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Author Topic: Five Two Splits For The First Player - Anyone Looked Into This?  (Read 7870 times)

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Triumph44

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This has probably been asked/answered somewhere but it's a tricky thing to search for - I'm curious if anyone has looked at winrates where the player who goes first (hereafter Player A) gets a 5 2 split and Player B does not.  I play most of my Dominion with one other player on Goko, and we've agreed that when Player A has a 5 2 split and Player B does not, we reshuffle.  I recognize this is 'part of the game' and that were I playing against a worse player, I'd want to keep 5 2 splits in the game to increase variance, but for the most part it makes for a worse game among players of intermediate skill and above.  It took years for Magic: The Gathering to realize that the advantage inherent in going first meant that that player should not draw a card on his or her first turn, and I suspect something like this is going on in Dominion as well.  I'd estimate that among equally skilled players, the winrate is around 70% for a Player A going first and getting 5 2 while his or her opponent has a 4 3.

I'd also be curious about winrates where Player B gets a 5 2 split and Player A does not.
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sudgy

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #1 on: April 23, 2014, 01:53:36 am »
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There are often times where I don't like getting the 5/2 split.  There's some really good $4 (Remake comes to mind), and/or the $5s aren't the best, and it usually isn't that great.
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BadAssMutha

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #2 on: April 23, 2014, 02:45:45 am »
+2

Sometimes 5/2 is much better than 4/3. Sometimes it is much worse. Sometimes it's about the same, and makes for a very interesting game with competing strategies. Sure, on boards where one person opens Mint/Fool's Gold and the other can't, it's probably not worth playing, but you're missing out on some interesting games by skipping the different opens.

If the 5/2 is really that much better than the 4/3, I don't think first-turn advantage is going to increase its power that much more in most cases. I would imagine P2's winrate should be pretty close to P1's given the favorable split.
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eHalcyon

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #3 on: April 23, 2014, 02:58:16 am »
+10

Earlier this month, there was a feature request for the Dominion Salvager extension to automatically have players play dead turns until they have identical hands (if all players are mutually agreed, of course).  You can see the suggestion here.  What follows is a lengthy (and sometimes heated) discussion about the merits of forcing identical starting hands.  If you wish, you can jump to Donald X's response here.

Opinions are varied, but I think it's safe to say that the opening split is not the be all end all.  There is some luck there, but there is luck all throughout the game.  Having a better split at the start does not tilt the odds that much, and note that 5/2 is not always favourable anyway.
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SCSN

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #4 on: April 23, 2014, 03:59:30 am »
+5

I think that averaged over all boards, if P1 is equal to or higher in skill than P2, P2's winrate would actually be higher with a 4/3 split than with a 5/2 if P1 has 5/2, and vice versa.

I do think that 5/2 is a bit (but not a lot) better on average, but I expect this difference to be quite small and as P2 worth giving up on in exchange for the large increase in variance, which clearly benefits him and him alone.

So, OP, I think what you're doing has the opposite effect of what you intend.
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jaybeez

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #5 on: April 23, 2014, 01:39:39 pm »
+8

The more I play Dominion, the more I think that the shuffle luck you have before the second reshuffle actually has a bigger impact on the game than your opening split.
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Triumph44

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #6 on: April 23, 2014, 03:06:50 pm »
0

Hmm, not quite the 'You're a genius, that's a brilliant idea' reception I expected.

Sometimes 5/2 is much better than 4/3. Sometimes it is much worse. Sometimes it's about the same, and makes for a very interesting game with competing strategies. Sure, on boards where one person opens Mint/Fool's Gold and the other can't, it's probably not worth playing, but you're missing out on some interesting games by skipping the different opens.

If the 5/2 is really that much better than the 4/3, I don't think first-turn advantage is going to increase its power that much more in most cases. I would imagine P2's winrate should be pretty close to P1's given the favorable split.

Keep in mind that we're not default 'skipping the different opens' - if Player 2 gets 5/2, he keeps it.

Earlier this month, there was a feature request for the Dominion Salvager extension to automatically have players play dead turns until they have identical hands (if all players are mutually agreed, of course).  You can see the suggestion here.  What follows is a lengthy (and sometimes heated) discussion about the merits of forcing identical starting hands.  If you wish, you can jump to Donald X's response here.

