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Author Topic: The Replayability Factor  (Read 8810 times)

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Elanchana

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The Replayability Factor
« on: June 03, 2015, 06:13:17 pm »
0

I know one of the things people love about Dominion is its replayability, but how much is that exactly? How many games can you actually play without playing the same kingdom twice?

(People have probably done this before but Adventures just came out so it's worth another shot.)

Here are all the factors I can come up with:

10-card kingdom: (number of possible kingdom cards)!/(10!x(number of possible kingdom cards-10)!)
Young Witch bane: multiply result by number of possible $2/$3 kingdom cards, somehow factor in probability of card already being in kingdom???
Colony/Platinum and Shelters: multiply result by 4
Events: multiply result by... um... whatever combination formula can include different size groups?

Possible things to consider: Black Market contents (on Goko at least) and order, Knights order, Ruins order
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Re: The Replayability Factor
« Reply #1 on: June 03, 2015, 06:28:22 pm »
+12

Ignoring everything but 10 card kingdoms (so not counting Black Market order, Knights order, etc.)

If I'm doing the math right, with 236 kingdom cards, there are (236*235*234*...*228*227)/10! kingdoms. That's 1.23*1017 kingdoms. If you played one game a minute since the Big Bang, you still wouldn't be done.
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Re: The Replayability Factor
« Reply #2 on: June 03, 2015, 06:41:36 pm »
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Possible things to consider: Black Market contents (on Goko at least) and order, Knights order, Ruins order
If Ruins order counts, you might also want to consider the contents of the Ruins pile. In which case the number of players would also be something to consider.
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Re: The Replayability Factor
« Reply #3 on: June 03, 2015, 06:45:54 pm »
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Also player order and starting hand (and shuffling in general) can change how the game plays for you more than some changes to the kingdom.
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Re: The Replayability Factor
« Reply #4 on: June 03, 2015, 07:30:08 pm »
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Also player order and starting hand (and shuffling in general) can change how the game plays for you more than some changes to the kingdom.

While we're at it, we can try to determine the possible number of non-identical Dominion games that can be played. Of course you need to add in some rule to make it finite, like Chess has. The game is automatically a draw if the exact same game state is seen 3 times in a row?

Off the top of my head I'm thinking it's much larger than the number of possible games of Chess.
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Re: The Replayability Factor
« Reply #5 on: June 03, 2015, 07:41:26 pm »
+2

Also player order and starting hand (and shuffling in general) can change how the game plays for you more than some changes to the kingdom.

While we're at it, we can try to determine the possible number of non-identical Dominion games that can be played. Of course you need to add in some rule to make it finite, like Chess has. The game is automatically a draw if the exact same game state is seen 3 times in a row?

Off the top of my head I'm thinking it's much larger than the number of possible games of Chess.
Yeah, much larger. My estimate: 10^555

Guaranteed to be correct to within an order of magnitude of the orders of magnitude.

Also your rule is not enough, because we can play monuments forever. Better would be to put a turn cap at 100, which would decrease possibilities by a lot, but it works.
« Last Edit: June 03, 2015, 07:44:29 pm by liopoil »
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Re: The Replayability Factor
« Reply #6 on: June 03, 2015, 10:55:39 pm »
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Ignoring everything but 10 card kingdoms (so not counting Black Market order, Knights order, etc.)

If I'm doing the math right, with 236 kingdom cards, there are (236*235*234*...*228*227)/10! kingdoms. That's 1.23*1017 kingdoms. If you played one game a minute since the Big Bang, you still wouldn't be done.

Wait, hold on a sec... I entered 236!/(10!226!) into WolframAlpha and got 121734197783750266 or 1.21*1017. But your statement still stands about the one game a minute thing and my mind has been successfully blown.

While I was on WA I thought I'd have it spit out the possibilities for a Base game (which is probably what a lot of newbies would consider): 3268760. Which is still huge. One game every 15 minutes would take over 93 years.
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Re: The Replayability Factor
« Reply #7 on: June 03, 2015, 11:03:22 pm »
+8

All these factorials make it look like you're all very excited about numbers.
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Re: The Replayability Factor
« Reply #8 on: June 03, 2015, 11:23:51 pm »
+4

..the possibilities for a Base game (which is probably what a lot of newbies would consider): 3268760...

50% of which would be dominated by Big Money + X.
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Re: The Replayability Factor
« Reply #9 on: June 04, 2015, 10:25:49 am »
+6

All these factorials make it look like you're all very excited about numbers.

Wait...

Are you not excited about numbers!

Numbers are awesome! 8! 55! 39! 43! 83!

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Re: The Replayability Factor
« Reply #10 on: June 04, 2015, 12:40:08 pm »
+10

Ignoring everything but 10 card kingdoms (so not counting Black Market order, Knights order, etc.)

If I'm doing the math right, with 236 kingdom cards, there are (236*235*234*...*228*227)/10! kingdoms. That's 1.23*1017 kingdoms. If you played one game a minute since the Big Bang, you still wouldn't be done.

