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Subject: Modification of technology setup for two players? rss

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Edwin Priest
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I played my first game of Eclipse last night as a two-player learning game. Eclipse is obviously an amazing game and seems to play pretty well with two. The major, and perhaps only, problem I had was with the mechanics of the technology system with this number.

Only four techs are drawn each turn, and with the large number of tiles in the bag many of the technologies never became available and many of them only once (we never saw the missile or orbital techs for instance). To me, this added an unpleasant element of randomness into this otherwise quite streamlined game.

I am wondering if I anyone else has had this problem. Maybe a modification is needed for two players, such as removing a certain number of tiles of each tech type before starting, thereby reducing the chances of this happening.

Any thoughts?
 
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Forrest & Ryan Driskel
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I believe that was done on purpose, most specifically so that you couldn't rely on the same exact strategy every game.
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Edwin Priest
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Vanish wrote:
I believe that was done on purpose, most specifically so that you couldn't rely on the same exact strategy every game.


That makes sense, but it sure seems hard to rely on ANY strategy when you have no idea what techs will be available or when they might come out.
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Lacombe
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I was thinking the same thing, for all player counts.

It would be incredibly difficult to actually balance across player counts, though, and it's likely that the current solution is good enough. Not only are there different counts of each technology tile, but each tile has different utility early / late in the game.

There are at least 3* things to consider in the balance:

1) How many of each tile can you expect to see in the initial draw / what is the probability of any given tile being in the initial draw?

2) How many of each tile can you expect to see in the entire game / what is the probability of any given tile not being drawn in the game?

3) How many of each tile can you expect to see in any given round / what is the probability of drawing x number of tiles by round n?

And then the *. *) Do you want the ratio of the expected number of tiles in each tech to the number of players in the game to be the same across all player counts? Or is there reason for it to be different? Should it be same/different for only some stages of the game, or for all?

This is actually a really interesting probability problem.
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Daniel Hammond
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Vanish wrote:
I believe that was done on purpose, most specifically so that you couldn't rely on the same exact strategy every game.


I totally agree with this. I have now played 2 games (a 3 and a 2) and missiles never came up in either. Realistically you will never know what tech you might be able to research and when. In my second game my opponent (also new to the game) was hoping for monoliths and it never came out and I won easily. I haven't been this impressed with a game and its mechanics since Puerto Rico.
 
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Lacombe
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Unless I've screwed up, here are the probabilities of any given tech being drawn [at least once], by player count and round number:

5-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.70 0.84 0.93 0.97 0.99 1.00 1.00 1.00 1.00
5 players 0.65 0.80 0.89 0.95 0.98 0.99 1.00 1.00 1.00
4 players 0.61 0.75 0.85 0.92 0.96 0.98 0.99 1.00 1.00
3 players 0.55 0.70 0.80 0.88 0.93 0.96 0.98 0.99 1.00
2 players 0.49 0.61 0.70 0.77 0.83 0.88 0.91 0.94 0.96

4-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.61 0.77 0.87 0.94 0.97 0.99 1.00 1.00 1.00
5 players 0.57 0.72 0.83 0.90 0.95 0.98 0.99 1.00 1.00
4 players 0.52 0.67 0.78 0.86 0.92 0.96 0.98 0.99 1.00
3 players 0.47 0.61 0.72 0.81 0.87 0.92 0.95 0.97 0.99
2 players 0.42 0.52 0.61 0.69 0.75 0.81 0.85 0.89 0.92

3-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.51 0.66 0.78 0.87 0.93 0.97 0.99 1.00 1.00
5 players 0.47 0.62 0.74 0.83 0.89 0.94 0.97 0.99 1.00
4 players 0.42 0.56 0.68 0.77 0.85 0.90 0.94 0.97 0.99
3 players 0.38 0.51 0.62 0.71 0.78 0.85 0.89 0.93 0.96
2 players 0.33 0.42 0.51 0.58 0.65 0.71 0.76 0.81 0.85


And these are the expected number of tiles drawn of each technology based on those probabilities, by player count and round number:

5-ct tech 1 2 3 4 5 6 7 8 9
6 players 1.04 1.51 1.98 2.45 2.92 3.39 3.85 4.32 4.79
5 players 0.94 1.35 1.77 2.19 2.60 3.02 3.44 3.85 4.27
4 players 0.83 1.20 1.56 1.93 2.29 2.66 3.02 3.39 3.75
3 players 0.73 1.04 1.35 1.67 1.98 2.29 2.60 2.92 3.23
2 players 0.63 0.83 1.04 1.25 1.46 1.67 1.88 2.08 2.29

