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Author Topic: How many points is 1st player advantage?  (Read 6367 times)

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soulnet

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How many points is 1st player advantage?
« on: May 11, 2013, 10:56:32 am »
0

Lets assume for a moment no alt-VP cards nor VP chips, no Colonies and 2 players. How many points for 2nd player would balance 1st payer advantage?

So, if both had the same number of turns, we count as always and if the score is tied, the game is a tie.

But, if the first player had an extra turn and wins by 1 point, it seems like the 1st player advantage may have played a huge role. Even 2 or 3 points.

Do you think there is some threshold that could be established that is better (i.e., more balanced) than .5 points for 2nd player as it is now?

Lets try to avoid "depends on the kingdom" which of course is true, but it does not really contributes much to discussion.
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Grujah

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Re: How many points is 1st player advantage?
« Reply #1 on: May 11, 2013, 11:00:11 am »
0

Imo this:
Quote
So, if both had the same number of turns, we count as always and if the score is tied, the game is a tie.

Could change to:
If tied, player who played last wins.

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Kirian

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Re: How many points is 1st player advantage?
« Reply #2 on: May 11, 2013, 11:37:06 am »
+1

I don't think you can give it a generalized point value that won't immediately give a second player advantage; in some cases a huge advantage.

The only possibility would be to play a variant where you bid a number of points to go first.  This would, obviously, DOTB.  But it would be fairer.
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GwinnR

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Re: How many points is 1st player advantage?
« Reply #3 on: May 11, 2013, 01:49:47 pm »
0

You could note it after every game. If you count enough games that would give you an nearly exact number of points.

But I try to make some calculations. In accordance with councilroom I win about 10% of the games more, if I'm first player. Assuming, that you normaly win with about 35 points that would make an advantage of 3,5 points, what seems realstic to me.
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soulnet

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Re: How many points is 1st player advantage?
« Reply #4 on: May 11, 2013, 01:54:29 pm »
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But I try to make some calculations. In accordance with councilroom I win about 10% of the games more, if I'm first player. Assuming, that you normaly win with about 35 points that would make an advantage of 3,5 points, what seems realstic to me.

I don't think the reasoning is correct. The proper use would be, what number would make you win at exactly the same rate as 1st or 2nd player? That's not necessarilly the average of your win margin, and even less necessarilly the average of points.

Even more difficult would be to consider the change of strategy due to the change of rules, specifically, the change on PPR considerations.
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eHalcyon

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Re: How many points is 1st player advantage?
« Reply #5 on: May 11, 2013, 07:50:16 pm »
0

I don't think you can give it a generalized point value that won't immediately give a second player advantage; in some cases a huge advantage.

The only possibility would be to play a variant where you bid a number of points to go first.  This would, obviously, DOTB.  But it would be fairer.

I will re-emphasize this, because the acronym might be overlooked by some -- it Depends On The Board.

On some boards, you eke out a tough victory by 1 point in a very close game.  On other boards, you completely dominate and still only win by 1 point, because you leverage your dominance to end the game quickly.  In other games, you completely dominate by a wide margin, and in still other games, you win by a wide margin but the game was still close (e.g. blowout megaturn games where both players have finely tuned engines but one manages to pull the trigger first).  The value of being the first player is different in all these cases.  Sometimes being first isn't even worth a single point, other times you might give up 50 points or more just for the chance to trigger your megaturn first.
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rrenaud

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Re: How many points is 1st player advantage?
« Reply #6 on: May 11, 2013, 08:09:02 pm »
+2

The stats here might be useful.

http://forum.dominionstrategy.com/index.php?topic=20.msg438#msg438

Gwinn's estimate seems reasonable, in light of that data.
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dondon151

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Re: How many points is 1st player advantage?
« Reply #7 on: May 11, 2013, 10:01:13 pm »
+2

Lets try to avoid "depends on the kingdom" which of course is true, but it does not really contributes much to discussion.

Why not? FPA is as little as an Estate in some kingdoms and a huge blowout in others. Giving 2nd seat a handicap is equivalent to handing him a win in half of the kingdoms and still being insufficient in the other half.
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ednever

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Re: How many points is 1st player advantage?
« Reply #8 on: May 12, 2013, 01:46:22 am »
0

Imo this:
Quote
So, if both had the same number of turns, we count as always and if the score is tied, the game is a tie.

Could change to:
If tied, player who played last wins.

This.

If you run CR stats, even if 2nd player won on ties, 1st player would still win more often.

True that on some kingdoms this will give p2 a slight edge, but on average p1 still has an edge. And right now the alternative is that p1 always has a slight edge and sometimes has a significant one.

Ed
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Davio

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Re: How many points is 1st player advantage?
« Reply #9 on: May 12, 2013, 01:52:20 am »
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Depends mostly on attacks in the kingdom, P1 always had the first chance to attack. For instance if both players open 2/5 and buy IGG P2 gets a Curse before the reshuffle while P1 gets it after.

If both players have Militia on T3, P1 can play it and likely buy a €5, while P2 is often stuck with a €4.

