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Author Topic: Scrying Pool Math  (Read 19691 times)

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silverspawn

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Re: Scrying Pool Math
« Reply #50 on: August 06, 2014, 09:33:17 am »
0

Scrying Pool Math:

Scrying Pool = <3

QED.

that's awful and wrong in every single way

Witherweaver

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Re: Scrying Pool Math
« Reply #51 on: August 06, 2014, 09:34:32 am »
+1

Scrying Pool Math:

Scrying Pool = <3

QED.

that's awful and wrong in every single way

The Horse says: Doctorate denied.
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JW

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Re: Scrying Pool Math
« Reply #52 on: August 06, 2014, 11:18:36 am »
0

We can simplify the summation down to 1+a/(p+1) where a = actions in deck and p = non-actions in deck (this is without the spy effect). Now, we can add the spying-effect by saying that p/t times (where t = a+p is the total cards in deck), the spy-effect finds a non-action card and a/t times it doesn't. So we get to p/t*(1+a/p) + a/t*(1+a/(p+1)). Using the same set of cards as before:

The bolded part a/t*(1+a/(p+1)) isn't correct because you have an action on top of your deck, which the formula isn't taking into account. See my post directly above yours.

Correct! So I guess it should be a/t*(2+a/(p+1)). I'll recheck the expected values, but it should bump up the spy-effect pretty well. I thought the difference looked rather low.

That still doesn't look quite right, because if you have that action on top of your deck then going forward you have one fewer action in your deck. So presumably it should be (a-1) instead of the bolded a.

In your notation, my result is: 1 + [(A+2P+1)*A] / [(P+1)(A+P)].
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jomini

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Re: Scrying Pool Math
« Reply #53 on: August 06, 2014, 05:12:22 pm »
+3

when speaking about expert opinion, we have to remember that dominion is not just pick a set of cards and go; it is also a huge amount of decisions about what order to make buys. SCSN is likely better at picking a set of cards, but it is possible that the bigger issue is the ability to optimally play the game once a set of cards are chosen.

For instance say SCSN takes SP 92% of the time and wins those matches 80% of the time. Does that mean it is the dominant strategy 92% of the time? Not without a lot more priors. For instance, if SCSN wins 75% of his games anyways, there is extremely little information to be gained by his win rate. Further, it may well be that SCSN plays SP better than some alternative cards. Say we could exhaustively have a computer search all possible end game states for each decision SCSN makes after he picks SP and the rest of his strategy. He makes the optimal move 98% of the time. If, with other cards, he makes the optimal move only 95% of the time on average, then cards that intrinsically (e.g. you computed every possible game) are 3.16% better or less will still result in SP being the better call for SCSN, but worse for everyone else.

There are, broadly, two big skills in dominion. Strategic - picking a strategy from the cards in the kingdom and tactical - making correct decisions, particularly with timing, while playing the strategy.

Elite players win too many games simply off raw tactical skill to accurately gauge card strength off their win rate. It is only when they are playing equally skilled opponents that card strength has a larger impact on win rate that player tactical skill. SCSN could almost certainly beat his average opponent most of the time even if he intentionally picked the second best strategy on the board. Flawlessly playing the 2nd best strategy will very often beat marginally flawed play of the best strategy.

This is why Big Money is so strong until you really get to know the game. Your ability to screw up decisions (when should I start greening, should I take two components at $7 or a gold when I will eventually need both, do I reveal this moat against a Margrave or do I draw for 3 good cards, etc.) is relatively low. So even though the strategy, if played perfectly, is weaker than another, also played perfectly; a casual player can come close to perfection (say 80%) with BM strats but only makes 33% correct plays with a complicated engine build. The engine has to be more than twice as strong to come out ahead.

Disambiguation is really hard. I see way, way too much variance in the annual card rankings to say that player skill is sufficient to determine card strength.

That being said, SCSN is totally correct about the best course of action to get better. Improving your tactical play happens when you put yourself into difficult challenges and you get very good at getting the maximum amount out of a strat. Picking individual cards or classes of cards and always playing them will make you much better at playing them optimally.
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AdamH

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Re: Scrying Pool Math
« Reply #54 on: August 06, 2014, 05:34:05 pm »
+1

That being said, SCSN is totally correct about the best course of action to get better. Improving your tactical play happens when you put yourself into difficult challenges and you get very good at getting the maximum amount out of a strat. Picking individual cards or classes of cards and always playing them will make you much better at playing them optimally.

To be clear, I fully intend on playing lots of games like this, but playing games and getting a gut feeling and not doing anything else isn't enough for me. I want to have some idea of why things are happening and some of the theory behind it or else it's not going to click for me.

All of the other things they're saying I should do are great advice. But should I do them instead of theoretical stuff? No. Absolutely not. And if the implication is that I don't have the "brain power" to do both of them and "gut" is the more important thing to focus on if I have to pick one; well my response is that I don't think I should have to choose. If the best players in the world can only do one of those things then it's not going to be long before someone else can do both and be better. I'm trying to be that person.
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Titandrake

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Re: Scrying Pool Math
« Reply #55 on: August 06, 2014, 06:39:15 pm »
0

Meanwhile I'm sitting here trying to get my math/probability calculation skills to go from 2/10 to something more like 3/10...:P

Personally, I don't get much value out of hard mathematical analysis like this - I'm noticing that I come up with some probabilities to figure out likely outcomes, then rely on my gut in the end.

If there was a Council Room, I'd be using that a lot, because the data helps give qualitative results - "I buy this much less than everyone else, am I underestimating it?" Whereas this feels more like the article on Treasure Map, "how likely is it to have these collide by this turn if I buy this many": not that useful and yet not that useless.
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