4-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.83 1.21 1.58 1.96 2.33 2.71 3.08 3.46 3.83
5 players 0.75 1.08 1.42 1.75 2.08 2.42 2.75 3.08 3.42
4 players 0.67 0.96 1.25 1.54 1.83 2.13 2.42 2.71 3.00
3 players 0.58 0.83 1.08 1.33 1.58 1.83 2.08 2.33 2.58
2 players 0.50 0.67 0.83 1.00 1.17 1.33 1.50 1.67 1.83

3-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.63 0.91 1.19 1.47 1.75 2.03 2.31 2.59 2.88
5 players 0.56 0.81 1.06 1.31 1.56 1.81 2.06 2.31 2.56
4 players 0.50 0.72 0.94 1.16 1.38 1.59 1.81 2.03 2.25
3 players 0.44 0.63 0.81 1.00 1.19 1.38 1.56 1.75 1.94
2 players 0.38 0.50 0.63 0.75 0.88 1.00 1.13 1.25 1.38


And, finally, here are the tile draw numbers as a ratio of expected number to player count, also by player count and round number:

5-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.17 0.25 0.33 0.41 0.49 0.56 0.64 0.72 0.80
5 players 0.19 0.27 0.35 0.44 0.52 0.60 0.69 0.77 0.85
4 players 0.21 0.30 0.39 0.48 0.57 0.66 0.76 0.85 0.94
3 players 0.24 0.35 0.45 0.56 0.66 0.76 0.87 0.97 1.08
2 players 0.31 0.42 0.52 0.63 0.73 0.83 0.94 1.04 1.15

4-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.14 0.20 0.26 0.33 0.39 0.45 0.51 0.58 0.64
5 players 0.15 0.22 0.28 0.35 0.42 0.48 0.55 0.62 0.68
4 players 0.17 0.24 0.31 0.39 0.46 0.53 0.60 0.68 0.75
3 players 0.19 0.28 0.36 0.44 0.53 0.61 0.69 0.78 0.86
2 players 0.25 0.33 0.42 0.50 0.58 0.67 0.75 0.83 0.92

3-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.10 0.15 0.20 0.24 0.29 0.34 0.39 0.43 0.48
5 players 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.51
4 players 0.13 0.18 0.23 0.29 0.34 0.40 0.45 0.51 0.56
3 players 0.15 0.21 0.27 0.33 0.40 0.46 0.52 0.58 0.65
2 players 0.19 0.25 0.31 0.38 0.44 0.50 0.56 0.63 0.69

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Lacombe
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Examples of possible interpretations:

NateStraight wrote:
4-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.83 1.21 1.58 1.96 2.33 2.71 3.08 3.46 3.83
5 players 0.75 1.08 1.42 1.75 2.08 2.42 2.75 3.08 3.42
4 players 0.67 0.96 1.25 1.54 1.83 2.13 2.42 2.71 3.00
3 players 0.58 0.83 1.08 1.33 1.58 1.83 2.08 2.33 2.58
2 players 0.50 0.67 0.83 1.00 1.17 1.33 1.50 1.67 1.83


The above table [of expected tile draws] would tell you that by the end of a 4-player game, you would expect 3 out of the 4 players to have access [given science production, etc] to any given 4-count technology, since you expect 3 tiles to be drawn of each 4-count tech. By round 4 in a 2-player game, you would expect 1 of the 2 players to have access to any given 4-count technology. Etc.

Quote:
3-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.51 0.66 0.78 0.87 0.93 0.97 0.99 1.00 1.00
5 players 0.47 0.62 0.74 0.83 0.89 0.94 0.97 0.99 1.00
4 players 0.42 0.56 0.68 0.77 0.85 0.90 0.94 0.97 0.99
3 players 0.38 0.51 0.62 0.71 0.78 0.85 0.89 0.93 0.96
2 players 0.33 0.42 0.51 0.58 0.65 0.71 0.76 0.81 0.85


The above table [of probabilities] would tell you that by round 4 in a 6-player game, there's roughly an 8 in 9 probability of any given 3-count technology being drawn. There are 9 such technologies overall, so you can roughly expect 1 of them to not have been drawn yet. By the end of a 2-player game, chances are also pretty good at least one of the nine 3-count techs won't have been drawn.
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Lacombe
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The overall, general trend seems to be that you're less likely to see any given tech drawn as player count decreases [makes sense], but you're also less likely to get shut out of any tech [also makes sense] as player count decreases.
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stu ma
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easiest solution is that you increase the tech draw by +2
 
