My preferred example for the "p2 likes variance, p1 likes certainty" is the following game:
First to 43 points wins. Each player has two available strategies:
-Safe: 43 points in 20 turns, no matter what
-Risky: 10% chance of getting 43 points in 15 turns, 90% chance of self-destructing and never getting 43 points.
p1 will always play the safe strategy, and p2 the risky one.
I guess I should respond to this, since I meant to earlier but apparently forgot. Shouldn't p2 also always take the safe strategy, because it ensures him the tie? 100% ties is better than 10% win and 90% loss, no? But in any case, this game has very little resemblance to Dominion.
"first to" means P1 wins, much like buying out provinces (its not in the normal 1-1-1-1-1-1-1-1 that BM games give us, but for 3-3-2 or something that engines can give us..
Ok. Makes sense. Thanks.
And it does have a resemblance.
Sure, it has SOME resemblance. Hey, poker has some resemblances, too, and in poker, the later player gets more information, which gives him (or her) a serious advantage. And that's also true in dominion. But it doesn't mean there's a second-player advantage in dominion...
People have posted game after game that demonstrates that the second player often should take a riskier strategy.
Other games, not dominion. And those games have really big and significant differences. You don't have such clear-cut options in dominion as you do in Stef's game. More importantly, p1 is not guaranteed an extra turn in dominion. More importantly still, dominion is much longer. Most importantly, he's not applying the full logical tree. Yes, you do take more risks when behind. Who's arguing that? The questions are how much does p1/p2 have to do with this, and to what extent do you play the riskier options? And these games have enough differences that you can't just say 'oh it's the same.' Empathy's game is much much different, because in VIRTUALLY no dominion game can you guarantee ending exactly on a timetable (big exception is something like the golden deck, though even here there are some adjustments to make...), and there's usually not such a big gambit option either. Things are much more subtle than that.
The mathematics is sound in the basic game systems,
Yeah, but incomplete. Actually I think I've posted the most mathematics here.
and the logs demonstrate that those concepts apply to dominion too.
What logs? Where do you see logs that show this? Where? I don't see any. Give me some logs. What I want is logs!
(OK, yes, anecedotal evidence does not prove statistical concepts. But you also rejected simulation as a viable method, so you seem to be unreasonable picky here.)
I'm not being unreasonably picky. I'm quite reaonably saying that there's no quick way to show what is right in dominion. It's a wonderful, terribly complex game, with lots and lots and lots of different paths to take, which makes it extremely difficult and complicated to come out at the right equilibrium. Indeed, if we narrow it down to one kingdom of ten cards, we can probably model out all the reasonable choices someone can make, and find the 'best way' of playing that kingdom, all the choices you should take, how to react to anything your opponent might do. It's like tic-tac-toe, except that instead of a 3x3 board with only a handful of choices, you have dozens of choices, or more, every turn, for a non-fixed number of turns, which can quite easily reach into the 30s. So let's conservatively say that there's 5 reasonable choices per turn (I submit that there are almost always more), and say 20 turns you need to prepare for (again, there's always more than this). Even not really taking into account your opponent's turns, you're almost at 100 trillion possibilities. On just a normal-ish board. So it's pretty complicated, you should not be trying to solve it. So given that, what I want is examples; give me a game, where you used this kind of thinking, and where that was definitely what you needed to do. And I'm sure they're out there, because it really is an important consideration to take in mind. On the other hand, choosing the strongest strategy, before the lead is that big and risk becomes such an important factor, is much more often going to be a bigger deal, at least until you get toward the endgame. But most of all, I want logical reasoning behind 'okay, in this particular situation, here's why you want to do this. There's reasons X, Y, and Z. You're in a bad spot, but you need to get lucky, so you play to let yourself. If you don't, you were probably going to lose anyway. If you do, then great, you stole a game'. Actually having said this, the youtube video at the bottom of my signature is a great example of this. I actually could have done it better, I'm sure, but the point is I kept picking up engine components, particularly things which would let me get more plays of monument in. I was so far behind, I knew the only chance I had would be for the game to somehow go long enough to let me play monument a thousand times to make up enough point difference. I played to get lucky. I could have taken more green earlier, and it would have totally killed my chances, because when he stalls out, I have no way of taking advantage. I'm sure that I lose less in those cases, but it doesn't matter how much you lose by, only if you have more than the other guy. So I played to get lucky, and I did get lucky, so I was able to steal a win. There's an example for you.