For Sale: An Interesting Case Study of Irrationality

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Pneuma
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For Sale: An Interesting Case Study of Irrationality

Post by Pneuma » 17 October 2019, 05:07

I am currently ranked #1 in For Sale and have won 15 out of 30 of my last games, mostly 5 and 6 player. No one asked for this, but I have decided to share my insights and strategies because I like the game so much. For Sale reminds me a lot of one of my favorite books, Predictably Irrational by Dan Ariely. It's a pop-psychology-economics book that takes you through study after study of situations where people tend to not think rationally. For Sale is a game where players are predictably irrational. I have learned many thing about how players think, and I have developed strategies to exploit this and that's how I have gotten so good at the game.

Note: in all my examples I'll use 5 player games and rounded down return for passing.
Color code:
How to become a god at For Sale
Advanced
Beginner

Phase 1: Bidding

Valuation of bids
Every round you ask yourself, did I get a good deal?

Poor play: Bad players think about was their price relative to the card. Someone might say 6$ is a good deal for the 30 card. Is it? It only depends on what other cards are available. If the cards available are 22-25-27-28-30, 6$ is not a good deal for the 30, because the opportunity cost is another high card.

Good play: Good players evaluate their card compared to the other cards available. In economic terms, this is called opportunity cost. In my experience, moving up 5 in number is worth about 1$. For example, Bob can get the 14 by passing, but believes he can get the 25 by spending two more dollars. Bob chooses to bid because moving up 11 numbers is worth the 2$ (11$>5*2$). 1$=5#s is the #1 guiding principle for how I choose my bids. But as I will explain, there are a lot of situations where I don't follow this principle exactly.

How I play: I take the previous paragraph and try to think about how I can get the best deal and try to force others to take bad deals. For example, the available cards are 1-7-13-20-29 and the current bids are 2$,3$,4$,5$,my turn to bid. What should I do? If you think about the above paragraph, it would make sense not to bid. Spending six vs spending 0 is worth about 30 numbers (6*5), but you'll be only moving up 28 numbers, so you shouldn't bid, right? Wrong. Assuming everyone else passes, you let all the other players get better deals than you. If you bid 6$, everyone gets a worse deal except the player who bid 5$. Also, if someone bids 7, you will get the best deal. This might seem obvious, because 6$ isn't that much for the 29, but the important part is that I evaluate both my position and everyone else's position every time I bid.

Sometimes you are in a bad situation where you get the worst deal if you pass and the worst deal if you upbid. In these situations you just have to choose the best one and hope to get better luck in the other rounds.

Overbidding for the 30
The 30 is a very valuable card. It gives you power over everyone in the 2nd round because you can choose to take the top card anytime you want. The 30 is not as valuable as everyone seems to think. On 30 rounds, I tend to pass earlier than usual because I know people will get into a bidding war when the 30 is out. Sometimes I'll upbid when the 30 is out even when it normally would be really bad if I won the bid. I do this when I'm confident someone will outbid me (even when it's bad for them). I've tried to determine if this is true for the 29 or even 28. I think this mostly applies to the 30 card. It is absolutely incredible.


Overbidding in the early rounds
Players tend to get overzealous in the early rounds and bid too high. I use this to my advantage by passing earlier than I normally would. Having more money than the other players gives you a lot of power in the 2nd to last and the last round.

Passive-Aggressiveness
If a player has spent a lot of money in the early rounds, they tend to be more passive than they should be in the middle rounds. Likewise, if a player has not spent a lot of money in the early rounds, they tend to be more aggressive than they should be in the middle rounds. It is very advantageous to know how much money the player in front of you has. If you think they are in a passive mode, you might decide not to bid so that you don't have to pay the highest price. If think they are in an aggressive mode, you might decide to bid since they will also bid higher, then you'll get a good deal.

Early passes
Let's say the available cards are 1-2-22-24-26 and I'm the first bidder. If you spend a lot of money in the early rounds, and need to save some cash, passing might be a good idea. You can expect that everyone will bid high because no one wants to take the 2 and lose out on the 20s cards. If the bids get up to 5$,6$,7$,8$ or something similar, you will be happy you took the 1. Another option is to start the bid high, maybe at 6$. You can expect to be outbid, but there is a possibility that you will be caught having to pay 3$ for the 2. The risk is a lot higher. I usually make this decision based on the passive-aggressiveness principle. I try to predict how high the bid will go and bid accordingly.

2nd phase: selling

Underselling in the early rounds
Let's say the available check are 7$,5$,2$,2$,0$ and you have the houses 3,11,16,17,26,29. What should you sell? Many good players, some of the best, would choose the 1. I would choose the 11. Since there is low variability, everybody is thinking that they will play there lowest card. I take advantage of that by playing a card slightly higher than everyone else's so that I get the highest card. This pattern of behavior is so consistent, I hardly ever see any of the best players doing it. I can almost guarantee if you play the 11 that you will get the 7$.

