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