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Subject: Analyzing splendor strategies with 7000+ game plays rss

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mattle elttam
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Have you ever wondered what's the best strategy in Splendor? What's the most efficient way to get to 15 points? Is it better to aim for high score cards directly or is it better to build up the engine first? Are noble tiles worth targeting at all?

We have been analyzing 7000+ game results in spendee (http://spendee.mattle.online), and here is a short summary of our findings!

Full report can be found at: http://spendee.mattle.online/lobby/forum/topic/mzXQmzjCBmyC5...


Of the 7307 games completed during the last month, we found that winners usually possessed around 11 to 13 cards, and surprising, less than 1 noble tile. It appears to us that noble tiles are relatively weak, and targeting high score cards looks like a good strategy in general.





Another interesting question is "What is the minimum number of turns to get to 15 points? Can you finish a game with 20 turns?". The answer is YES. the smallest number of turns we found to reach 15 points is only 19 turns! Although majority of games finish between 25 to 30.



We have also break down this number by the skill level of players (i.e. their ELO ratings on the site). If you are interested to know more, check out our original report: http://spendee.mattle.online/lobby/forum/topic/mzXQmzjCBmyC5...


=========== Updated on Sep 1, 2016 ===========

First Player Advantage

Here comes our answer for the most circulated question - Is there a first player advantage in Splendor? The answer is gonna surprise you!

Of the 6555 single champion games, charts below shows the distribution of winner positions:







and here comes the results for 2 players games involving ONLY 1600+ (446 games) and 1800+ rating players (88 games):





Apparently, there is no first player advantage in Splendor. In fact, for expert players, it's the second player who got higher chance of winning in a 2players game. :O

Ref: Original report of this part can be found at: http://spendee.mattle.online/lobby/forum/topic/hGiKKyy5oayGA...
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Max DuBoff
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Thanks so much for the stats! My informal observation based on largely 2P games on the site is that it should take an experienced player about 24-25 turns to hit 15. My own style generally uses 7-8 cards, but I've definitely seen experienced players use more. It's nigh impossible to win in below 22 turns in a 2P game, but I've seen 19 in 4P.


EDIT: Ah, this makes more sense:
Full Report wrote:
Interestingly, we saw a clear trend that higher ratings players tend to aim for higher scores card, thus allowing them to win by less amount of cards. For example, 1300+ winners posses an average of 15.58 cards, while 2000+ winners posses an average of only 9.29 cards.
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Billy McBoatface
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My biggest question isn't answered by your data at all: How many cards of each tier do people (especially the highly rated players) buy? I tend to buy mostly tier 1 and 3, skipping tier 2 except for the odd card now and then, but I suspect better players don't do that.
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Max DuBoff
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wmshub wrote:
My biggest question isn't answered by your data at all: How many cards of each tier do people (especially the highly rated players) buy? I tend to buy mostly tier 1 and 3, skipping tier 2 except for the odd card now and then, but I suspect better players don't do that.


I would say for me about 2/3/2 is pretty common. A big advantage of Tier 2 cards are that they can be bought earlier before you buy many other cards.
 
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Jason W
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MD1616 wrote:
My informal observation based on largely 2P games on the site is that it should take an experienced player about 24-25 turns to hit 15. My own style generally uses 7-8 cards, but I've definitely seen experienced players use more. It's nigh impossible to win in below 22 turns in a 2P game, but I've seen 19 in 4P.
Is the reason 2p games take longer is that it's easier to block your opponent in a 2p game than 4p game? Anyone have comments on the effect the gems per player ratio has?

The card difference and turn difference between 2p and 4p is surprising to me, since the end goal is the same: 15 points.
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Max DuBoff
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jdw734 wrote:
MD1616 wrote:
My informal observation based on largely 2P games on the site is that it should take an experienced player about 24-25 turns to hit 15. My own style generally uses 7-8 cards, but I've definitely seen experienced players use more. It's nigh impossible to win in below 22 turns in a 2P game, but I've seen 19 in 4P.
Is the reason 2p games take longer is that it's easier to block your opponent in a 2p game than 4p game? Anyone have comments on the effect the gems per player ratio has?

The card difference and turn difference between 2p and 4p is surprising to me, since the end goal is the same: 15 points.


It's simply because there are fewer chips of each color with fewer players. That means you need to buy more cards total and build up a little before going for the biggest cards.
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Bryan Thunkd
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MD1616 wrote:
jdw734 wrote:
Is the reason 2p games take longer is that it's easier to block your opponent in a 2p game than 4p game? Anyone have comments on the effect the gems per player ratio has?

The card difference and turn difference between 2p and 4p is surprising to me, since the end goal is the same: 15 points.


