I think this is exactly the kind of reasoning described in wiki for why mixed strategies are a thing (see the choosing how to pitch in baseball example there).
The thing that might be interesting is also exploring what "optimal" means. For simplicity let's assume the game rules itself don't randomize anything and that the game has a binary outcome (A wins or B wins, no scoring).
In battleships, if each player was forced to be deterministic, for each strategy for player A there is a strategy for player B that defeats it and v.v. This means that the standard approach of "optimal strategy is one that wins whenever it's possible to win" would imply lack of optimal strategies at all: after all, it's always possible to win but no strategy wins always. This is still true if you admit nondeterministic strategies: it's possible to win against each deterministic strategy with p=1, but there's no strategy that does that for all deterministic counter-strategies.
The reasoning you described is similar to looking at changes you'd make in your strategy in response to knowing that opponent's, then doing the same for your opponent, and iterating this. So, it seems that you describe looking for a fixpoint of that: a pair of strategies s.t. neither you nor the opponent would want to change theirs upon learning what other player's strategy is. Note that this necessarily speaks about pairs of strategies (IIRC there are games where you have multiple such pairs, but I sadly don't recall examples). It's been shown that every game with finite sets of moves has at least one such pair.
NB if you are after such pairs of strategies, then instead of iterating it's often easier to directly look at the fixpoint condition and infer what such a pair of strategies would need to satisfy for both players not to wish to amend theirs.
@freemo I'm not an expert but it is probably a case of mixed strategy.
If you read the example in this page, it fits a lot of real-world cases:
@medigoth what has been the precedence for past coronations?
@freemo The responses about mixed strategies are on-point mathematically/from a game theory perspective, but if you are talking about real-life scenarios (where no one really uses “optimal” strategies due to information constraints etc.) it might be convenient to use gaming terminology. In this case you could say you are “playing the meta[game]” – most people use a strategy currently considered very good and you find a strategy that might be bad in a vacuum, but counters the specific one everyone uses. Quite common in competitive e-sports, whether SC2 or Dota or whatnot.
@robryk Depends.
Might work better as an example.
Imagine a game of battleship but where one player is firing the other controls the ships. So we are trying to find an optimal firing pattern vs optimal ship placement.
By default there is no strategy for ship placement I can think of other than to make sure ships arent adjacent. So you have a more or less random placement.
But if ship placement is random then since there are more ship layouts that overlap closer tot he center of the board as opposed to near the edges, then the optimal firing strategy would be to avoid the edges, with the 4 corner spaces being the least favorable target to hit. So the optimal stregy here is to more or less focus away from the walls.
it should also be noted that while random placement does tend to cover squares near the center more often, there is a strategic reason to not prefer walls and intentionally place ships near the center too. That is, once a strike on a ship is made it is easier to guess the orientation of the ship and destroy it for ships next to walls than it is for ships away from walls. So for this reason as well it is generally optimal to place ships asway from walls.
Anyway as you can see this chain of logic can go on as per the premise.
@realcaseyrollins Not sure I see what the connection to diminishing returns might be. I also might be missing something.
@cobratbq Not sure I follow.. not sure how you dont know what your circumstance is... but we are way too meta for my brain right now :)
@cobratbq Dont know what?
@trinsec Also this is the funniest thing you have ever said, you have now just leveled up :)
@freemo Sounds like it's inconceivable!
@trinsec I didnt even think of the princess bride scene when I asked, but yea that is the perfect layperson example really :)
#GameTheory question for everyone...
Is there a name for when an optimal strategy is avoided because the optimal strategy is easily defended against when you know the person is using it in the first place?
Or the reverse, where someone might intentionally use a very poor strategy specifically because the user would never expect a user to pick a poor strategy and thus, at least when assumed it wont be used, becomes a strong strategy?
@cobratbq Fair enough. Well I hope your situation improves is all.
@cobratbq what sort of circumstances we talking about? I would say the political correctness probably needs to be adjusted for the tolerances of the environment you are in.
The key to a happy life:
Be just politically incorrect enough to ensure all the toxic easily triggered people want nothing to do with you, but still kind enough that you dont actually cause anyone any real harm.
I've made a conscious effort to do this for years in most social settings and I need to say, I have a pretty awesome circle of friends.
@Gaythia yea plenty of explanations. Though in my expiernce the poll is fairly legitimate, the left will block people who disagree with their views pretty quickly politically. the right doesnt, but the right has other issues, they are far more likely to follow you around and troll you instead, so im not sure thats any better.
@freemo @LouisIngenthron Indeed too much variability could be a problem, yet i would argue the status quo selection of parties available in many societys lacks multiple positions much needed by the general populace.
The fact that many people vote with regard to what they expect to be a "wasted vote" might have part in keeping it that way. Strategic voting, a similar way of thinking, is also something i consider harmful to the democratic process.
I think its more fundemental than even that,, it comes down to what you mean by a two party system...
I think the two party system we have simply means "whatever two parties are the most popular, even if its marginally more so, will receive disperportionatly more votes.
Whether this translates tot he fact that other third parties will have a harder time breaking in (and thus a wasted vote) Id say is the part that is untrue, which is why we see third parties break in all the time and go from 1% to 51% in a single election cycle historically.
@LouisIngenthron @admitsWrongIfProven
Its only a theory called a law erroneously. And with the major larties switching 8 times in us history and multiple times in other similar voting systems it shows it is not a twonparty system in thr typical sense in that other parties can and do break in and typically the shifts are fairly radical causing them to get majority shares in only one or two election cyles, showing that other parties can and do compete.
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