It’s a corporate Christmas party, around 1999. The dot com crash hasn’t happened yet, the party-organisers have a considerable budget, 200-300 guests, and an idea of a good time strongly influenced by the company’s sales and marketing teams – people who have a tendency to differ from my idea of a good time.<\/p>\n
After the main course and a few speeches, the MC explains the entertainment for the evening.<\/p>\n
A number of casino tables and croupiers have been hired for the night – roulette, blackjack, craps and the like. Each of the party-goers is issued with $100 worth of fake money, which can be turned into chips and gambled.<\/p>\n
After an hour or so of gambling at the over-crowded tables, everyone will return to their seats to use the fake money to bid in an auction on a few reasonably-valuable prizes.<\/p>\n
Ok, thinking caps on… what is a good betting strategy here? Give it some thought before reading on.<\/p>\n
If you’ve been listening to your maths teacher, you will probably know that (with a few exceptions) casino games are a losing proposition. The maximising strategy is bet zero dollars.<\/p>\n
What are the exceptions? I can think of: corrupt or incompetent croupiers, unbalanced roulette wheels, card-counting in some BlackJack variants and being the house!<\/p>\n
Now, I have seen a croupier, hired for a 21st party, with no real money being bet, attempt to impress a cute blonde by quietly dealing her 4 aces in her first ever game of Texas Hold’Em, and brag to her about it afterwards. So I don’t doubt the existence of corrupt croupiers, but the tables were surrounded by witnesses and bribing a croupier to cheat your workmates is frowned upon by Management, so let’s eliminate that.<\/p>\n
An hour is hardly enough time to detect if and how the roulette wheels was unbalanced. So let’s ignore that.<\/p>\n
Card-counting on BlackJack was possibly an option, but – in the cases where the rules even allow it to be profitable – that is only moving the edge slightly in the player’s favour. Within an hour of playing – especially on a busy table with lots of novices, and hence few hands played, – that edge will be hidden in the noise.<\/p>\n
No, it seems if you want to maximise your expected outcome of fake dollars, you are better off standing back from the tables, and watching.<\/p>\n
If you get a thrill of the chase from gambling, and don’t have a compulsion problem, there is an argument here to go for it, in this innocuous situation. <\/p>\n
You aren’t risking much; your expected value from the whole competition before you start is the value of the prizes (to you) divided by the number of party-goers. I don’t remember exactly what the prizes were, but that number was probably $5-$10.<\/p>\n
Craps is fun! It’s a good night’s entertainment.<\/p>\n
Well, at least, it is for some people. I enjoy playing games of skill, but games of pure luck don’t interest me much. I didn’t actually want to push through people to get to the tables. For me, conversation is fun, and I was happy to talk to the people left behind.<\/p>\n
Well, based on the previous point, the idea is to maximise fun – which is why some people should go gamble, and some people should sit and talk, independent of the competition. But this post is about the competition, so let’s get back to that.<\/p>\n
The idea is to maximise the number of prizes you get, not the number of fake dollars. The fake dollars are really just points. In two hours, they are worth absolutely nothing. <\/p>\n
Your normal gambling strategies (such as Martingale<\/a>, <\/a>Kelly<\/a>, Labouch\u00c3\u00a8re<\/a> – Pro tip: Two of these are mathematically bogus, and the other recommends not betting at a casino.) are designed to try to carefully win small amounts. They want you to walk away with a few more dollars than you started with.<\/p>\n However, in this competition there is an auction at the end. It is winner takes all (or at least, the top few winners share a bounty of a prize each; worse if the top grossing player has more than twice their next rival.)<\/p>\n At a regular casino, if you walk out with $110 after betting $100, you are a winner. If you walk out with $100, without betting any of it, you are a smart person, and doing better than average. But in this competition, 100 points is worthless; it isn’t likely to be in the top few players.<\/p>\n The goal is not to gamble to maximise your expected<\/em> (in the mathematical sense) dollars, but to maximise your chances of being in the top few rankings against your competitors.<\/p>\n All this was going through my mind, a decade ago, as I watched those competitors scramble for positions at the tables.<\/p>\n I kicked myself later for not factoring in another key aspect – that points were transferable, and people are social animals.