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Lacombe
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NateStraight wrote:
And, finally, here are the tile draw numbers as a ratio of expected number to player count, also by player count and round number:

5-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.17 0.25 0.33 0.41 0.49 0.56 0.64 0.72 0.80
5 players 0.19 0.27 0.35 0.44 0.52 0.60 0.69 0.77 0.85
4 players 0.21 0.30 0.39 0.48 0.57 0.66 0.76 0.85 0.94
3 players 0.24 0.35 0.45 0.56 0.66 0.76 0.87 0.97 1.08
2 players 0.31 0.42 0.52 0.63 0.73 0.83 0.94 1.04 1.15

4-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.14 0.20 0.26 0.33 0.39 0.45 0.51 0.58 0.64
5 players 0.15 0.22 0.28 0.35 0.42 0.48 0.55 0.62 0.68
4 players 0.17 0.24 0.31 0.39 0.46 0.53 0.60 0.68 0.75
3 players 0.19 0.28 0.36 0.44 0.53 0.61 0.69 0.78 0.86
2 players 0.25 0.33 0.42 0.50 0.58 0.67 0.75 0.83 0.92

3-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.10 0.15 0.20 0.24 0.29 0.34 0.39 0.43 0.48
5 players 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.51
4 players 0.13 0.18 0.23 0.29 0.34 0.40 0.45 0.51 0.56
3 players 0.15 0.21 0.27 0.33 0.40 0.46 0.52 0.58 0.65
2 players 0.19 0.25 0.31 0.38 0.44 0.50 0.56 0.63 0.69



Assuming this is the proper final metric [I'm not sure that it is] and that equivalent scarcity [what this purports to measure] across all player counts is the proper final goal [I'm also not sure that it is], an interestingly near-balanced result can be obtained with the following start / turn-by-turn draws:

6 players: Start 24, draw 9
5 players: Start 20, draw 7
4 players: Start 16, draw 6
3 players: Start 12, draw 4
2 players: Start 8, draw 3

This gives you the following set of ratios of expected tiles drawn to number of players in the game:

5-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.21 0.29 0.36 0.44 0.52 0.60 0.68 0.76 0.83
5 players 0.21 0.28 0.35 0.43 0.50 0.57 0.65 0.72 0.79
4 players 0.21 0.29 0.36 0.44 0.52 0.60 0.68 0.76 0.83
3 players 0.21 0.28 0.35 0.42 0.49 0.56 0.63 0.69 0.76
2 players 0.21 0.29 0.36 0.44 0.52 0.60 0.68 0.76 0.83

4-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.17 0.23 0.29 0.35 0.42 0.48 0.54 0.60 0.67
5 players 0.17 0.23 0.28 0.34 0.40 0.46 0.52 0.58 0.63
4 players 0.17 0.23 0.29 0.35 0.42 0.48 0.54 0.60 0.67
3 players 0.17 0.22 0.28 0.33 0.39 0.44 0.50 0.56 0.61
2 players 0.17 0.23 0.29 0.35 0.42 0.48 0.54 0.60 0.67

3-ct tech 1 2 3 4 5 6 7 8 9
6 players 0.13 0.17 0.22 0.27 0.31 0.36 0.41 0.45 0.50
5 players 0.13 0.17 0.21 0.26 0.30 0.34 0.39 0.43 0.48
4 players 0.13 0.17 0.22 0.27 0.31 0.36 0.41 0.45 0.50
3 players 0.13 0.17 0.21 0.25 0.29 0.33 0.38 0.42 0.46
2 players 0.13 0.17 0.22 0.27 0.31 0.36 0.41 0.45 0.50


An infinite number of alternative assumptions could be made, but with these I'm not sure a more balanced integer solution is found.
 
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JonGetsGames
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Does that mean in a 4 or 6 player game there is only a 50% chance that a single plasma missile (3 count tech) will show up? or 50% that all three will show up?
 
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Lacombe
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HappyHexagon wrote:
Does that mean in a 4 or 6 player game there is only a 50% chance that a single plasma missile (3 count tech) will show up? or 50% that all three will show up?


