Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Empathy]

I want to share an opening I once saw. I can't remember whom I copied it from, but it struck me as interesting at the time, although maybe for niche boards. After some practical experience, it's amazing against sea hag (and most other cursers), and pretty decent on silver-dominated boards (as opposed to engines or boards where hitting 5 is important). I do not know the probability of the following relevant events, and am too lazy to compute or simulate them out. Can anybody give me a hand?

1) Typical case: Watchtower misses Trader, hits $3 hand. Topdeck silver. Trader hits estate.

2) Good collision: Watchtower hits Trader together with estate. Topdeck two silvers. Most likely buy gold.

3) Bad collision: Watchtower hits Trader without estate. Cry. Trash watchtower with trader. Buy watchtower or silver depending on board.

4) Watchtower misses trader and does not hit $3, Trader hits estate.

5) Trader does not hit estate, Watchtower hits $3. Topdeck silver.

6) Trader does not hit estate and Watchtower does not hit $3. Cry.



1) + 5) are essentially equivalent to opening silver+Trader at the cost of getting hit by one bureaucrat. The defense provided by WT makes it totally worth it in cursing games.

2) is amazing, as it compares to having a double-silver opening that draws into a gold on first reschuffle. You get hit by a ghostship but trash an estate.

3) + 6) are pretty bad.

4) means replacing an estate by a watchtower, but getting hit by a ghostship (as both the trader and WT didn't do anything significant), which is pretty bad.

[Drab Emordnilap]

3) Bad collision: Watchtower hits Trader without estate. Cry.

Trader the Watchtower, buy a new Watchtower? Not that awful, if you wanted Silver anyways. (And you have to have $3 if you didn't have an Estate in hand.)

[Kirian]

So let's assume you want a ton of Silver, either just to smooth out your deck or for Fedoum/Gardens/whatever.

(2)  Two topdecked Silvers.  Pretty amazing.
(1)  One topdecked Silver, two more in discard.  Great.
(3)  Use Trader on WT, buy a new WT, Three Silvers in discard.  Still pretty darn good.
(5)  One Silver in discard, one Silver topdecked.  Not bad but not great.
(4)  Two Silvers in discard.  No better or worse than hitting 3/4 on turns 3/4.
(6)  This sucks.

Given how awesome both Trader and WT are in cursing games, I think this opening works pretty well!

[Empathy]

I somehow missed the trader on watchtower play. Probably didn't turn up in the couple of games I played. Good catch!

This definitely strengths my intuition that this is a strong opening in cursing games, and probably also very good in alternate green and boards with weak $5s. To make an article however we need the probabilities of all these events.

Any other ideas?

[Drab Emordnilap]

(4)  Two Silvers in discard.  No better or worse than hitting 3/4 on turns 3/4.

You're forgetting the $3 buy on your Trader turn, so that's a third silver in the discard. (If Watchtower misses Trader and $3, that hand must be W/c/c/e/e, so Trader gets T/c/c/c/e.)

Although, it looks like you're leaving off buys on most of them, except 3). If you take away buys, then 3) and 4) are similar results. (One has an extra Estate in the deck.)

[florrat]

Probabilities: [Note: in the computations I assumed you did not topdeck anything. This is unlikely, but it does not change the probability of getting trader or watchtower in the same hand. If it really matters, I'll try to recompute everything including topdecking]

23.99%	Watchtower with at least 3 copper and trader with at least 1 estate in different hands on T3/T4	(1)
21.46%	Watchtower and trader in the same hand on T3/T4, with estate	(2)
12.63%	Trader in T3/T4 with estate, watchtower in T5	(4) or (1)
10.1%	Watchtower in T3/T4 with at least 3 copper, trader in T5	(5) or (1)
8.84%	Watchtower and trader in the same hand on T3/T4, without estate	(3)
7.58%	Watchtower with at most 2 copper and trader with at least 1 estate in different hands on T3/T4	(4)
5.05%	Watchtower in T3/T4 with at most 2 copper, trader in T5	(6) or (4)
5.05%	Watchtower with at most 2 copper and trader without estate in different hands on T3/T4	(6)
2.53%	Trader in T3/T4 without estate, watchtower in T5	(6) or (5)
1.52%	Trader and Watchtower both in T5	(3) or (2)
1.26%	Watchtower with at least 3 copper and trader without estate in different hands on T3/T4	(5)
100.01%	Total

