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Author Topic: Homage to the Best Card  (Read 900904 times)

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Awaclus

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Re: Homage to the Best Card
« Reply #5950 on: March 21, 2017, 12:02:34 pm »
0

Not on a small scale.  But on a larger-scale discussion, you absolutely should take that into account.  Say you're planning to go fight a dragon with a 5-player team.  In your planning, you presumably have some idea of roughly how much damage your group can deal per round, on average.

And that average ABSOLUTELY includes the likelihood that you're going to roll one or two crit fails/successes.   You'd instinctively take that into account.


A similar principle applies here.  "On average I'll do a little bit of damage to my opponent's deck with my Warrior - that average amount is increased somewhat by the possibility that I hit my opponent's Warrior." 
The upside is so huge here that the overall "average damage" (as it were) is probably dragged up noticeably even if the likelihood of the event is small.

But this is a small scale. You have one chance of hitting something with Warrior before you want to turn it into a Hero, and in 90-93% of cases, it doesn't hit your opponent's Warrior. So if your opponent willingly gave himself a small disadvantage in order to prepare for his Warrior getting hit, 90-93% of the time he just has the small disadvantage and that's all it did for him (and probably around 7-10% of the time he still loses because he's still one shuffle behind you even if he has a backup Page going on). Obviously if you want the second Page for other reasons, you want it anyway so yeah.

If I was teaching Dominion to sentient computers, I would mention that when the disadvantage from getting a second Page instead of something else is almost negligible, as well as when you're already so much ahead that your opponent's only chance of winning is pretty much to hope for that small chance of hitting your Warrior, you might still want a second Page just in case your Warrior gets trashed. Unfortunately, we are humans and humans are garbage at estimating any probabilities so it's better to forget about these edge cases when you're actually playing the game.

faust

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Re: Homage to the Best Card
« Reply #5951 on: March 21, 2017, 01:03:36 pm »
0

In other words, E[X] = sum_x(x*P(X=x)).

P(X=x) can be very small, but x can be large enough (or can not be)  to overcome that.
But if we're talking about a game of Dominion, x has to be between 0 and 1 (assuming it indicates winning probability). Such an x is only ever large if your overall winrate is pretty low otherwise.
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Witherweaver

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Re: Homage to the Best Card
« Reply #5952 on: March 21, 2017, 01:06:44 pm »
0

In other words, E[X] = sum_x(x*P(X=x)).

P(X=x) can be very small, but x can be large enough (or can not be)  to overcome that.
But if we're talking about a game of Dominion, x has to be between 0 and 1 (assuming it indicates winning probability). Such an x is only ever large if your overall winrate is pretty low otherwise.

That's true for all such x's in that interpretation, though.  Its contribution (i.e., weighted by the density function) to the expectation is what is important.
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Haddock

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Re: Homage to the Best Card
« Reply #5953 on: March 21, 2017, 03:53:16 pm »
0

Not on a small scale.  But on a larger-scale discussion, you absolutely should take that into account.  Say you're planning to go fight a dragon with a 5-player team.  In your planning, you presumably have some idea of roughly how much damage your group can deal per round, on average.

And that average ABSOLUTELY includes the likelihood that you're going to roll one or two crit fails/successes.   You'd instinctively take that into account.


A similar principle applies here.  "On average I'll do a little bit of damage to my opponent's deck with my Warrior - that average amount is increased somewhat by the possibility that I hit my opponent's Warrior." 
The upside is so huge here that the overall "average damage" (as it were) is probably dragged up noticeably even if the likelihood of the event is small.

But this is a small scale. You have one chance of hitting something with Warrior before you want to turn it into a Hero, and in 90-93% of cases, it doesn't hit your opponent's Warrior. So if your opponent willingly gave himself a small disadvantage in order to prepare for his Warrior getting hit, 90-93% of the time he just has the small disadvantage and that's all it did for him (and probably around 7-10% of the time he still loses because he's still one shuffle behind you even if he has a backup Page going on). Obviously if you want the second Page for other reasons, you want it anyway so yeah.

If I was teaching Dominion to sentient computers, I would mention that when the disadvantage from getting a second Page instead of something else is almost negligible, as well as when you're already so much ahead that your opponent's only chance of winning is pretty much to hope for that small chance of hitting your Warrior, you might still want a second Page just in case your Warrior gets trashed. Unfortunately, we are humans and humans are garbage at estimating any probabilities so it's better to forget about these edge cases when you're actually playing the game.
I wasn't really arguing that getting a second page just to defend against a warrior hit is automatically a good idea.

