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Author Topic: Strictly Better  (Read 2479 times)

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Commodore Chuckles

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Re: Strictly Better
« Reply #75 on: July 03, 2019, 06:18:35 pm »
+1

You guys are forgetting Possession again. A Mining Village in your deck is something you can trash once but that your opponent can trash every time they Possess you.

Also, if card A is not strictly better than card B when it gives you everything card B gives you plus a risky option, then I'm pretty sure nothing can ever be strictly better than anything else. The same argument can be used that Goons is not strictly better than Militia because it might motivate you to buy Coppers that will screw you over later, and so on.
« Last Edit: July 03, 2019, 06:29:53 pm by Commodore Chuckles »
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crj

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Re: Strictly Better
« Reply #76 on: July 03, 2019, 07:37:35 pm »
+3

No I think he's right... imagine in your analogy you gave person B a dollar plus the option to roll a d-1000 for double or quits... he gets $2 on 2-1000, and nothing on 1. The mathematically right move is to always take the roll, and that's also the practical right move unless a person is in a situation where they really need 1 dollar, but don't need 2.
Turn that around, though. A player can adopt the strategy of never trashing a Mining Village unless they're certain doing so will enable them to buy a Province they otherwise wouldn't be able to afford. If you do adopt that strategy, Mining Village is always better than Village, even if only ever so slightly.

I claim that if there is at least one strategy for using card A which is better than any strategy for using card B, then A is, indeed, strictly better than B.
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segura

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Re: Strictly Better
« Reply #77 on: July 04, 2019, 05:08:10 pm »
0

That's not a genuine edge case. You may decide you'll never trash Mining Village, in which case it is identical in behaviour to regular Village. It's better unless you somehow deem worthless the option to decide otherwise.

To take an extreme and pared-down analogy: I give person A a dollar. I give person B a dollar plus the option to toss a coin for double or quits. What I've given person B is better.

No I think he's right... imagine in your analogy you gave person B a dollar plus the option to roll a d-1000 for double or quits... he gets $2 on 2-1000, and nothing on 1. The mathematically right move is to always take the roll, and that's also the practical right move unless a person is in a situation where they really need 1 dollar, but don't need 2.

The fact that a person can choose to not roll doesn't seem to matter here, because basically everyone will roll; it's the correct decision financially and in terms of game theory.

But for the person who rolls a 1, it would have been better for them if they hadn't had the option to roll.

*Edit* This just comes down to a part of the definition of "strictly better" that I don't think has ever been defined. For a person who has incredibly bad luck, his overall outcome will be worse if he's given the die roll choice with his dollar every time, assuming that he plays correctly. But it's still true that a person can choose not play correctly and instead pretend that his dollar is just a dollar without the die roll.
Ignoring your probabilities which heavily favour one outcome, I disagree. What faust mentioned is a risk management issue and has less to do with "strictly better". I know too little about stochastic game theory but I guess that technically speaking you could say something like: not liquidating does not stochastically dominante liquidating Mining Village or vice versa and thus by extension, Mining Village does not stochastically dominate Village as you can pick an option which is good ex ante but turns out to suck afterwards. In other words, via buying Mining Village instead of Village, you gave yourself rope to hang yourself (more technically speaking, more options are not better than fewer options in a stochastic world or when you cannot calculate everything; e.g. in chess keeping the position opaque and giving your opponent more options instead of forced moves can be a decent strategy, especially if the opponent is in time trouble).

This risk management issue would still occur if, as DXV has suggested somewhere, Mining Village could be trashed for Coins at the start of the Buy phase (as you can still make a mistake concerning judging how long the game will take; you can still trash the Mining Village too early) but Mining Village 2.0 would then be superior to Village (ignoring funky edge cases like Possession, Will-of-Wisp with cost reduction and a deck with Forge and a lot of 5s that want matching 3s instead of 4s to forge into Provinces).
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