28% likely to fail, stay away. (<a href=\"https:\/\/milesearnandburn.com\/wp-content\/uploads\/2024\/08\/output.png\">I generated a boring graph illustrating how float percentage varies with the probability of loss for turbo-nerds here<\/a>).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Conclusion<\/h4>\n\n\n\n<p>The Kelly criterion is surprisingly insensitive for churning problems, switching from above 100% (1.0) to below 0 very quickly. But, if you&#8217;re 3\/4 certain that Pepper isn&#8217;t going to fail before your rewards are paid out, keep going.<\/p>\n\n\n\n<p>Special thanks to <a href=\"https:\/\/x.com\/halfkelly\">John Reeder<\/a> for poking me on the subject, and another special thanks to John for the idea for a follow-up piece on the subject: what if you know they&#8217;re gonna steal your money, but not when? Stay tuned, or, like yesterday, don&#8217;t; you do you.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"606\" src=\"https:\/\/milesearnandburn.com\/wp-content\/uploads\/2024\/08\/image-10-1024x606.png\" alt=\"\" class=\"wp-image-10195\" style=\"width:420px\" srcset=\"https:\/\/milesearnandburn.com\/wp-content\/uploads\/2024\/08\/image-10-1024x606.png 1024w, https:\/\/milesearnandburn.com\/wp-content\/uploads\/2024\/08\/image-10-300x178.png 300w, https:\/\/milesearnandburn.com\/wp-content\/uploads\/2024\/08\/image-10-768x454.png 768w, https:\/\/milesearnandburn.com\/wp-content\/uploads\/2024\/08\/image-10-1536x909.png 1536w, https:\/\/milesearnandburn.com\/wp-content\/uploads\/2024\/08\/image-10-1320x781.png 1320w, https:\/\/milesearnandburn.com\/wp-content\/uploads\/2024\/08\/image-10.png 1974w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center\" style=\"font-size:14px\">Another helpful MEAB plot.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>EDITOR&#8217;S NOTE: If the math formula doesn&#8217;t render correctly in your reader, check the website at this link. Introduction In advantage play (gambling with an<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_editorskit_title_hidden":false,"_editorskit_reading_time":0,"_editorskit_is_block_options_detached":false,"_editorskit_block_options_position":"{}","footnotes":""},"categories":[53,56],"tags":[],"class_list":["post-10191","post","type-post","status-publish","format-standard","hentry","category-gift-cards","category-wisdom"],"_links":{"self":[{"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/posts\/10191","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/comments?post=10191"}],"version-history":[{"count":6,"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/posts\/10191\/revisions"}],"predecessor-version":[{"id":10204,"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/posts\/10191\/revisions\/10204"}],"wp:attachment":[{"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/media?parent=10191"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/categories?post=10191"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/milesearnandburn.com\/index.php\/wp-json\/wp\/v2\/tags?post=10191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}