It seems like the same logic can be used to say that in any game with an auction mechanic, the mechanic doesn't work because the optimal thing is simply for the first player who bids to bid the exact correct amount that the thing is actually worth. If both players know exactly that paying $51 for the up-for-bid power plant reduces your chances of winning, while paying $50 for it increases your chances of winning, then the right move is simply to immediately bid $50. Bidding any less than that allows your opponent the chance to be the one to bid $50 himself.
Why bother starting with a small bid and then gradually increasing it, until one player is no longer willing to pay that much? Surely both players should just be bidding the correct amount to start with.
Except, these mechanics DO work, because of 3 main factors:
1) Neither player knows exactly the correct amount. While there is some statistical calculation possible to determine the exact dollar amount where your chances go from increasing to decreasing if you win the auction, neither player is capable of actually making that calculation.
2) There is a risk/reward prospect at play. Purchasing the plant for more money may be riskier; but each player may have a different threshold for how much risk they are willing to take.
3) Humans are not robots; there is psychology at play here. The idea that you may want to bid a little bit higher, in hopes that your opponent bids even higher, just to cost him more money, comes into play. The slowly increasing cost of the power plant makes it harder to judge the exact point where it is way too expensive. Bidding on a plant is also egging your opponent on to bid higher.
All 3 of these reasons should apply just as well to Bottle Imp.
Thanks for bringing up an actually reasonable argument.
Here are some reasons I disagree (first overall, and then corresponding to each of your three points). It basically boils down to, for bottle imp the bidding goes the wrong way (the less you pay, the bigger your reward).
In auction games, I believe that bidding tends to go around in a circle increasing. Maybe player A can bid 5, then player B bids 7, then player C bids 8, then player A goes again and bids 9. Why didn't player A bid 9 to begin with? The answer is that the gamestate has changed. Since their first bid, player A has learned what the other two players think they should bid, and has updated their bid accordingly.
On the other hand, if for some reason player A already knew that for all players it was good to purchase the auction prize for 9 or less and bad to purchase it for 10 or more, then yes player A should immediately bid 9. Cursed bottle does not have this circular bidding mechanic (although even if it did, you would always want to fold or bid min amount).
1. In the case of cursed bottle, the correct amount is either the minimum amount or not to take cursed bottle. So in fact it is very possible to compute the exact amount.
2. This does not come into play with cursed bottle. Paying more for the bottle imp is both a higher cost and a lower reward. On the other hand, if you had to pay more than the previous time, it could work very nicely.
3. Again, this doesn't apply to cursed bottle because of how you have to underbid. Like, am I going to buy bottle imp for 6 hoping that my opponent will spend 5 on it? That's nonsense; they are losing less than me, and regardless they can still just buy it for min amount.
You could also do something silly like pay a lot for bottle imp on a board where it is bad to have (if such a board even exists!), hoping that your opponent will take it away from you. This is kind of nonsense also, clearly ignoring psychology this is just worse than not getting bottle imp, and if you allow psychology your opponent should be suspicious the moment you pay more than min amount.
Holunder:
I think that you are trolling, sorry if you aren't, I won't respond to you anymore.