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ehunt

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prizes
« on: January 24, 2013, 02:01:00 pm »
+1

i would like to know the answer to the following:

imagine that followers is a kingdom card costing n.

Player A's strategy is to buy only money and green cards.
Player B's strategy is to buy only money until he can afford followers, at which point he buys it, then to revert to buying money and green cards.

What is the smallest value of n such that player A is expected to defeat player B?

(assume player B's play strategy for followers is just "always play followers," that player A's discard strategy is the obvious one, etc., if there are choices. also note that in the presence of followers Player A may wish to buy duchies later or earlier than "standard," probably later.)
« Last Edit: January 24, 2013, 02:02:44 pm by ehunt »
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sudgy

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Re: prizes
« Reply #1 on: January 24, 2013, 02:24:14 pm »
0

So player B only buys one followers?
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Drab Emordnilap

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Re: prizes
« Reply #2 on: January 24, 2013, 02:33:31 pm »
0

"expected to defeat"? How much of a percentage are we talking about?

If it's anything better than 50% is your goal, then I say that n is $15.
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Axxle

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Re: prizes
« Reply #3 on: January 24, 2013, 02:36:37 pm »
0

Well at 8 you need to play it three times to get a point swing equal to the opportunity cost of not buying a province, and it also allows you to buy green slightly easier with the draw and make them have less buying power with the militia attack.  I think a bit more than that might be a good start, 9 or 10?

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ehunt

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Re: prizes
« Reply #4 on: January 24, 2013, 05:02:05 pm »
0

So player B only buys one followers?

that's what i had in mind, although maybe it's best to give player B the option to buy "optimally many" if it's not much harder to code
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Morgrim7

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Re: prizes
« Reply #5 on: January 24, 2013, 06:02:13 pm »
0

id say 6 or 7
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Re: prizes
« Reply #6 on: January 25, 2013, 02:10:42 am »
+5

modified my version of dominiate...

$9 seems to tie, mayby with a close win for Followers, $10 is a clear win [Edit: for BM].  Buying Provinces also for Followers and the Followers only if you can afford it by chance also gives a clear win at $9, and ties at $10.
« Last Edit: January 25, 2013, 08:41:56 am by DStu »
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Morgrim7

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Re: prizes
« Reply #7 on: January 25, 2013, 02:44:53 am »
0

modified my version of dominiate...

$9 seems to tie, mayby with a close win for Followers, $10 is a clear win.  Buying Provinces also for Followers and the Followers only if you can afford it by chance also gives a clear win at $9, and ties at $10.
9? Wow. I guess I overestimated that Estate...
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Re: prizes
« Reply #8 on: January 25, 2013, 02:40:08 pm »
0

Don't forget the discard attack...

Axxle

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Re: prizes
« Reply #9 on: January 25, 2013, 02:58:21 pm »
0

modified my version of dominiate...

$9 seems to tie, mayby with a close win for Followers, $10 is a clear win [Edit: for BM].  Buying Provinces also for Followers and the Followers only if you can afford it by chance also gives a clear win at $9, and ties at $10.
I guessed right!
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ednever

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Re: prizes
« Reply #10 on: January 25, 2013, 04:56:33 pm »
0

Hey simulators:

How would followers compete against other cursers?

Specifically:
Followers at $5, win rate vs optimal witch, mb, etc
Followers at $6, same
Followed at $7, same.

My instinct is that followers wins at $5 by a significant margin. I'll bet it wins at $6 too, but close. It loses at $7.

(but obviously a combined strategy of buying witch+followers at $7 may dominate. The early curser being more important than the more powerful one)

Ed
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ehunt

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Re: prizes
« Reply #11 on: January 25, 2013, 05:42:15 pm »
0

Hey simulators:

How would followers compete against other cursers?

Specifically:
Followers at $5, win rate vs optimal witch, mb, etc
Followers at $6, same
Followed at $7, same.

My instinct is that followers wins at $5 by a significant margin. I'll bet it wins at $6 too, but close. It loses at $7.

(but obviously a combined strategy of buying witch+followers at $7 may dominate. The early curser being more important than the more powerful one)

Ed

but counterargument -- followers vs. witch, the followers benefits over witch only by being a discard attack in a curse game, which isn't that strong, whereas the witch benefits by not giving you an estate. i think the reason followers is so dominant in tournament games is that it's the exclusive curser, no?
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SirPeebles

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Re: prizes
« Reply #12 on: January 25, 2013, 05:48:36 pm »
0

I wonder how many plays that $9 Followers is getting.  If it shows up late, then the Estates might be good, and the discard might hurt quite a bit.  I doubt the $9 Followers is emptying the Curse pile, but the Estates and Curses could certainly make up for any slips in the Duchy Dance.

