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Enter Secret Auction; Exit Avocado vs. Cucumber

Note: I was considering omitting this note, but all I'll say is that the post overall has very little moderate-quality fantasy storytelling.


An auctioneer, named Honesty*, greets you as you walk into the gem shop. "We have five gems," she says. "An amethyst, a ruby, an onyx, an emerald, and, most valuable of all, a diamond.** We shall have five rounds of bidding in all. Each round, you provide us with the money you think the gem is worth. The highest bidder has earned the beautiful gem." She begins to whisper. "Oh, and don't tell the boss that you know, but they're actually plastic knockoff gems manufactured in China. That's why we sell them so cheap." As a middle-aged man walks over, the auctioneer starts talking at normal volume again. "Anyway, enjoy the auction." As Honesty walks away, you sit down to play - though this wasn't the gem shop you were expecting.

"Oh, and don't tell the boss that you know, but they're actually plastic knockoff gems manufactured in China. That's why we sell them so cheap." –The fictional auctioneer Honesty
Plastic knockoff gems. Source: veseygallery.co.uk.

Introduction

The Avocado vs. Cucumber game is going on hiatus. I could use this post to try to talk about why, but I'll just leave it in this long footnote.*** What I want to talk about today is my new game, Secret Auction! I'll start things off by explaining the rules to Secret Auction,**** and then what I learned from the playtest. I hope that sounds somewhat fun, because that's where this post is going.


Basic Rules Each player starts with a budget of $15, which happens to equal $1+$2+$3+$4+$5. In each round, progressively more valuable gems will be auctioned off. In Round 1, the gem will be worth 1 point; in Round 2, 2 points; and so on. You can bid any amount of your budget, from $0 to $15, on each gem. Whoever bids highest gets to keep that gem and all of the points that come with it. There's a catch, though. Whether or not you win each secret auction, your bid money is lost. For example, Alice bids $1 on the 1-point amethyst while Bob bids $2. Bob wins 1 point from bidding highest on the amethyst. Both players lose their bids, so Alice now has $14 and Bob has $13 in their pockets. This continues for all five rounds, until each gem is auctioned off. Whoever gets the most points wins.

Whether or not you win each secret auction, your bid money is lost.

Now some less basic rulings:

Handling Ties

If there's a tie for highest bid, I will split the points from the gem between all winning players. For instance, if Alice and Bob both bid highest on the 3-point ruby, I will give Alice and Bob 1.5 points each. If Alice, Bob, and Carol are in a three-way tie, I will give them each 1 point. You get the idea.


Bidding Increment The bidding increment is $0.01. In other words, you don't have to bid a whole number of dollars, but you do have to bid a whole number of cents. Legal bids: $3, $3.50, $3.01 Illegal bids: $3.001, $3.33..., $π

Negative Bids

No negative bids. I'm slightly disappointed no one tried this during the game. (I wouldn't have let you, of course, but you would have gotten a style point...)


The Conventional Wisdom...

There was a lot of hype early on about the bid-$15-on-the-diamond strategy. The "conventional wisdom" went that if you bid it all on the final round, you had a good chance to earn the diamond's 5 points. However, if this strategy was too popular, the 5 points might be split among many players, and then lose to a sole winner of the 4-point emerald or 3-point onyx. Many players, I assume, looked at this and thought to themselves, I better bid most of my money on the early rounds, or spread it out, since I don't want to go for a $15 prize only for it to be divided.


...Is Proven Wrong

And then the game happened. By Round 3, only one player, the eventual winner, had all $15 remaining. Despite the conventional wisdom, not a single player bid their entire budget on the diamond. (To be fair, if the winner had seen another player with $15 in the bank, they might have changed their strategy.)

Despite the conventional wisdom, not a single player bid their entire budget on the diamond.

In fact, nothing shows this effect more starkly then this chart displaying the average bids on each gem. Remember that the gems get more valuable as the game goes on, so you'd expect bids to increase as we move from the left to the right of the graph.

Average bid in each round of Secret Auction.

Whoa! People bid more, on average, for the amethyst than the diamond despite it being worth only one fifth of the point value!


Yet More Avocado vs. Cucumber References

Flash back to Game 1 of Avocado vs. Cucumber. Rounds 4 and 5 weren't even about avocados and cucumbers, so we'll set those aside. In Round 1, avocado won by a single point. In Round 2, avocado won by a healthier margin. In Round 3, only one person even voted for cucumber!


Use Reverse Reverse Psychology

Let's think about someone using psychology–no reverse, just psychology. This person would look at this scenario and think, Well, cucumber earned points in the last round, so I'll vote for it again next round. In Secret Auction, they would think, Everyone keeps talking about the bid-$15-on-the-diamond strategy, so I'll use it to earn 5 points.