Opinions are varied, but I think it's safe to say that the opening split is not the be all end all.  There is some luck there, but there is luck all throughout the game.  Having a better split at the start does not tilt the odds that much, and note that 5/2 is not always favourable anyway.

Ah, okay, excellent, thanks for the link.  I haven't read the non-Vaccarino posts yet, but I will.  No, obviously there is luck throughout the game, but it can be particularly disspiriting when someone opens Mountebank or Witch on a no-trash board.  It's a particularly visible element of chance (and fwiw, I agree with jaybeez that 2nd reshuffle luck may be a bigger factor but obviously that can't be controlled in any way).  Having matching hands as a default is terrible and I agree with Mr. Vaccarino that people who play that way are monsters.  Okay, that's a bit harsh, but by no means would I want to have matching hands as a default.

I think that averaged over all boards, if P1 is equal to or higher in skill than P2, P2's winrate would actually be higher with a 4/3 split than with a 5/2 if P1 has 5/2, and vice versa.

I do think that 5/2 is a bit (but not a lot) better on average, but I expect this difference to be quite small and as P2 worth giving up on in exchange for the large increase in variance, which clearly benefits him and him alone.

So, OP, I think what you're doing has the opposite effect of what you intend.

Entirely possible that I don't have enough experience with all sets and am making a conclusion based on too many games where I've not played all sets (I estimate I've played 500 All Sets games out of the 2300 or so Dominion games I've played).  Alchemy-heavy boards become more difficult with most 5/2 splits, e.g.  It's just the kind of thing I wish we had 10,000 game results on.

Also now I'm not sure I follow your point, and am not sure you followed mine.  Just to clarify, if Player 1 gets a 5 2 split and Player 2 does not, we skip the first 4 turns and reshuffle.  Player 1 still gets to go first.  I guess you're saying that given one player has 5 2, the other player has a better winrate with 4 3 than with a 5 2 also - I could see being true, but don't see how it necessarily negates my idea.
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eHalcyon

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #7 on: April 23, 2014, 03:18:17 pm »
+3

Hmm, not quite the 'You're a genius, that's a brilliant idea' reception I expected.

The f.ds community has been around for quite a while now, so we've discussed most of these things to death already.  I'm pretty sure we could find years-old discussions about this very topic. :P

I think that averaged over all boards, if P1 is equal to or higher in skill than P2, P2's winrate would actually be higher with a 4/3 split than with a 5/2 if P1 has 5/2, and vice versa.

I do think that 5/2 is a bit (but not a lot) better on average, but I expect this difference to be quite small and as P2 worth giving up on in exchange for the large increase in variance, which clearly benefits him and him alone.

So, OP, I think what you're doing has the opposite effect of what you intend.

Entirely possible that I don't have enough experience with all sets and am making a conclusion based on too many games where I've not played all sets (I estimate I've played 500 All Sets games out of the 2300 or so Dominion games I've played).  Alchemy-heavy boards become more difficult with most 5/2 splits, e.g.  It's just the kind of thing I wish we had 10,000 game results on.

Also now I'm not sure I follow your point, and am not sure you followed mine.  Just to clarify, if Player 1 gets a 5 2 split and Player 2 does not, we skip the first 4 turns and reshuffle.  Player 1 still gets to go first.  I guess you're saying that given one player has 5 2, the other player has a better winrate with 4 3 than with a 5 2 also - I could see being true, but don't see how it necessarily negates my idea.

My understanding of your proposal is that there is a gentleman's agreement to prevent the opening scenario where p1 opens 5/2 (or 2/5) and p2 does not.  The specific method to do so in Dominion Online is to just play dead hands to essentially reset the game.