Since the smaller houses tend to played earlier in the game, I usually save my lowest card till the last rounds. When there is a low variability amount of checks, like 14$,6$,5$,5$,4$, I will play my 3. The other players will be playing cards in the teens and the 20s.

When there is a medium variability, like 13$,10$,6$,5$,3$, I would go with the 16. You can expect players to bid higher, but most don't play their higher cards on the first couple rounds unless there is a high amount of variability in the checks. With playing the 16 I would expect to get at least the 10$, but probably the 13$.

Overselling for the 15$
If the checks are 15$,13$,13$,11$,9$, it's pretty much equivalent to 6$,4$,4$,2$,0$. It's the concept of opportunity cost. This is the kind of thing where you either understand it or you don't, so this knowledge is only usable when there are weaker players in the game.

Passive-aggressiveness
Similar to the first phase, when a player has played a lot of low cards, they are more likely to play their higher cards. Also, if a player has just played a high card, they are more likely to play reserved the next round. If I notice a lot of low cards have been played recently and the checks are 15$,14$,7$,3$,2$, I believe that it is a lot more likely that players will try to get the 15$ and 14$. So if I have the 30 or 29, I will play it now. If I do not, I might want to play a low card and sluff the round. If a lot of high cards had been played recently, I might try to bid in the low to mid 20s to try to get the 15$ or the 14$ because I believe a lot of players will bid low.


I hope you enjoyed reading this. If you are a good player and have approached this in a different way with success, I'd like to hear about it.

Also, I am currently looking for work in actuarial, data science, or other related fields. I imagine this post alone demonstrates an amount of analytical skills that hiring managers only dream about. So, worth a shot, right? :lol:

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RicardoRix
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Re: For Sale: An Interesting Case Study of Irrationality

Post by RicardoRix » 17 October 2019, 10:48

Pneuma wrote:
17 October 2019, 05:07
I imagine this post alone demonstrates an amount of analytical skills that hiring managers only dream about. So, worth a shot, right? :lol:
If you're a hiring manager, then you can cut your work by 50% easy:
Take a half of the CV's and put them in the bin - you don't want anyone unlucky.

Nice post, congrats on #1 ;)

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sprockitz
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Re: For Sale: An Interesting Case Study of Irrationality

Post by sprockitz » 18 October 2019, 02:40

Interesting post. I generally follow this strategy, though in the second half while I agree with most of those tendencies I don't think I've seen them consistent enough that they'll always work (granted I only played 22 games and mostly when it first game out, so maybe people have become more predictable with more plays). Which is kinda funny if the 'good' players are predictable because that is a pretty big weakness. Like if you predictably are using a 10-14 rang mid card on a small spread stack people can counter that by going with the 15-18 card :-P...it is certainly a bluff counter bluff scenario. I'll often go for the win of a smaller spread set with a mid tier card, but isn't 100%...but it is usually predictable what the majority of people will use...like I see a draw and I can guess they'll be at least 3 cards of 25+ coming out even when only 2 will pay out...making it a good time to toss a weak card.

What are your thoughts on the luck of turn order...to me this seems to ruin several of the games. I find some players always jump the bid while others usually go just over the previous bid. When you get stuck behind an over jumper it can ruin your game. It consistently puts you in a situation between 2 bad choices...where no matter what you do you will be one of the worst off people...and the person who goes before the constant price jumper ends up getting stuff for really cheap and usually wins the game.

The 5:1 valuation is a bit high because even looking at start money to end money you are only going about 4:1 or best 4.5:1 (about 56-63 money at the end from 14 starting money). And clearly number of player dependent with 6 players and one less bidding round it drops to 3.5-4:1. The strict valuation to break even is roughly 2:1 as the houses are a uniform spread up to 30 and the payments 'uniform' spread to 15. Since the spread in a group of 5 is only 10-12 on average that bumps it up to 2.5-3:1 (but again money is short so you’d do poorly at that valuation)

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Pneuma
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Re: For Sale: An Interesting Case Study of Irrationality

Post by Pneuma » 19 October 2019, 02:59

Ricardo... :lol: :lol: :lol: , that's right, you don't want unlucky employees.

Sprockitz, I think you completely misunderstood my valuation system, which might be my fault for not using precise language. The 5:1 ratio is not meant to be starting dollars to ending dollars. I meant the ratio to be (#of house attained by bidding-# of house attained by passing)/dollar. For example, If I could the 30 for 6$ compared to the 1 for 0$, that's about fair (without considering what my opponents got).

I told myself I wasn't going to do this, but I did it anyway :roll:. I wrote R code that calculated the average distance between houses in a 5p game.

R code:
____________
sum = 0
trials = 10000
for(i in 1:trials)
{
x= sort(sample(1:30,5,replace=F))
sum = sum + x[5]-x[1]
}
sum/4/trials

Output: 5.17
____________

You can move up 0,1,2,3, or 4 spots in a round (average of 2). There are 6 rounds, so you move up an average of 12 spots per game.

5.17*12 spots /14$ = 4.43

So 4.43 is our magic number. Obviously, that # would change game to game based on the randomness of the spread, so you need to take that into consideration.