Edit:  Ah, I think I misunderstood ehunt here.  I think it would depend on the price point.  A $5 Witch may be better than a $5 Followers, while a $10 Followers may be better than a $10 Witch.
« Last Edit: January 25, 2013, 05:53:36 pm by SirPeebles »
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WanderingWinder

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Re: prizes
« Reply #13 on: January 25, 2013, 05:53:10 pm »
0

Hey simulators:

How would followers compete against other cursers?

Specifically:
Followers at $5, win rate vs optimal witch, mb, etc
Followers at $6, same
Followed at $7, same.

My instinct is that followers wins at $5 by a significant margin. I'll bet it wins at $6 too, but close. It loses at $7.

(but obviously a combined strategy of buying witch+followers at $7 may dominate. The early curser being more important than the more powerful one)

Ed

but counterargument -- followers vs. witch, the followers benefits over witch only by being a discard attack in a curse game, which isn't that strong, whereas the witch benefits by not giving you an estate. i think the reason followers is so dominant in tournament games is that it's the exclusive curser, no?
Discard attacks are still good, and the estates aren't all bad. I mean, by your logic, we should be willing to pay 10+ for witch in a BM game.
I'd probably say at 6 it will be close.

Diadem is trivially equivalent to gold in this case.
Trusty Steed is probably worth 7-8 here (good at 7, not so hot at 8). (You should obviously never play it for the actions, but cards and money is very strong, and silver flood is nothing to sneeze at at the right moments especially).
Bag of Gold is probably decent at 6, not terribly good at 7.
And Princess is probably similar to that but slightly worse - a very mild improvement (but close to a wash) at 6, not very good at 7.

Of course, this isn't close to the best way to evaluate them in general, but it is kind of fun.

SirPeebles

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Re: prizes
« Reply #14 on: January 25, 2013, 05:56:42 pm »
+4

 8)
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Re: prizes
« Reply #15 on: January 25, 2013, 08:02:14 pm »
0

And Princess is probably similar to that but slightly worse - a very mild improvement (but close to a wash) at 6, not very good at 7.

Princess without support is like, barely better than Bridge. The only benefit is that it reduces the cost of Estates to $0.
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WanderingWinder

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Re: prizes
« Reply #16 on: January 25, 2013, 08:15:46 pm »
0

And Princess is probably similar to that but slightly worse - a very mild improvement (but close to a wash) at 6, not very good at 7.

Princess without support is like, barely better than Bridge. The only benefit is that it reduces the cost of Estates to $0.
It's better any time you buy more than one card (by a buck). In the case where you only buy one card, it's uh, well it's not better than silver. But I assume you could adjust to grabbing like gold+silver with $5 and princess in play, etc. It will certainly be a clear win at $5, and my guess is that it's a very close win for princess at 6, but I wouldn't be all that surprised if it weren't.

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Re: prizes
« Reply #17 on: June 21, 2013, 03:23:44 pm »
+3

My answer is n=10.  You may find the following data useful:

Followers Cost, Followers Win %, Big Money Win%, Tie%
0, 95.15, 4.45, 0.4
1, 95.15, 4.45, 0.4
2, 95.15, 4.45, 0.4
3, 94.78, 4.75, 0.47
4, 94.7, 4.83, 0.47
5, 90.65, 8.63, 0.72
6, 80.4, 18.19, 1.41
7, 76.41, 22.01, 1.58
8, 68.96, 29.49, 1.55
9, 53.39, 45.12, 1.49
10, 30.9, 67.95, 1.15
11, 13.18, 86.22, 0.6
12, 4.12, 95.73, 0.15
13, 1.02, 98.94, 0.04
14, 0.12, 99.86, 0.02
15, 0, 100, 0

Eventually, the followers buyer never wins because he can't afford the followers, and thus never allowed to buy green according to the rules ... ;)

Details on player behavior: (modulo the followers constraint, they play identically)

Buy Province only after owning 3 gold
Otherwise Buy Duchies if available Province count <= 4
Otherwise Buy Estate if available Province count <= 2
Otherwise Buy gold
Otherwise Buy Silver
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Axxle

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Re: prizes
« Reply #18 on: June 21, 2013, 04:10:03 pm »
0

winning just over 50% against big money is very poor for an attack though.  It needs to be exciting so $9 would be a much better cost.
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