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Dice Roll Probability Distribution

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#1 morisimo

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Posted 18 May 2017 - 07:31 AM

I have been enjoying TS on the iPad for a while now, thanks for all your hard work in bringing one of my favourite games to my tablet!

Having played plenty of games now, one of my feelings is that the probability distribution of the dice rolls is off. While I don't have concrete numbers, I feel there is an over indexing of 1s, especially when playing 4 ops cards for coups.

Further to this, I also feel there is an improbably high number of same roll runs, especially on coups. Having played 100 plus games, I have experienced at least 3 or 4 runs of 1 rolls up to 4 times in a row. Based on my simple maths, this should only occur with a probability of 1/1296. Assuming 20 coups per game (a high estimate) this translates to 2000 rolls based on 100 games. So having at least 3 or 4 same roll runs feels too much for my taste. Clearly this is a possibility, but the four 1s in a row feel much more prevalent that 4 roll runs of other numbers. There may well be some bias based on 1 rolls being more painful and therefore more memorable, but I'm pretty sure something is off...

Have you run any logging on the dice rolls?

If so, can you please do some distribution analysis to verify that your random number generator is not biased? I know they are not perfect but having played a lot of the actual board game as well, the rolls in the iOS version do not match the feel of the tabletop version.

Has anyone else noticed this? Forgive me if my maths is off...

Many thanks.
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#2 Benkyo

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Posted 18 May 2017 - 07:35 AM

Has anyone else noticed this? 

 

No.

 

I think it is very very hard to screw up an RNG these days. I'd be very surprised if they had. There would also be a much bigger outcry, lots of hardcore stats analysis going in forums, etc., etc. Hell, you usually get that anyway, even when the RNG is fine.

 

It just doesn't seem to be an issue.


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#3 morisimo

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Posted 18 May 2017 - 04:48 PM

Fair enough. Only the numbers would tell but I appreciate there are more tangible and pressing things to deal with. Appreciated.

Happy TSing!

#4 strategery

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Posted 20 May 2017 - 03:43 AM

I noticed this myself to such an extent that I decided to start logging every coup roll in a spreadsheet to see what's up.  After every game, I click through every tab in the game log and jot down the coup rolls per player.

 

After a sample size ~800 rolls, I've rolled 1s more than two standard deviations above the mean.  On top of that, my most common rolls were 1s and 2s and my least common rolls were 5s and 6s.  I don't complain about it though, because certainly everyone will hand-wave it away as random chance or simply not believe me.  It also does not happen to everyone either, because the opposite is true of my collective opponents - their most common rolls are 5s and 6s.  Seems too convenient to be true, right?  I noticed that my personal stats have not been reverting towards the mean over time either.

 

If you are curious enough, you can try doing the same.  If it turns out you do have a statistical disadvantage, you just have to live up to the extra challenge.  Secretly, I think the rolls are determined in the app via some repeatable pattern, maybe based off of time or mouse movements or something like that.



#5 Benkyo

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Posted 20 May 2017 - 04:05 AM

Secretly, I think the rolls are determined in the app via some repeatable pattern, maybe based off of time or mouse movements or something like that.

 

Sounds like you just described standard PRNG. The important thing is that the "repeatable pattern" is long enough (we're talking about numbers thousands of digits long) and that there is no way for us to predict the next number in the sequence. I don't see any reason why they would fail to provide such basics.



#6 strategery

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Posted 20 May 2017 - 04:33 AM

Well they do fail to implement basics such as draw results.  And they haven't updated the game in 4 months while plenty of bugs are being reported.  It wouldn't surprise me at all if playdek took shortcuts in their rng implementation.  They seem to spend the most effort on the visual appeal of the app.



#7 Benkyo

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Posted 20 May 2017 - 04:37 AM

Well they do fail to implement basics such as draw results.  And they haven't updated the game in 4 months while plenty of bugs are being reported.  It wouldn't surprise me at all if playdek took shortcuts in their rng implementation.  They seem to spend the most effort on the visual appeal of the app.

 

Fair point.



#8 mkiefte

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Posted 20 May 2017 - 05:31 PM

I noticed this myself to such an extent that I decided to start logging every coup roll in a spreadsheet to see what's up.  After every game, I click through every tab in the game log and jot down the coup rolls per player.

 

After a sample size ~800 rolls, I've rolled 1s more than two standard deviations above the mean.  On top of that, my most common rolls were 1s and 2s and my least common rolls were 5s and 6s.  I don't complain about it though, because certainly everyone will hand-wave it away as random chance or simply not believe me.  It also does not happen to everyone either, because the opposite is true of my collective opponents - their most common rolls are 5s and 6s.  Seems too convenient to be true, right?  I noticed that my personal stats have not been reverting towards the mean over time either.

 

If you are curious enough, you can try doing the same.  If it turns out you do have a statistical disadvantage, you just have to live up to the extra challenge.  Secretly, I think the rolls are determined in the app via some repeatable pattern, maybe based off of time or mouse movements or something like that.

 

Would you be willing to share your raw data?



#9 morisimo

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Posted 23 May 2017 - 10:33 AM

Strategery, nice analysis, thanks for jumping on and sharing your experience. I second the request for your raw data, would be useful for Playdek I'm sure.

I also agree that this may be an intentional skew, possibly as a difficulty balancing modifier to mitigate against some of the more basic things the AI does (like couping the Philippines and playing Indo-Pakistani war just for mil-ops with no influence in either territory etc.).

Shame if this is the case as it detracts from the gameplay and undermines enjoyment of the game somewhat. Much better playing against human characters of course. I just hope Playdek have made enough money to keep fixing these sorts of underlying issues. Good visuals are important but only if the underlying engine is right!





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