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[flies]

Thing is, the law of averages makes the overall outcome of most chance-based cards pretty definite in the long run. In fact, every card that's a card-drawer is chance based, you almost never know what you're gonna get. None of those cards really have much more to do with luck than many other cards. Take the wishing well for example. Massing them up makes for a decent card-drawer. You can have a reasonable measure of its efficiency despite of the randomness involved. It's not really luck.

I think you're missing the point.  Variance isn't accounted for by an average.

[dominion123]

Thing is, the law of averages makes the overall outcome of most chance-based cards pretty definite in the long run. In fact, every card that's a card-drawer is chance based, you almost never know what you're gonna get. None of those cards really have much more to do with luck than many other cards. Take the wishing well for example. Massing them up makes for a decent card-drawer. You can have a reasonable measure of its efficiency despite of the randomness involved. It's not really luck.

I think you're missing the point.  Variance isn't accounted for by an average.

I think you're wrong, variance may be accounted for by the law of averages throughout a game. Like wishing well as a car-drawer. It's not luck that makes that work.

[Warfreak2]

The average result of a card isn't the only factor in the card's strength. If Silver were instead "flip a coin, if it's Heads, +$4" then the expected value would be the same, but it would not be a reliable way to hit $5 in the opening, and the strategies using it would be totally different, because of variance. Another very important factor is how much control you have over the probabilities of the outcomes - e.g. you can build an homogenous deck, so that Wishing Well is more likely to hit - and I think the negative outcomes are only really frustrating when you don't have that kind of control. (It's also a missed opportunity for strategic depth). This is why I am glad there are no Dominion cards which make you flip a coin or roll a dice.

[flies]

Thing is, the law of averages makes the overall outcome of most chance-based cards pretty definite in the long run. In fact, every card that's a card-drawer is chance based, you almost never know what you're gonna get. None of those cards really have much more to do with luck than many other cards. Take the wishing well for example. Massing them up makes for a decent card-drawer. You can have a reasonable measure of its efficiency despite of the randomness involved. It's not really luck.

I think you're missing the point.  Variance isn't accounted for by an average.

I think you're wrong, variance may be accounted for by the law of averages throughout a game. Like wishing well as a car-drawer. It's not luck that makes that work.

I can't tell if you're missing some facts about statistics or if you're being inconsistent in considering statistics on the same quantity.  To be clear about the statistics, in general (i.e. not just Dominion but in all cases), the average and the variance are independent statistical quantities.  Taking an average explicitly ignores the variance and vice versa.  Neither one can account for the other.

In the end, all that matters is something like "win expectation", which is an average.  So whether a card is high or low variance per play is definitely accounted for by its average effect on win expectation, but per-play-effect and win expectation are different.  The variance and the mean per-play-effect are going to have *different* effects on win expectation.  Sometimes you want a higher mean (e.g. when you're ahead) sometimes you want a higher variance (when you're behind).  So maybe you're thinking that the variance in the per-play-effect is accounted for in the average win expectation, which is true but missing the point that the variance and mean of the per-play-effect must be considered independently.  Or maybe I'm just not picking up what you're putting down.

You might want to take a look at Stef's account of a toy model of a game where a higher variance but lower average (per-play-effect) choice is superior (in win expecation) to a higher average lower variance play: http://dominionstrategy.com/2012/09/10/taking-risks-driving-the-p2-seat/  . 

[dominion123]

Consider the normal distribution as an analogue. The higher the sample size (wishing wells) is, the lower the deviation will be.  Variance is inversely proportional to sample size. But I think you misunderstand, I'm not actually talking about the average, but the law of averages (or rather, the law of large numbers). It was not my intention to get into a discussion about statistical details, my point was simply that having a lot of wishing wells makes for a reliable card drawer. It may have a low variance, depending on your deck. The more wishing wells you have, the lower the variance will be. And it isn't really fundamentally different from any other way of drawing cards, like chaining villages and smithies, which also is dependent on luck in some sense. It's just a different dynamic.