If there are no attacks and it's mostly 2P solitaire, the advantage will be lower.
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popsofctown

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Re: How many points is 1st player advantage?
« Reply #10 on: May 12, 2013, 05:59:23 am »
0

I don't think you can give it a generalized point value that won't immediately give a second player advantage; in some cases a huge advantage.

The only possibility would be to play a variant where you bid a number of points to go first.  This would, obviously, DOTB.  But it would be fairer.

I will re-emphasize this, because the acronym might be overlooked by some -- it Depends On The Board.

On some boards, you eke out a tough victory by 1 point in a very close game.  On other boards, you completely dominate and still only win by 1 point, because you leverage your dominance to end the game quickly.  In other games, you completely dominate by a wide margin, and in still other games, you win by a wide margin but the game was still close (e.g. blowout megaturn games where both players have finely tuned engines but one manages to pull the trigger first).  The value of being the first player is different in all these cases.  Sometimes being first isn't even worth a single point, other times you might give up 50 points or more just for the chance to trigger your megaturn first.

I'm pretty skeptical that giving up 50 points is ever appropriate.  A fifty point lead will let you empty Goons/Estates/Village using would-be-unwise single-goons Estate purchases.
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Davio

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Re: How many points is 1st player advantage?
« Reply #11 on: May 12, 2013, 07:23:41 am »
+1

It's just that the seesaw swings in the direction of P1 more often. If both players are going for a megaturn and they shuffle identically, P1 has a clear advantage.

This is also true with splits. P1 can open X/Fool's Gold (where X is say Great Hall to not overcomplicate things) and still get 5 of them while if P2 does that he can only get 4.

Dominion is often about dominance, unsurprisingly. It's much easier for P1 to dominate P2 than the other way around because it's easier to win splits. If we take an exponential approach where on the first turn you can get 1X, 2 on the 2nd turn etc, it will go like this: P1 gets 1, P2 gets 1, P1 gets 2, P2 gets 2, P1 gets 4, pile is empty. Result: P1 had 7, P2 has 3.

This may be oversimplifying a bit, but you get the idea. The piles are not deep enough for P2 to catch up if the gaining is non-linear (1 per turn max).

It would be fun to see games with the following rule: if a pile is emptied on P1's turn, P2 may still buy cards from that pile, but just uses some placeholders for that card.

For example you can use Gardens (if they're not in the kingdom themselves) as placeholders for Provinces etc. Of course in an online setting you don't need physical placeholders and can just create copies out of thin air.


Alternatively, you can do a blind bid for first player. Both players just "write down" a number of VPs they think going first is worth. Whoever writes down the highest number goes first, obviously. But the second player gets the amount of VPs offered by the winner. You could also give P2 the average of both bids (rounded up or down) so both players can't undervalue P1's worth. You wouldn't want to offer just 1 VP, have the other offer 9 VP and only get 5 VP as compensation instead of 9. Players do this after seeing the board.

I don't know how this works in multiplayer, but I'm just focusing on 2P here, because that's easiest and most "pro" games where it matters are 2P anyway.
« Last Edit: May 12, 2013, 08:12:53 am by Davio »
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ragingduckd

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Re: How many points is 1st player advantage?
« Reply #12 on: May 12, 2013, 04:46:03 pm »
+1

Alternatively, you can do a blind bid for first player. Both players just "write down" a number of VPs they think going first is worth. Whoever writes down the highest number goes first, obviously. But the second player gets the amount of VPs offered by the winner.

I really like this idea.  It's simple, obviously fair, and takes a lot of the luck out of the game.  Not only does it eliminate the random advantage of who goes first, it also creates another opportunity for the stronger player to make a better decision.

You could extend this approach to every random outcome to create a completely luck-free version of Dominion... if you and your opponent had infinite patience.
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GwinnR

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Re: How many points is 1st player advantage?
« Reply #13 on: May 13, 2013, 01:13:19 am »
0

Alternatively, you can do a blind bid for first player. Both players just "write down" a number of VPs they think going first is worth. Whoever writes down the highest number goes first, obviously. But the second player gets the amount of VPs offered by the winner.

I really like this idea.  It's simple, obviously fair, and takes a lot of the luck out of the game.  Not only does it eliminate the random advantage of who goes first, it also creates another opportunity for the stronger player to make a better decision.

You could extend this approach to every random outcome to create a completely luck-free version of Dominion... if you and your opponent had infinite patience.
Yeah, nice idea. "I give you 10VP, when i draw my Smithy here" xD There was an idea in the german forum, that you don't shuffle, but arrange the cards as you want. So there would be really no luck. That really seems like infinite patience ;-)
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Davio

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Re: How many points is 1st player advantage?
« Reply #14 on: May 13, 2013, 01:26:56 am »
0

Well, that just diminishes the value of Scout even more! I have another topic on here proposing the use of a doubling cube which didn't seem that far fetched.
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Re: How many points is 1st player advantage?
« Reply #15 on: May 13, 2013, 07:09:37 am »
+1

Quote
You could extend this approach to every random outcome to create a completely luck-free version of Dominion... if you and your opponent had infinite patience.
I kind of like that luck is part of the game. There are always games like Diplomacy, Chess or Go that are deterministic if you want to go that route.