It's simply because there are fewer chips of each color with fewer players. That means you need to buy more cards total and build up a little before going for the biggest cards.
When there's only 4 green chips in play, you can't as easily complete the card that costs 7 green chips. You have to either build some green cards first, or reserve some cards to get wild chips, which is inefficient. When there's 7 green chips in play, you could build that card entirely with green chips not needing to build any cards or use any wilds to help.
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Adam P
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I'm disappointed that the nobles are not integrated more into a winning strategy. I wonder if the game was extended to 17 points if this would change?
 
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mattle wrote:
Of the 7307 games completed during the last month, we found that winners usually possessed around 11 to 13 cards, and surprising, less than 1 noble tile. It appears to us that noble tiles are relatively weak, and targeting high score cards looks like a good strategy in general.

Do the number of cards/nobles held by *losing* players differ significantly from this? That might help interpret the results.
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Chris L
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Does the data show that there is a first player advantage or not?
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I'm wondering if you can track how aggressivly winning players reserve cards....

How many time per game?
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mattle elttam
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wmshub wrote:
My biggest question isn't answered by your data at all: How many cards of each tier do people (especially the highly rated players) buy? I tend to buy mostly tier 1 and 3, skipping tier 2 except for the odd card now and then, but I suspect better players don't do that.


We are working on that. We are also interested in the popularity of specific cards as well (not only the level). For example, my personal gut feeling is that the 5-same-colors and 6-same-colors cards on the second level are the best, but we'll see. Stay tuned!
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mattle elttam
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adamredwoods wrote:
I'm disappointed that the nobles are not integrated more into a winning strategy. I wonder if the game was extended to 17 points if this would change?


Yes, I also agreed that noble tiles should play a more important role in the game to make it more interesting. I guess 17 points could be a good variant.
 
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mattle elttam
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tempus42 wrote:
mattle wrote:
Of the 7307 games completed during the last month, we found that winners usually possessed around 11 to 13 cards, and surprising, less than 1 noble tile. It appears to us that noble tiles are relatively weak, and targeting high score cards looks like a good strategy in general.

Do the number of cards/nobles held by *losing* players differ significantly from this? That might help interpret the results.


I'm not sure counting the numbers for the "losing" players are statistically sound. The reason is that they haven't finished the game (haven't reached 15 points yet). I'm not sure how to interpret the result. :O
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mattle elttam
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igelkott255 wrote:
Does the data show that there is a first player advantage or not?


I've just added a section on this. Check it out! It's gonna surprise you.
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mattle elttam
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joelddhans wrote:
I'm wondering if you can track how aggressivly winning players reserve cards....

How many time per game?


That's an interesting idea. Sure, we can do that. Stay tuned for the result!
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mattle wrote:
igelkott255 wrote:
Does the data show that there is a first player advantage or not?


I've just added a section on this. Check it out! It's gonna surprise you.

Surprising indeed! Intuitively it seems like there should be a first player advantage. Can you (or anyone) explain how going second turns out to be advantageous? You're behind on actions, after all, so what is compensating for that?
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russ wrote:
mattle wrote:
igelkott255 wrote:
Does the data show that there is a first player advantage or not?


I've just added a section on this. Check it out! It's gonna surprise you.

Surprising indeed! Intuitively it seems like there should be a first player advantage. Can you (or anyone) explain how going second turns out to be advantageous? You're behind on actions, after all, so what is compensating for that?

If you look at the numbers, they're pretty close to even spread, especially given the smallish (a few thousand per player count) sample size. I'm guessing there is no advantage to either player. There could easily be a very small first player advantage and still see a 49.7%/50.3% result.

But the good news is that the data shows that even for serious play, there is no need for additional compensation to any player - everybody has a decent shot at winning.
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russ wrote:
mattle wrote:
igelkott255 wrote:
Does the data show that there is a first player advantage or not?


I've just added a section on this. Check it out! It's gonna surprise you.

Surprising indeed! Intuitively it seems like there should be a first player advantage. Can you (or anyone) explain how going second turns out to be advantageous? You're behind on actions, after all, so what is compensating for that?
Every player gets the same number of turns in the game. So you're not really behind on anything.

The advantage of going first is that there may be easy cards in the tableau at game start. The start player has first crack at these cards that take fewer chips to complete. So the start player can get the chips to build the 3 cost card first while the other players get left with 5 cost cards. Of course, there are ways to mitigate that. Reserve the 3 cost card away from him. Or stockpile chips and hope something cheap gets revealed for you.

Personally I've always felt that the start player advantage isn't as big a factor as the randomness in cards that pop up after another player builds a card. The start player advantage gives you first crack at a card at the beginning of the game, but that's swamped by whether easy to build cards pop for you after other players build. If cheap cards, especially if you already have virtual gems that fit for them, come out for you very often, that's far more advantageous than being start player.