SCSN is suggesting that your proposal will actually decrease the win rate of p2, all else equal.  If I am reading it correctly, the reasoning is that the advantage of opening 5/2 is, on average, smaller than first player advantage (FPA).  If p2 also starts with a 5/2 split, FPA matters a lot more.  But if the second player starts with 4/3 instead, the variance from the different opening hands will give them a better chance of overcoming FPA.
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theblankman

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #8 on: April 23, 2014, 09:34:41 pm »
+2

Hello OP... I'm the poor schlub who started that discussion you've been reading :) 

I think the split difference is primarily noticeable when there's a $5 card that dominates for the player who gets to play it first (you mentioned Witch and Mountebank, Cultist is another).  There are some strong 5/2-only combos too, like Mint/FG.  But unless those cards are out there, 5/2 isn't as huge as you think it is.  Put it this way... if your opponent's opening buys are Hunting Party and nothing, and yours are two Silvers, are you so far behind that you should resign right there?  And even if his opening buy is Mountebank, if you open Silver/Silver there's a pretty decent chance you get yours on turn 3 or 4.  After that, you just need your opponent's Mountebank(s) to miss one shuffle and you have a chance to even up the total Mountebank plays. 

So if I'm saying all that, why did I suggest the feature in the first place???  Several reasons:
1) I also thought the opening split was a bigger deal than it probably is.  The ensuing discussion, as heated as it got, taught me quite a bit about the game. 
2) Isotropic had this option, other players had mentioned it, and I figured as an option, it's cool for players who agree that they want as little variance as possible, say if they're in a tournament or other highly competitive context.  I do like giving people choices.  But it was not something I thought should be default. 
3) I thought my method of doing it with Salvager, instead of getting MF/Goko to provide the option, was a little bit clever and I wanted to get other programmers' opinions about it :) 

Since you play primarily with a friend, you're obviously free to have any agreement you want about openings, but especially after the discussion in the other thread, I'd encourage you to play out those 5/2 openings for at least a few shuffles... sometimes they're as great as advertised, sometimes not.  If it becomes clear that one player is dominating because they got to open Witch or whatever, you can always resign and start a new game.  Even use the same kingdom if you're playing Casual or Unrated.  No shame in resigning if you honestly think your chance to win is that low, but you shouldn't jump to that conclusion prematurely. 
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popsofctown

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #9 on: April 24, 2014, 01:42:46 am »
+1

Did councilroom not have one nice big flat % winrate for 5/2 vs. 4/3?
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c4master

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #10 on: April 24, 2014, 04:36:21 am »
0

I've also come around another example where 5/2 split was really bad, even as P1:

I opened Soothsayer/nothing.
My opponent opened Warehouse/Marauder.

I got really crushed. Reasons are probably
a) Warehouse (sifting is good and playing Marauder more often is even better)
b) Card draw for opponent due to Soothsayer (even more Marauder plays)

It would have been another story if there had been Cellar, Pearl Diver or even Chapel on the board. But in general, opening a power $5 card and nothing or just a mediocre (terminal) $2 like maybe Embargo is not such a great advantage. On avarage, there are a lot more reasonable $3 and $4 attacks than $5 attacks. Finding a board with no way to strike back is not that easy. And, $2 cards are always an option for the 4/3 player as well.

Taking into account that mirroring your P1 opponent means you'll be depending on shuffle luck to win this game, you have to commit that taking the variance of a 4/3 opening might be the better strategy (if you were to chose).

I wonder whether letting players chose their opening, espicially letting P2 chose after P1 made his first turn, would strengthen any of the seats.
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Qvist

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #11 on: April 24, 2014, 05:26:39 am »
+2

It really depends, but it's often a bigger disadvantage to open 5/2 on a board with Masquerade or Ambassador than opening 4/3 on a Mountebank board.

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #12 on: April 24, 2014, 05:38:44 am »
0

The important thing to note is that 4/3 has pretty decent fallback options for missing out on the $5.
You could always grab Silver/Silver for instance or a Silver equivalent to make up a bit with some extra economy.

With 5/2, you can get the same card or a better one than the 4/3 guy, but are often hampered by your $2.
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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #13 on: April 24, 2014, 05:41:04 am »
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I've also come around another example where 5/2 split was really bad, even as P1:

I opened Soothsayer/nothing.
My opponent opened Warehouse/Marauder.

I got really crushed. Reasons are probably
a) Warehouse (sifting is good and playing Marauder more often is even better)
b) Card draw for opponent due to Soothsayer (even more Marauder plays)

It would have been another story if there had been Cellar, Pearl Diver or even Chapel on the board. But in general, opening a power $5 card and nothing or just a mediocre (terminal) $2 like maybe Embargo is not such a great advantage. On avarage, there are a lot more reasonable $3 and $4 attacks than $5 attacks. Finding a board with no way to strike back is not that easy. And, $2 cards are always an option for the 4/3 player as well.