Ugly Mathematica code: (please don't read this, I only included this if you don't believe me or something - and sure, I could have made a mistake)

Code: [Select]

perm=Permutations@Join[Array["c"&,7],Array["e"&,3],{"w","t"}];
f[{}]:=-1
f[{x_}]:=x
g[x_]:=1/;x>=3
g[x_]:=0/;x>=0
g[x_]:=-1
result=SortBy[Tally[{Sign@f@Cases[#,{_,_,1,1}][[All,2]],Sign@f@Cases[#,{_,_,0,1}][[All,2]],g@f@Cases[#,{_,_,1,0}][[All,1]]}&/@({Count[#,"c"],Count[#,"e"],Count[#,"w"],Count[#,"t"]}&/@{#[[1;;5]],#[[6;;10]]}&/@perm)],-#[[2]]&];
MapAt[Round[(100#)/15840.,.01]&,#,2]&/@result//Column

[Avalanchian]

I was trying to do this with pen and paper. Not only was I beaten to the punch, but it looks like my reasoning was entirely flawed too.

Stop trying to be clever Ava =/

[florrat]

I was trying to do this with pen and paper. Not only was I beaten to the punch, but it looks like my reasoning was entirely flawed too.

Stop trying to be clever Ava =/

I started by hand, then started Mathematica to use as calculator, and then I thought: oh well, let's just brute force it, there are just 15840 different deck orders when shuffling after turn 2.

[Empathy]

Impressive florrat!

Ok, between florrat's simulation and Drab and Kirian's analysis and the fact that I wasn't even the first one to come up with this opening, I do feel like

a) We should be able to conclude and write a cute little article.

b) That I shouldn't be the primary author. How do you guys want to organize it?


I guess before we get to b) we first need to compile all this nice data and compare the opening to both double silver and  joat/silver. I want the comparison to joat, because it is a very strong opening that achieves similar objectives: trashes estates, floods silvers and defends cursers. It therefore will be good on similar boards (presence of cursers, pro-silver boards, non-essential $5).

[florrat]

About an article: I'd prefer not to write it, but I'd like to have my name mentioned in there somewhere. I'm willing to do similar analysis for other openings if you say what the exact strategy is.

I like to play with Mathematica, and I liked this puzzle, so I did a little more analysis, including the topdecking of silver in turn 3. Probably what I computed is not that interesting, but anyway, here I go 

First some abbreviations:
WT:watchtower
T:trader
tw+: draw WT, T, and at least 1 estate [trash estate, topdeck 2 silver]
tw-: draw WT, T, and no estate [trash WT, buy WT]
t+: draw T, at least 1 estate (no WT) [trash estate]
t-: draw T, and no estate (and no WT or silver)
t=: draw T and no estate (and no WT), but with a silver
w+: draw WT with at least $3 (no T) [buy and topdeck silver]
w-: draw WT with at most $2 (no T)
!t: do not draw trader in T3/T4
!w: do not draw watchtower in T3/T4

It is possible to draw a trader without watchtower or estate, but with a silver you just topdecked with WT, in that case you can do three things: buy with $5; trash copper, buy with $4, trash silver (gaining 3), buy with $3.