The start player could theoretically have a head start on getting a noble, but that's usually more dependent on whether the right color cards come out at the right time for you vs him. In a multiplayer game it might be advantageous to go later as the earlier players usually fight to compete for some nobles and you can go after an undesirable noble of different color or just collect the colors that aren't being fought over. They're likely to slow each other down and prevent anyone from getting the "hot" nobles quickly while you'll be able to pursue your plan uncontested. Doing what nobody else does is often a smart play.
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joelddhans wrote:
I'm wondering if you can track how aggressivly winning players reserve cards....

How many time per game?
Whether reserving cards makes sense or not really depends on the board layout, the nobles in play, how many chips are available to take, and how many chips you currently have. And sometimes whether it prevents someone else from getting the winning card they need. It's highly situational. Thus I don't think there's a correct answer for this. Generally it is inefficient, so doing it a lot will cost you efficiency, but there are definitely times it makes sense. I suspect better players generally do it less often, but again, it's highly situational.
 
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wmshub wrote:
If you look at the numbers, they're pretty close to even spread, especially given the smallish (a few thousand per player count) sample size. I'm guessing there is no advantage to either player. There could easily be a very small first player advantage and still see a 49.7%/50.3% result.

But that's including all players including newbies; the graphs for stronger players do show a pronounced difference. 56.8% vs 43.2% seems significant to me!
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Thunkd wrote:
Every player gets the same number of turns in the game. So you're not really behind on anything.

True, but as you then note:

Quote:
The advantage of going first is that there may be easy cards in the tableau at game start. The start player has first crack at these cards that take fewer chips to complete. So the start player can get the chips to build the 3 cost card first while the other players get left with 5 cost cards. Of course, there are ways to mitigate that. Reserve the 3 cost card away from him. Or stockpile chips and hope something cheap gets revealed for you.

Reserving the card means you only get 1 chip instead of 3 though. And "hope" for a favorable random event does not seems a serious compensation.

Quote:
Personally I've always felt that the start player advantage isn't as big a factor as the randomness in cards that pop up after another player builds a card.

This does seem plausible.

But then it still doesn't explain why there's (apparently) such a strong second player advantage (among strong players in 2-player games, I mean)!
 
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russ wrote:
Thunkd wrote:
Every player gets the same number of turns in the game. So you're not really behind on anything.

True, but as you then note:

Quote:
The advantage of going first is that there may be easy cards in the tableau at game start. The start player has first crack at these cards that take fewer chips to complete. So the start player can get the chips to build the 3 cost card first while the other players get left with 5 cost cards. Of course, there are ways to mitigate that. Reserve the 3 cost card away from him. Or stockpile chips and hope something cheap gets revealed for you.

Reserving the card means you only get 1 chip instead of 3 though. And "hope" for a favorable random event does not seems a serious compensation.
Reserving cards is always inefficient. But reserving a 3 cost card isn't so bad. You don't get as many chips as you could, but that's a little bit offset by the fact that you won't have to spend as many chips to build the card. And you'll likely be able to collect chips normally and get the colors you need and bank the wild for later. If the card was a color that matched the nobles that are in contention, I'd seriously consider doing it, especially if the other cards in the display are all 5 cost.

Alternatively you could bank chips and hope that someone else reveals a cheap card for you to build. If you're forced to spend 5 chips to build a card while your opponent builds that 3 cost card, you've spent 2 extra chips than them... which is just as inefficient as reserving the card in the first place. So reserving a card isn't as bad as you might think it would be. Again, the randomness of what cards comes out is a big factor here.

russ wrote:
Quote:
Personally I've always felt that the start player advantage isn't as big a factor as the randomness in cards that pop up after another player builds a card.

This does seem plausible.

But then it still doesn't explain why there's (apparently) such a strong second player advantage (among strong players in 2-player games, I mean)!
I don't really play 2 player that often, so I'm not really sure. If there's no good card in the display at the beginning of the game, the start player will be forced to build first, usually taking an expensive card and possibly revealing a cheaper card? That's all I can think of off the top of my head.
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Max DuBoff
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Wow, I'm pretty shocked by those new stats. Worth noting that the sample size of 1800+ 2P games for that last chart is 88, not enough to be statistically significant, but there are 446 1600+ 2P games, which I would call statistically significant. Not sure why going second might be better in 2P; maybe second player has a better idea of what to do based on what first player did? It certainly depends on the board, though.

Also, thunkd, I think you'd be surprised by how often better players reserve cards. I'd estimate 5-6 times per game in 2P.
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MD1616 wrote:
Also, thunkd, I think you'd be surprised by how often better players reserve cards. I'd estimate 5-6 times per game in 2P.
I don't often play 2 player, so I don't really know how that typically plays out. I could see, for example, a denial strategy making more sense in 2 player than it might in multiplayer.

Oh... and there's fewer chips, which means gold chips probably make more sense generally in order to get higher cards without being forced to build lower level cards as much.
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