Taking into account that mirroring your P1 opponent means you'll be depending on shuffle luck to win this game, you have to commit that taking the variance of a 4/3 opening might be the better strategy (if you were to chose).

I wonder whether letting players chose their opening, espicially letting P2 chose after P1 made his first turn, would strengthen any of the seats.
Warehouse is very good agaist Soothsayer. It likes the increased hand size and isn't that bothered with the Curse.
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Triumph44

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #14 on: April 24, 2014, 11:44:03 am »
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Like I said, I think 5/2 has gotten less powerful, but I was just wondering if someone had the numbers, it seems not.  Obviously we could go back and forth debating boards where it's advantageous and disadvantageous. 
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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #15 on: April 24, 2014, 12:08:10 pm »
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I agree with SCSN. Player 2 is inherently at a disadvantage, and needs some luck to catch up assuming identical skill. Forcing identical starting hands decreases the randomness and thus player 2's chances of getting the luck he needs to catch up.
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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #16 on: April 24, 2014, 12:18:46 pm »
+1

I don't know if you've seen this data.  Most of the best openings are 5/2.

http://councilroom.com/openings

I don't think I ever aggregated 5/2 vs 4/3 across all boards though.
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Stealth Tomato

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #17 on: April 24, 2014, 12:54:52 pm »
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Earlier this month, there was a feature request for the Dominion Salvager extension to automatically have players play dead turns until they have identical hands (if all players are mutually agreed, of course).  You can see the suggestion here.  What follows is a lengthy (and sometimes heated) discussion about the merits of forcing identical starting hands.  If you wish, you can jump to Donald X's response here.

It would be hilarious if someone wrote a malicious script that causes the Salvager extension to take additional dead turns while the player using the script is live (or autocontrolled but picks up a few Silver before turning over control).
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Triumph44

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #18 on: April 24, 2014, 02:28:51 pm »
0

I don't know if you've seen this data.  Most of the best openings are 5/2.

http://councilroom.com/openings

I don't think I ever aggregated 5/2 vs 4/3 across all boards though.

Yeah, that's what I think and that's why we do this - that the best 5/2 opens are better than the best 4/3 opens, but that the worst 5/2 opens are worse than the worst 4/3 opens (because opening Silver Silver is always a possibility and is rarely awful [please don't give me cases where opening Silver Silver is clearly terrible, I'm aware there are plenty of boards where that is true, I'm saying when a skilled opponent opens Silver Silver he has a reason for doing so]).  This misses Dark Ages and Guilds which besides Cultist I don't think there's really any other overpowered 5 type opening in either set (and Baker mitigates the 5/2 problem - we play through on Baker boards where P1 gets 5/2)
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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #19 on: April 24, 2014, 02:49:38 pm »
+1

I don't know if you've seen this data.  Most of the best openings are 5/2.

http://councilroom.com/openings

I don't think I ever aggregated 5/2 vs 4/3 across all boards though.

Knowing that the best openings are 5/2 doesn't necessarily prove that 5/2 is the best opening, so to speak. Like, there are a couple 5/2 power combos, and if one of them is in the kingdom then 5/2 dominates. But those combos are necessarily quite rare, and it might well be that the advantage that 5/2 has on those boards is far outweighed by the flexibility of 4/3 in the more common case where no power combo is present.
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theblankman

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Re: Five Two Splits For The First Player - Anyone Looked Into This?
« Reply #20 on: April 24, 2014, 02:59:22 pm »
0

It would be hilarious if someone wrote a malicious script that causes the Salvager extension to take additional dead turns while the player using the script is live (or autocontrolled but picks up a few Silver before turning over control).
I think AI and I actually discussed that possibility during the short time where we thought the proposed Salvager feature might be implemented.  Or maybe I just thought about it myself.  To my knowledge there's not an easy easy way to prevent it, but we figured anyone who tried would be immediately blacklisted, and if the victim frequented these forums, they'd probably name-and-shame as well.  So someone might grab an advantage in one game but at the cost of getting future games at all.
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