The probabilities are as follows:

20.45%	option 1 (w+ and t+)
21.46%	option 2 (tw+)
8.84%	option 3 (tw-)
7.58%	option 4 (w- and t+)
2.27%	option 5 (w+ and t- has probability 0.63% and w+ and t= has probability 1.64%)
5.05%	option 6 (w- and t-)
12.63%	t+ and !w
12.63%	w+ and !t
5.05%	w- and !t
2.53%	t- and !w
1.52%	!t and !w

Also you'll reach $5 in T3/T4 with probability 8.59% and you reach at least 6 with probability 9.97%

If you maximize your silver (that is, buy silver whenever you hit $3-$5; and trash silver in the case "t=") then after turn 4 there is
30% chance you have 4 silver;
33% chance you have 3 silver;
24% chance you have 2 silver;
13% chance you have 1 silver.
This gives an average of 2.8 silvers. You always will have 1 WT and 1 T, and an average of 0.1 gold (if you buy one with $6 or $7), and have trashed on average 0.08 copper (if you always trash in case t-) and 0.62 estate. Oh, and you have on average 0.4 silver topdecked for turn 5.

Raw data:

Code: [Select]

Format: Probability (%)  [turn 3]  [turn 4]
5.0505 t+;$3;  w+;$3;
4.5455 tw+;$2; $6;
4.5455 w+;$3;  t+;$4;
3.7879 w-;$2;  t+;$3;
3.7879 t+;$2;  w+;$3;
3.7879 t+;$3;  w-;$2;
3.7879 $3;     tw+;$2;
3.7879 $4;     tw+;$2;
3.0303 w+;$3;  $5;
2.5253 tw-;$3; $3;
2.5253 t+;$3;  $3;
2.5253 $3;     t+;$3;
2.5253 $3;     w+;$3;
2.5253 $3;     tw-;$3;
2.2727 tw+;$2; $7;
2.2727 w+;$3;  $4;
1.8939 t+;$2;  $4;
1.8939 w-;$2;  $4;
1.8939 w-;$2;  t-;$4;
1.8939 t+;$2;  w+;$4;
1.8939 $4;     t+;$2;
1.8939 t-;$4;  w-;$2;
1.8939 $4;     w-;$2;
1.8939 $4;     tw+;$1;
1.5152 tw+;$1; $7;
1.5152 w+;$3;  t=;$3;
1.5152 w+;$3;  t+;$3;
1.2626 t+;$3;  $4;
1.2626 $4;     t+;$3;
1.2626 $4;     w+;$3;
1.2626 $2;     tw-;$3;
1.2626 tw-;$3; $2;
1.1364 w+;$4;  $4;
1.1364 tw+;$1; $6;
1.1364 w+;$4;  t+;$4;
1.1364 tw+;$2; $5;
1.1364 w+;$4;  t+;$3;
0.7576 $5;     tw+;$1;
0.6313 tw-;$3; $4;
0.6313 $3;     $4;
0.6313 w-;$1;  t-;$4;
0.6313 $2;     t-;$4;
0.6313 $3;     t-;$4;
0.6313 t+;$1;  w+;$4;
0.6313 t+;$3;  w+;$4;
0.6313 $2;     w+;$4;
0.6313 $3;     w+;$4;
0.6313 t-;$4;  $3;
0.6313 $4;     $3;
0.6313 t-;$4;  w+;$3;
0.6313 $4;     tw-;$3;
0.6313 t-;$4;  $2;
0.6313 t-;$4;  w-;$1;
0.3788 t+;$2;  $5;
0.3788 w-;$2;  $5;
0.3788 w+;$3;  $6;
0.3788 w+;$4;  $5;
0.3788 $5;     t+;$2;
0.3788 $5;     w-;$2;
0.3788 $5;     tw+;$2;
0.3788 w+;$4;  $3;
0.2525 t+;$1;  $5;
0.2525 w-;$1;  $5;
0.2525 $5;     t+;$1;
0.2525 $5;     w-;$1;
0.1263 $2;     $5;
0.1263 tw+;$0; $7;
0.1263 w+;$4;  t=;$3;
0.1263 $5;     $2;
0.1263 w+;$4;  t+;$2;
0.1263 $5;     tw+;$0;

[Powerman]

Just played a game like this... it went great!

http://dominion.isotropic.org/gamelog/201302/11/game-20130211-133800-9063e728.html