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sprockitz
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Re: For Sale: An Interesting Case Study of Irrationality

Post by sprockitz » 21 October 2019, 00:30

I understood. I'm saying those ratios should come out the same.

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asd123321
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Re: For Sale: An Interesting Case Study of Irrationality

Post by asd123321 » 21 October 2019, 04:15

Do you keep track of how much money everyone has? This can make a big difference
and give someone a big advantage. But it makes the game more work. These 2
reasons are why I think money should be visible.

In many situations, it seems good to bid high in the second to last round. This can be good if
you know the people before you don't have a lot of money. If you win, then in the last round,
your $1 bid if 2 pass, gets the third best for $1. This avoids where someone bids 3 or
4 and you can't beat them giving you the worst card in the last round. Bidding first in the
last round can be safer because you don't have much money at that point.

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nandblock
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Re: For Sale: An Interesting Case Study of Irrationality

Post by nandblock » 21 October 2019, 20:37

Many thanks for this very interesting post! I will be curious to see how it affects bidding in games on this site--it would be interesting to observe a game by a group of players who proceed according to roughly this set of principles for evaluating bids.

I've indeed often witnessed (or engaged in) the practice of sloughing off low property cards in early bids for cheques in hopes of having a handful of high cards for the last rounds. Good to have a more subtle analysis of when to do this and when not to lowball reflexively.

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Pneuma
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Re: For Sale: An Interesting Case Study of Irrationality

Post by Pneuma » 22 October 2019, 05:53

sprockitz wrote:
18 October 2019, 02:40
What are your thoughts on the luck of turn order...to me this seems to ruin several of the games. I find some players always jump the bid while others usually go just over the previous bid. When you get stuck behind an over jumper it can ruin your game. It consistently puts you in a situation between 2 bad choices...where no matter what you do you will be one of the worst off people...and the person who goes before the constant price jumper ends up getting stuff for really cheap and usually wins the game.
Yeah, that can be really annoying. The worst is when the first bidder bids 8 for the 30. Why...? In most games I've found that you can get above average cards almost every game even if you get bad luck. When I do get bad luck in the first round I have confidence that I'll be able to gain ground in the 2nd round. I used to think the 1st round is everything, but now I think the 2nd round is more important.
asd123321 wrote:
21 October 2019, 04:15
Do you keep track of how much money everyone has? This can make a big difference
and give someone a big advantage. But it makes the game more work. These 2
reasons are why I think money should be visible.
I don't keep track of everyone's money, just the person bidding after me. I feel like that is going too far. From a game design perspective, I think keeping the coins hidden makes it so the game is more chill. I've played it with a lot of non-gamers in real life and they all like it. Weaker players might really do a lot worse if coins were visible. With that being said, I would prefer being able to see the coins on BGA.
asd123321 wrote:
21 October 2019, 04:15
In many situations, it seems good to bid high in the second to last round. This can be good if
you know the people before you don't have a lot of money. If you win, then in the last round,
your $1 bid if 2 pass, gets the third best for $1. This avoids where someone bids 3 or
4 and you can't beat them giving you the worst card in the last round. Bidding first in the
last round can be safer because you don't have much money at that point.
This is a very good strategy. If I were to include this in my OP I would list that as "how to become a god at for sale."
nandblock wrote:
21 October 2019, 20:37
Many thanks for this very interesting post! I will be curious to see how it affects bidding in games on this site--it would be interesting to observe a game by a group of players who proceed according to roughly this set of principles for evaluating bids.

I've indeed often witnessed (or engaged in) the practice of sloughing off low property cards in early bids for cheques in hopes of having a handful of high cards for the last rounds. Good to have a more subtle analysis of when to do this and when not to lowball reflexively.
That would be fun to try, but I don't think enough people care to look at these forums.

A lot of people use that same strategy, which is why I tried to do something different. For my last card, I prefer it to be either a high 20 or one of my lowest cards because almost always the everyone else's last cards will be high teens and 20s.

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nandblock
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Re: For Sale: An Interesting Case Study of Irrationality

Post by nandblock » 12 November 2019, 07:40

A follow-up question: how much premium is it worth paying, in your opinion, aside from the intrinsic value of a property, to have the privilege of bidding first next round? Obviously the main considerations here are how much money you have left and what cards remain in the deck. I've often found myself wishing that I bid higher in a round simply because losing the bid leaves me in a bad position next round, turn-order-wise, even if I otherwise get a decent deal on a card.

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asd123321
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Re: For Sale: An Interesting Case Study of Irrationality

Post by asd123321 » 15 November 2019, 00:24

I don't think you have enough money to also pay to go first, except to go first on the last round if you know how
much money everyone has.

Ideally, I think often you would like to get the second best card for 3 rather than get the best for 7.

I think it is dangerous to start the bidding high. If you start with a 6, then you are saying the next
person is supposed to spend half their money on 1 card. IF 1 person passes, then they typically all
do. I have seen someone get a 28 for free. They then have a significant advantage.

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