It's more that I object to your arguing style. But this is not news.

Hooray, pedantry!
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M Town Wins-Losses (6-2, 75%): 71, 72, 76, 81, 83, 87 - 79, 82.  M Scum Wins-Losses (2-1, 67%): 80, 101 - 70.
RMM Town Wins-Losses (0-1, 0%): x - 31.  RMM Scum Wins-Losses (3-3, 50%): 33, 37, 43 - 29, 32, 35.
Modded: M75, M84, RMM38.     Mislynched (M-RMM): None - None.     Correctly lynched (M-RMM): 101 - 33, 33, 35.       MVPs: RMM37, M87

Awaclus

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Re: Homage to the Best Card
« Reply #5954 on: March 21, 2017, 04:16:50 pm »
0

It's more that I object to your arguing style. But this is not news.

What's wrong with my arguing style?

Minotaur

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Re: Homage to the Best Card
« Reply #5955 on: March 21, 2017, 05:37:16 pm »
0

In other words, E[X] = sum_x(x*P(X=x)).

P(X=x) can be very small, but x can be large enough (or can not be)  to overcome that.
But if we're talking about a game of Dominion, x has to be between 0 and 1 (assuming it indicates winning probability). Such an x is only ever large if your overall winrate is pretty low otherwise.

That's true for all such x's in that interpretation, though.  Its contribution (i.e., weighted by the density function) to the expectation is what is important.

It think in theory, you want to do a min-max on the probability of winning.  I think it's called min-max?  You want a strategy that has the highest probability of winning against the best possible strategy that may be played against it.  In theory, you would need to search a tree of all possible Dominion games for the given kingdom, but that's computionally freaking impossible, obviously.  So instead you try to figure out something good enough and take heuristic shortcuts to whatever you can manage, and then you lose against Lord Rattington sometimes and omg I want die.
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Minotaur

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Re: Homage to the Best Card
« Reply #5956 on: March 21, 2017, 05:41:07 pm »
0

How likely am I to lose if I don't get another Page (perhaps because the Warrior died lolol)?

vs

How likely am I to lose if I do get another Page (perhaps because of too much Silver or terminal collisions or whatever)?

It's complicated, because we have to assume that you're doing everything else 100% perfect like a god except for that one decision.

This has been a(n - I think -) technically correct but 100% useless and impractical answer.  Good day.
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AdrianHealey

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Re: Homage to the Best Card
« Reply #5957 on: March 21, 2017, 08:34:40 pm »
0

Getting additional pages increases the chance your warrior hits something interesting btw
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Minotaur

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Re: Homage to the Best Card
« Reply #5958 on: March 22, 2017, 12:28:16 am »
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Getting additional pages increases the chance your warrior hits something interesting btw

Such as the Silvers your opponent has from also buying too many Pages.

(Page is complicated!)   :-[
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Minotaur

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Re: Homage to the Best Card
« Reply #5959 on: April 09, 2017, 04:23:02 pm »
+17

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Minotaur

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Re: Homage to the Best Card
« Reply #5960 on: April 13, 2017, 11:51:08 pm »
0

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Minotaur

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Re: Homage to the Best Card
« Reply #5961 on: May 07, 2017, 12:36:51 pm »
+19

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Minotaur

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Re: Homage to the Best Card
« Reply #5962 on: May 10, 2017, 11:56:37 am »
+7

Roses are red.
Wine is for pleasure.
Lord Rattington always
misplays his alt-treasure.
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SirClemens

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Re: Homage to the Best Card
« Reply #5963 on: June 26, 2017, 05:21:42 pm »
+9



Talking about the german version of Empires
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Minotaur

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Re: Homage to the Best Card
« Reply #5964 on: June 27, 2017, 12:19:09 am »
0

My brain is microscopic.  I put alt VP in with regular VP by cost in addition to the rest of the small-brain stuff.
« Last Edit: June 27, 2017, 12:45:28 am by Minotaur »
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werothegreat

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Re: Homage to the Best Card
« Reply #5965 on: August 03, 2017, 04:41:55 pm »
+5

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Re: Homage to the Best Card
« Reply #5966 on: August 13, 2017, 12:14:02 pm »
+5

Oh hey look took me long enough

« Last Edit: August 13, 2017, 02:40:08 pm by werothegreat »
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Re: Homage to the Best Card
« Reply #5967 on: September 17, 2017, 02:52:55 am »
+2

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ThetaSigma12

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Re: Homage to the Best Card
« Reply #5968 on: September 18, 2017, 07:08:33 pm »
+10

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