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Dreww

Member Since 23 Oct 2005
Offline Jan 25 2016 09:45 AM

Posts I've Made

In Topic: What would a decent 1p set for a lab rat be?

02 January 2016 - 11:11 AM

I'm just getting back into the loop of the BD, so I'm filling out my 1p/2p sets as well.  What's the budget you're going for and how much HP does the rat have so far?


In Topic: Survey of Bagatelle Outcomes

02 January 2016 - 03:39 AM

Well then, I'm only about four years late with this reply, but here it is!

 

rbFVrdj.png

 

From the 5488 rolls collected, the breakdown was as follows:

   1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16
2832 1332  766  269  179   67   25   10    4    1    2    1    0    0    0    0

No rolls above 13 occurred, which is to be expected when dealing with a sample size this small. This resulted in the following actual percentage, which I'll use for extrapolating the hypothetical probabilities:

       1        2        3        4        5        6        7        8        9       10       11       12 
51.6035% 24.2711% 13.9577%  4.9016%  3.2617%  1.2208%  0.4555%  0.1822%  0.0729%  0.0182%  0.0364%  0.0182%

Eyeballing this, the game likely uses the simplest infinite series possible.  The odds we're looking for 2-n would be:

       1        2        3        4        5        6        7        8
50.0000% 25.0000% 12.5000%  6.2500%  3.1250%  1.5625%  0.7813%  0.3906%
       9       10       11       12       13       14       15       16
 0.1953%  0.0977%  0.0488%  0.0244%  0.0122%  0.0061%  0.0031%  0.0015%

Our deviations from the pattern are all due to sampling error, which is a byproduct of using a finite sized dataset.  Emulating these results have a wide range of outcomes that show how much variation occurs purely due to chance:

> table(sample(1:16,5488,replace=T,prob=prob))
   1    2    3    4    5    6    7    8    9   10   11   14 
2777 1363  652  345  180   90   42   23   10    4    1    1 

> table(sample(1:16,5488,replace=T,prob=prob))
   1    2    3    4    5    6    7    8    9   10   11   12   13   14 
2764 1346  671  349  179   85   51   16   12    6    4    2    2    1 

> table(sample(1:16,5488,replace=T,prob=prob))
   1    2    3    4    5    6    7    8    9   10   11   12   13 
2723 1398  689  340  159   84   46   19   16    9    2    1    2 

> table(sample(1:16,5488,replace=T,prob=prob))
   1    2    3    4    5    6    7    8    9   10   11   12   13   14   16 
2767 1374  656  340  167   92   43   17   15    8    2    3    1    2    1 

> table(sample(1:16,5488,replace=T,prob=prob))
   1    2    3    4    5    6    7    8    9   10   11   12 
2752 1356  711  338  172   77   41   24   13    1    1    2 

> table(sample(1:16,5488,replace=T,prob=prob))
   1    2    3    4    5    6    7    8    9   10   11   12   14 
2807 1299  710  318  178   94   42   10   15    8    2    4    1 

> table(sample(1:16,5488,replace=T,prob=prob))
   1    2    3    4    5    6    7    8    9   10   11   13 
2766 1343  694  329  194   83   46   17   10    3    2    1

Chi-Square Test:

> prob<-2^(-(1:16))
> chisq.test(tab/length(cc),prob)


        Pearson's Chi-squared test


data:  tab/length(cc) and prob
X-squared = 176, df = 165, p-value = 0.2646


Warning message:
In chisq.test(tab/length(cc), prob) :
  Chi-squared approximation may be incorrect

A p-value lower than a cut-off of 1 standard deviation (p=0.05) would suggest the game does not follow this payout pattern.

 

If you paid 250 million to play Bagatelle one million times, and each jackpot ambitiously gave you 500,000 NP, you would only win back between 160 and 165 million NP.  With a jackpot payout of 1,000,000 NP, this goes up to a whopping 161 to 169 million NP.

 

TL;DR : Bagatelle is a pretty predictable game when you play it enough, and pays out 2/3 of the money you put in.

 

 

 


  1. Viewing Profile: Posts: Dreww