Wait, hold on a sec... I entered 236!/(10!226!) into WolframAlpha and got 121734197783750266 or 1.21*1017. But your statement still stands about the one game a minute thing and my mind has been successfully blown.

While I was on WA I thought I'd have it spit out the possibilities for a Base game (which is probably what a lot of newbies would consider): 3268760. Which is still huge. One game every 15 minutes would take over 93 years.

I have a physics background. The fact that I was in the right order of magnitude means it's sufficiently accurate.
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Elanchana

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Re: The Replayability Factor
« Reply #11 on: June 04, 2015, 01:27:51 pm »
+1

Ignoring everything but 10 card kingdoms (so not counting Black Market order, Knights order, etc.)

If I'm doing the math right, with 236 kingdom cards, there are (236*235*234*...*228*227)/10! kingdoms. That's 1.23*1017 kingdoms. If you played one game a minute since the Big Bang, you still wouldn't be done.

Wait, hold on a sec... I entered 236!/(10!226!) into WolframAlpha and got 121734197783750266 or 1.21*1017. But your statement still stands about the one game a minute thing and my mind has been successfully blown.

While I was on WA I thought I'd have it spit out the possibilities for a Base game (which is probably what a lot of newbies would consider): 3268760. Which is still huge. One game every 15 minutes would take over 93 years.

I have a physics background. The fact that I was in the right order of magnitude means it's sufficiently accurate.

Point definitely taken. I originally started making that post because I thought your numbers were wrong (which they weren't) but as long as I had the post up I thought I'd use it to elaborate.
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Re: The Replayability Factor
« Reply #12 on: June 04, 2015, 01:42:28 pm »
+2

Ignoring everything but 10 card kingdoms (so not counting Black Market order, Knights order, etc.)

If I'm doing the math right, with 236 kingdom cards, there are (236*235*234*...*228*227)/10! kingdoms. That's 1.23*1017 kingdoms. If you played one game a minute since the Big Bang, you still wouldn't be done.

Wait, hold on a sec... I entered 236!/(10!226!) into WolframAlpha and got 121734197783750266 or 1.21*1017. But your statement still stands about the one game a minute thing and my mind has been successfully blown.

While I was on WA I thought I'd have it spit out the possibilities for a Base game (which is probably what a lot of newbies would consider): 3268760. Which is still huge. One game every 15 minutes would take over 93 years.

I have a physics background. The fact that I was in the right order of magnitude means it's sufficiently accurate.

You have 2 significative numbers right. In Physics, that's two more than expected!
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Re: The Replayability Factor
« Reply #13 on: June 04, 2015, 03:06:23 pm »
0

..the possibilities for a Base game (which is probably what a lot of newbies would consider): 3268760...

50% of which would be dominated by Big Money + X.
I thought Big Money broke Dominion. Who needs 10^17 possibilities when you can just buy victory and treasure?
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Re: The Replayability Factor
« Reply #14 on: June 04, 2015, 03:08:20 pm »
+2

Who needs 10^17 possibilities when you can just buy money and treasure?

What about buying coins and dollars?

EDIT: Too late!  :P
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Re: The Replayability Factor
« Reply #15 on: June 04, 2015, 04:23:13 pm »
+5

Who needs 10^17 possibilities when you can just buy money and treasure?

What about buying coins and dollars?

EDIT: Too late!  :P

Ugh, every time AdamH says "dollars" while playing, part of me dies
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Re: The Replayability Factor
« Reply #16 on: January 25, 2017, 07:04:50 am »
0

Sorry for rescuing this old threat, but I could not find anything better on this topic:

Playing with the ShuffleIT client for a while now, I realized that I have seen some cards quite more often than others. For instance, I remember playing 4 or 5 games with the teacher line and at least 5 with Goons. Given that I played maybe 100 games in this timeframe, the probability for such events to occur randomly seems to me rather low when I follow my intuition. But the mind is a curious thing and it has many biases, so I am interested in the statistics. I played almost exclusively against bots (so no purchase bias from other players), had all expansions active and all cards were set to familiar. As far as I know, ShuffIT picks the cards fully random.
 
So, for the statisticians out there:
- What is the probability for any given Supply Card to occur in any kingdom in general?
- What are the odds for a single card to occur in multiple matches?
- How many matches would you need to play in order to see all kingdom cards at least once?
- What is the likelihood that you get a kingdom which comes only from a single expansion?
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Re: The Replayability Factor
« Reply #17 on: January 25, 2017, 09:52:17 am »
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Streaks and clusters are expected parts of a random sequence. If you saw a uniformly even appearance of cards then that would probably be more unusual.
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Re: The Replayability Factor
« Reply #18 on: January 25, 2017, 09:53:52 am »
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All these factorials make it look like you're all very excited about numbers.

Wait...