But that's not what the majority did. Most people went one step further, reasoning (if implicitly) that other people would do just that. Therefore, they should vote avocado, or bid most of their budget on earlier rounds. On the other hand, the winning players in both cases correctly foresaw other players doing this and followed reverse reverse psychology–which, interestingly, is the same as the straight-psychology strategy.***** Reverse reverse psychology for the win.


One Big Family

In fact, I believe Avocado vs. Cucumber and Secret Auction are part of the same family. A family of games where the goal is essentially to play a strategy that other players don't play. Other members of the "Avocado vs. Cucumber family" include Greed Control and Blotto. Personally, I'm just fascinated by this family of games.

It just gives me so much joy and pride to share this all with you.

It just gives me so much joy and pride to share this all with you. Ciao.

–beautifulthorns


Next: Addenda


*Random name generator, but we're keeping it.


**This makes it easy to color code the rounds.


***I think people were getting tired of the repetitive nature of the game–yes, it's true that there is strategy. A good win rate in the past is a good predictor of win rate in the future, I've found. Anyway, look at the data.

Total number of person-rounds (so a person who plays each round counts for 5) in Avocado vs. Cucumber over time.

Quick interlude–in perhaps my favorite game, Magic: the Gathering, there exist five basic land cards. These basic land cards are very important, and almost every deck in the game requires many copies. Therefore, the basic lands are reprinted in virtually every expansion set. For one expansion, Magic tried something different. The basic lands would be full-art, meaning the art box stretched all the way to the bottom of the card.

Zendikar's full-art basic lands.

These full-art lands were very popular. However, Magic didn't decide to make every land from then on full-art. I wondered why not. After all, almost everyone preferred them to the normal lands, or at least didn't care. They didn't seem to cost more to produce. So why shouldn't full-art lands be used to make every set prettier?


Mark Rosewater, the Head Designer of Magic, did a mailbag article where he answered this very question:


"I often talk about the role of design in making fun game play. There's another equally important role that I don't talk about as much. Design has to not only make [expansion] sets that people will enjoy when they play them, but we also have to make sets that people want to buy. There are numerous ways to do this, but a very successful one is to find elements of the game people like and withhold them for some amount of time. (Magic is luckily large enough that we do not need all aspects of the game at any one point in time.) When you bring those elements back, the players get very excited. [Full-art lands] fall into this category. They are awesome and we will bring them back someday. They weren't a one-time thing. It's important, though, to have things in our arsenal that players are eager to have return."

"A very successful [way to make products people buy] is to find elements of the game people like and withhold them for some amount of time." –Mark Rosewater

Interesting. If putting Avocado vs. Cucumber on hiatus for a while wouldn't increase the excitement when it did return, nothing would. (I mean, I assume paying players $50 a round would, but you know what I mean.)


In any case, dear Avocado, you served the world well so far. (Not you, Cucumber.) If you want more Avocado vs. Cucumber content, check out my two earlier blog posts here and here, and the raw data here.

In any case, dear Avocado, you served the world well. (Not you, Cucumber.)

In other news, since I don't think the updated rules live anywhere, I'm going to paste the final Avocado vs. Cucumber rules blurb. Note that I've added a new option to predict spreads other than a tie, a+1, and c+1. If you predict larger spreads, you get larger payouts. For instance, if I predict: c+2, then I get 2 points if there are exactly 2 more cucumber votes than avocado. Predict: a+2, a+3, c+2, and c+3 have 2 point payouts; and higher than that have 3 point payouts. Anyway, rules:


Very Basic Rules

Vote for either avocado or cucumber. You're just picking one - it's not about which is tastier or better. The objective is to be in the minority among all players. For example, let's say you pick avocado, and a total of 5 people pick avocado, and 7 people pick cucumber. In that case, avocado is in the minority, so since you voted for avocado, you get 1 point.


But Isn't It Just Random

In some sense, this game is random, but really, it's a game about psychology. Your goal is to think about how other people will vote; like, do other people prefer avocados or cucumbers, and how can you use that? (Avocados are superior.) Also, there are multiple rounds in a game, and so you can say, in the last round avocado had 6 and cucumber had 5, so people will move to cucumber, so I should vote avocado, or whatever it may be. There are many different layers to that.


Advanced Option: Predict

Let's say you think it will be very close between avocado and cucumber. Say, 6 avocado and 7 cucumber. In that case, voting for avocado would make it a tie and wouldn't get you a point. Yet, voting for cucumber would also lose. So, if you think that this is the case, you should utilize the predict option. If you predict: tie, you get a point when it's a tie. If you predict: a+1, you get a point when avocado is ahead by 1. Surprise surprise, if you predict: c+1, you get a point when cucumber is ahead by 1. So, in the above scenario, predict: c+1 would be the winning move. You can also predict larger spreads for bigger payouts. For example, if you predict: a+3, and avocado is ahead by 3, you win a payout of 2 points.


****Much of it is from the explanatory blurb I wrote for actual game players. Sorry, or whatever the appropriate phatic expression is.


*****Or maybe I'm giving them too much credit and they just voted semi-randomly. Not sure.

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