[Assuming you're referring to the immediately prior table...] Neither. It means that the expected number of plasma missiles drawn divided by the players in the game is 0.50. That is, 3 missiles over 6 players or 2 missiles over 4 players. The interpretation is that exactly half of the players in either scenario can be expected to have plasma missile technology by the final turn.
 
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Lacombe
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Something very important to point out is that regardless of the expected value [of number of each type of tile drawn during the game], the uncertainty is going to be greater in a smaller player count [because of the smaller number of tile draws] unless you adjust the total pool of tiles [as suggested by the OP]. In the alternative [or really in the official, also] tile distribution chart above, there's no uncertainty about what will be drawn over the course of a 6-player game... all 96 tiles will be, exactly. Only 1/3 of the tiles [exactly] will be drawn in a 2-player game using the above table. While the expected ratios of tiles drawn to players in the game are equivalent, the uncertainty / variance around those expected values are not. It's quite likely that Touko tweaked the game intentionally [or maybe unintentionally / subconsciously / by gut feel] to have higher relative expected values at lower player counts to make up for the greater uncertainty.
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Chris Cieslik
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You could possibly have a one or two turn view into the future, laying out the tech tiles that will become available. It'd add some tension to passing first, knowing what's available to purchase.
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Lacombe
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angelkurisu wrote:
You could possibly have a one or two turn view into the future, laying out the tech tiles that will become available. It'd add some tension to passing first, knowing what's available to purchase.


That's an excellent idea.
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Edwin Priest
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NateStraight wrote:
angelkurisu wrote:
You could possibly have a one or two turn view into the future, laying out the tech tiles that will become available. It'd add some tension to passing first, knowing what's available to purchase.


That's an excellent idea.


Agreed. And thanks for the probability analyses.
 
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Troy Creamer
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Hey Ed it was great playing with you and thanks for the thread. When Ed and I played I guess I didn't share Ed's concern as much. I enjoy the random element in the 2-player game a bit. I personally really enjoy games where you have to think on your feet and adapt. However in reading this thread i really like the idea of laying out the next turn tiles. Thematically it works as civilizations see upcoming technologies and then can plan ahead if they want to invest in them. The other option that i discussed with Ed a bit is maybe just up the draw # per turn to 6 or 8 instead of 4. This would retain the randomness but also you would have more opportunity to see more technologies. Overall this is very minor for me and I am super happy i picked this game. I think this game is one of if not my favorite games in my collection. Everything in it is awesome and its even easy to understand the rules and play. I am super super excited to maybe get this to the table next week again and hopefully with more players.

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Andrew Davidson
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It's lame if more tiles for a tech come out than there are players. A simple remedy would be to discard a tech tile draw if there are already enough copies of that tech for everyone. And you pull again if a tech tile draw is discarded.

-- Andrew
 
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Carlos Alves
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That's is not a bad idea.

In 2 Player gam, if you do as the games states.

Setup: 12
Each turn: 4
Tiles drew in the end: 48

Conclusion: You will never see all technology available in the end of game.

Your idea, if you do draw a tech tile than surpasses the number of players in play (2P), you discard a draw a new one tech. That way, all technology will become available at the end of game, with 48 tiles drew.

What rule would you choose to play, the game rules or your house rule?
 
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Cliff
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Regarding Nate's probability tables, I don't understand the difference between a 5 count tech table and other count tech. I've only a few plays under my belt over a few years. Nate, could you or someone explain?
 
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Lacombe
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aboveriver wrote:
Regarding Nate's probability tables, I don't understand the difference between a 5 count tech table and other count tech. I've only a few plays under my belt over a few years. Nate, could you or someone explain?


Not every tech has the same number of tiles in the bag. Some have 5, some 4, and some 3.
 
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Cliff
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Thanks!
 
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Brent Dill
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One wacky idea I've been trying (mentioned in another thread) that makes the tech tree much more controllable is:

1. Always start the tech tree with the first 3 techs of each row.
2. Have a separate tech bag for each row.
3. Rather than drawing new tech at the start of each turn, always draw 2 new tech whenever a tech is researched, drawing from the same bag as the researched tech.

This means that you drive new technology by researching existing technology on the same tech row, which makes sense and gives the players more control over what techs appear.
 
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Bryan Vyrath
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This thread is old, but an easy solution I've found for this issue is using the other variant I posted: playing to a certain score instead of certain rounds.

Works great for me. Doesn't change much at all, either. I like the techs random (as others have pointed out).
 
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