<\/p>\n As people walked away from the tables with $50 or so, when the realisation dawned on them that the fake money was now worthless to them, they gave the money to their friends with the most chance of winning a bid.<\/p>\n These parcels of money started to snowball, into larger parcels.<\/p>\n A competitor didn’t need to win – they just needed to convince a large group of gullible friends that they had<\/em> won – in order to come into a sizable windfall after the gambling had finished – especially, if they could cast themselves into a underdog position, well-deserving of a little boost to take on the big winners.<\/p>\n How much money would it take to be competitive in the auction? Most people would lose money on the games – that’s how casinos pay their bills, after all. It was likely that some people, betting their normal strategies were likely to do well – perhaps doubling or tripling their money. Combine that with the donations, maybe they would double that again.<\/p>\n Maybe there were a few others out there, like me, who could see the bigger picture, and were betting with the goal of maximising their chances of being in the top few. <\/p>\n I made my decision.<\/p>\n I elbowed my way to the roulette table, converted my fake $100 bill into chips, and placed them all on number 18.<\/p>\n Winning would mean I would walk away with $3600, and a very good chance of taking one of the auction items. Losing would mean I was out of the game. A 1 in 37 chance of winning a prize was much better than my original position.<\/p>\n With this in the back of my mind, I waited for the other bets to be laid, the ball to spin and erratically bounce until it settled into a slot.<\/p>\n …<\/p>\n Of course, it wasn’t at all surprising that my number didn’t win. This is a real story, not a Hollywood movie. Defeated, I pushed back through the crowd and returned to the conversations happening away from the tables. <\/p>\n But I stand by my approach.<\/p>\n I don’t recall how much the auction items went for. In fact, I have a suspicion I left the party before the auction was held. It’s a shame. It is the one data-point that would be good to know if this ever happened again. If the auction items went for $500, then I need not have taken such a big risk; I could have spread my chips over several numbers. If they went for more than $3,600, I would have had to go for more risk.<\/p>\n This story is ostensibly about gambling, but the reason it came to mind is that I have been pondering the design of an AI (artifical intelligence) player for a simple game – totally unrelated to gambling activities.<\/p>\n I am aware that the AI should play looser, make riskier moves with higher payoffs, when it finds itself in a losing position. Even if the expected point value of the game move equivalent to “put it all on 18 equivalent” is less than the expected value of the game move equivalent of “keep your money in your pocket” it may be worthwhile. The true goal is not to maximise your expected points, but to maximise your chance of having more points than your opponent the end of the game.<\/p>\n Alas, I haven’t worked out the right approach yet to do this analysis: I need to be able to answer the question: “If I need 500 points to win, and my competitor needs 225, should I make a move that guarantees me 200 points, or one that has a one in three chance of getting me 400, and two in three of nothing.” I think this question is going to be harder to solve that the entire rest of the AI.<\/p>\n","protected":false},"excerpt":{"rendered":" It’s a corporate Christmas party, around 1999. The dot com crash hasn’t happened yet, the party-organisers have a considerable budget, 200-300 guests, and an idea of a good time strongly influenced by the company’s sales and marketing teams – people who have a tendency to differ from my idea of a good time.<\/p>\n I consider how to maximise my happiness in this situation.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_s2mail":"","footnotes":""},"categories":[23,33],"tags":[195,88],"class_list":["post-1320","post","type-post","status-publish","format-standard","hentry","category-based-on-a-true-story","category-puzzle-solving","tag-christmas","tag-gambling"],"_links":{"self":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts\/1320","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/comments?post=1320"}],"version-history":[{"count":3,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts\/1320\/revisions"}],"predecessor-version":[{"id":1323,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts\/1320\/revisions\/1323"}],"wp:attachment":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/media?parent=1320"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/categories?post=1320"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/tags?post=1320"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Social Factors<\/h3>\n
The Big Unknown<\/h3>\n
My Betting Strategy<\/h3>\n
Coda<\/h3>\n
Coda To The Coda<\/h3>\n