Are you not excited about numbers!

Numbers are awesome! 8! 55! 39! 43! 83!

Just smile and nod- don't make eye contact, patient is highly excitable.
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Re: The Replayability Factor
« Reply #19 on: January 29, 2017, 02:51:24 pm »
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- How many matches would you need to play in order to see all kingdom cards at least once?

Oooohhhh, I can do this math! Answer is basically infinite. It's possible that randomly picking 10 cards will never ever pick Rebuild.

I think what you mean to ask is something more like "How many matches would you need to play on average in order to see all kingdom cards at least once?"
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Re: The Replayability Factor
« Reply #20 on: February 26, 2017, 11:51:02 pm »
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Divide the final answer by 1,000 and you're still good to go.  That's about the number of "unique enough" games to suit a typical style.  For example, if you swap out Woodcutter for Chancellor, it can make no difference whatsoever.  Plus, I did enjoy replaying some of the same Kingdom cards just to see how an alternative path works out (of which some Kingdoms can have 3 distinct ways to go for example).

Otherwise, you reach a number where it's impractical due to not being able to hit that many plays anyways, unless you play the game for a living.  Closest I'd reckon would be the play testers, and even they may not be quite there.
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Re: The Replayability Factor
« Reply #21 on: February 27, 2017, 12:04:21 am »
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Sorry for rescuing this old threat, but I could not find anything better on this topic:

Playing with the ShuffleIT client for a while now, I realized that I have seen some cards quite more often than others. For instance, I remember playing 4 or 5 games with the teacher line and at least 5 with Goons. Given that I played maybe 100 games in this timeframe, the probability for such events to occur randomly seems to me rather low when I follow my intuition. But the mind is a curious thing and it has many biases, so I am interested in the statistics. I played almost exclusively against bots (so no purchase bias from other players), had all expansions active and all cards were set to familiar. As far as I know, ShuffIT picks the cards fully random.
 
So, for the statisticians out there:
- What is the probability for any given Supply Card to occur in any kingdom in general?
- What are the odds for a single card to occur in multiple matches?
- How many matches would you need to play in order to see all kingdom cards at least once?
- What is the likelihood that you get a kingdom which comes only from a single expansion?

Try taking a look at your "familiar cards" settings, which skew the randomizer towards cards you are familiar with.

Also, as long as the thread has been revived, anyone want to do the math including empires and sauna/avanto?
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Re: The Replayability Factor
« Reply #22 on: February 27, 2017, 12:10:43 pm »
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since there are ~200 kingdom cards and you take ~10 per game, a card appearance in any single game is around 5%. So seeing 5 appearances of those cards out of 100 games is entirely normal.

You will have reasons to doubt if you see a few two card combos appearing in 5 or more games, or any 3 card combos in 5 or more games  at all in the mean time.
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Re: The Replayability Factor
« Reply #23 on: February 27, 2017, 02:01:38 pm »
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Ok, just did the math for empires:
Just cards: 278!/(10!268!)=6.45*10^17
Including events/landmarks: 278!/(10!268!)*(56+55*54)=1.95*10^21
The above plus plat/colony and shelters: 7.81*10^21
Things not accounted for: young witch bane, ruins order, knights order, which ruins are available, black market contents/order.

Edit:If anyone wants to know why I did what I did with events, ask
« Last Edit: February 27, 2017, 02:06:55 pm by Doom_Shark »
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Re: The Replayability Factor
« Reply #24 on: February 27, 2017, 02:11:52 pm »
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Ok, just did the math for empires:
Just cards: 278!/(10!268!)=6.45*10^17
Including events/landmarks: 278!/(10!268!)*(56+55*54)=1.95*10^21
The above plus plat/colony and shelters: 7.81*10^21
Things not accounted for: young witch bane, ruins order, knights order, which ruins are available, black market contents/order.

Edit:If anyone wants to know why I did what I did with events, ask
Also not accounted for: Obelisk.
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Re: The Replayability Factor
« Reply #25 on: February 27, 2017, 02:16:22 pm »
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Oh yeah, that's a thing...honestly forgot that obelisk existed
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Re: The Replayability Factor
« Reply #26 on: February 27, 2017, 02:26:55 pm »
0

I miss Elanchana.
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Re: The Replayability Factor
« Reply #27 on: February 27, 2017, 03:02:30 pm »
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I miss Elanchana.

She still streams and stuff.
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Re: The Replayability Factor
« Reply #28 on: February 27, 2017, 03:09:25 pm »
0

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Re: The Replayability Factor
« Reply #29 on: February 27, 2017, 03:14:56 pm »
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I miss Elanchana.

She still streams and stuff.

Did she leave or something?

Well, I just know what you know: she hasn't posted in 7-8 months and hasn't visited the forum in 17 days.
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Re: The Replayability Factor
« Reply #30 on: February 27, 2017, 03:20:46 pm »
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I kinda assumed she left with Adam and WW.
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