It would be more interesting, though to start the bids after players see their starting hands.
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ragingduckd

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Re: How many points is 1st player advantage?
« Reply #16 on: May 13, 2013, 07:57:47 am »
0

I kind of like that luck is part of the game. There are always games like Diplomacy, Chess or Go that are deterministic if you want to go that route.

Fie! For shame! Go find some dice to roll.
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Re: How many points is 1st player advantage?
« Reply #17 on: May 13, 2013, 09:04:12 am »
+4

By changing the starting decks in the simulator you can replace estates with tunnels (say) and see how many starting points will create a roughly even match. For a big money deck just adding one extra point made it 46-49 in second player's favour. It was similar for a smithy+treasure game. Playing witch+treasure the second player needed 2 extra points when both started 4/3 and 3 extra points when both started 5/2.

Changing the starting hands isn't perfect since it changes the supply size too however the results seem to match my intuition.
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Re: How many points is 1st player advantage?
« Reply #18 on: May 13, 2013, 10:26:25 am »
+2

I kind of like that luck is part of the game. There are always games like Diplomacy, Chess or Go that are deterministic if you want to go that route.

Fie! For shame! Go find some dice to roll.

Or some…cards to shuffle?
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Jack Rudd

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Re: How many points is 1st player advantage?
« Reply #19 on: May 13, 2013, 10:37:18 am »
0

Quote
You could extend this approach to every random outcome to create a completely luck-free version of Dominion... if you and your opponent had infinite patience.
I kind of like that luck is part of the game. There are always games like Diplomacy, Chess or Go that are deterministic if you want to go that route.
What's with this meme that Diplomacy is deterministic? There's plenty of luck in Diplomacy.
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Re: How many points is 1st player advantage?
« Reply #20 on: May 13, 2013, 10:44:10 am »
0

Quote
You could extend this approach to every random outcome to create a completely luck-free version of Dominion... if you and your opponent had infinite patience.
I kind of like that luck is part of the game. There are always games like Diplomacy, Chess or Go that are deterministic if you want to go that route.
What's with this meme that Diplomacy is deterministic? There's plenty of luck in Diplomacy.

That depends on your definition of luck. Other than deciding who gets what country, there is no randomness in Diplomacy.
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Just a Rube

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Re: How many points is 1st player advantage?
« Reply #21 on: May 13, 2013, 06:46:49 pm »
+2

But there is luck. Or at least as much as in Rock-Paper-Scissors. E.g. I have one army that could attack either of your supply centers. You have one army to defend them. If we both choose the same one to attack/defend, you hold both; but if we choose differently, I capture one from you. In that case, the optimal strategy would be for you to flip a coin to pick which one to defend. Me guessing which way the coin flipped is pure luck.
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soulnet

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Re: How many points is 1st player advantage?
« Reply #22 on: May 13, 2013, 06:53:54 pm »
+1

There is nothing really deterministic, not even Chess or Go, because human brain is imperfect and it can be considered lucky that you make the "better" association needed to win or that your opponent does not see some possibility, etc.
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yudantaiteki

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Re: How many points is 1st player advantage?
« Reply #23 on: May 13, 2013, 11:04:41 pm »
+1

This "luck vs. strategy" debate was already had in another topic:
http://forum.dominionstrategy.com/index.php?topic=5542.0

There's a difference between luck that is written into the rules of the game and "luck" arising from human mistakes.
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Re: How many points is 1st player advantage?
« Reply #24 on: May 13, 2013, 11:26:34 pm »
0

Quote
This "luck vs. strategy" debate was already had in another topic:
http://forum.dominionstrategy.com/index.php?topic=5542.0
tl;dr

Quote
But there is luck. Or at least as much as in Rock-Paper-Scissors. E.g. I have one army that could attack either of your supply centers. You have one army to defend them. If we both choose the same one to attack/defend, you hold both; but if we choose differently, I capture one from you. In that case, the optimal strategy would be for you to flip a coin to pick which one to defend. Me guessing which way the coin flipped is pure luck.

But then you are adding luck to the system in the form of a coin flip. The game itself is all about choices with imperfect information. Choices aren't lucky or unlucky, they are good or bad, with the goodness or badness of them being determined by the information that you don't have (what your opponent will do). In fact, even 'adding luck' in this way doesn't really add luck: if every decision in Diplomacy was made by a coin toss, then who wins and loses would be able to be calculated using probability. The outcome of any one game might be random but on average we can know the distribution of wins and losses exactly. So, even in being random its still deterministic.

Quote
There is nothing really deterministic, not even Chess or Go, because human brain is imperfect and it can be considered lucky that you make the "better" association needed to win or that your opponent does not see some possibility, etc.

The game is deterministic. People's choices are not. If you could see the 'best possible' move or moves at every turn, you would always be able to achieve the same result. I don't think you can consider choices lucky or unlucky.
« Last Edit: May 13, 2013, 11:35:52 pm by serakfalcon »
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