Game IS broken ... Player wins in 2 moves!!!

[RicardoRix]

Seriously, just quit. The results are so hilariously biased, it's not even a game at this point.

So I made the effort to use BGA Studio and the same php random functions that are available to all developers that create games on this site, running test code on the same servers.

500,000 samples of each function:
php: rand()
php: random_int()
bga_rand() that apparently is based on random_int()

All of the files: http://www.filedropper.com/bgarand

I used the ent program used accoring to this paper, coming from random.org.
https://www.random.org/analysis/Analysis2001.pdf
The statistical analysis program used:
http://www.fourmilab.ch/random/

The results:

C:\Users\dudealert\Documents\BGA\random>ent php_rand.bin
Entropy = 7.999661 bits per byte.

Optimum compression would reduce the size
of this 500000 byte file by 0 percent.

Chi square distribution for 500000 samples is 234.61, and randomly
would exceed this value 81.55 percent of the times.

Arithmetic mean value of data bytes is 127.4652 (127.5 = random).
Monte Carlo value for Pi is 3.144012576 (error 0.08 percent).
Serial correlation coefficient is -0.000040 (totally uncorrelated = 0.0).

C:\Users\dudealert\Documents\BGA\random>ent php_random_int.bin
Entropy = 7.999609 bits per byte.

Optimum compression would reduce the size
of this 500000 byte file by 0 percent.

Chi square distribution for 500000 samples is 270.36, and randomly
would exceed this value 24.31 percent of the times.

Arithmetic mean value of data bytes is 127.6915 (127.5 = random).
Monte Carlo value for Pi is 3.136572546 (error 0.16 percent).
Serial correlation coefficient is -0.000604 (totally uncorrelated = 0.0).

C:\Users\dudealert\Documents\BGA\random>ent bga_rand.bin
Entropy = 7.999635 bits per byte.

Optimum compression would reduce the size
of this 500000 byte file by 0 percent.

Chi square distribution for 500000 samples is 252.83, and randomly
would exceed this value 52.66 percent of the times.

Arithmetic mean value of data bytes is 127.3624 (127.5 = random).
Monte Carlo value for Pi is 3.150780603 (error 0.29 percent).
Serial correlation coefficient is 0.002800 (totally uncorrelated = 0.0).

[Jest Phulin]

The results are so hilariously biased, it's not even a game at this point.

If you have concrete data to show the results are biased, please list them (without lots of extra arguments that make it difficult to wade through). If the results are biased, BGA should be able to track down the source and correct it. The term bias indicates that the numbers do not have an equal probability of appearing, which would indicate a failure of what any random source is trying to accomplish.

[mikey-cabin-fever]

Aesche, he's a pastor. As a religious figure, he feels he must preach his view of the world regardless of what the scientific community has to say. Many people will stop listening to him, but there may be the odd person out there who will become a follower.

How do you know the player is a pastor? Ah, you read it on the internet.....got it.

[Jest Phulin]

Aesche, he's a pastor. As a religious figure,

How do you know the player is a pastor? Ah, you read it on the internet.....got it.

Actually, I was referring to his username, Pastor Flapps

[zoomboom]

Have a look at this guy:
https://boardgamearena.com/forum/viewto ... 35&t=13118

I have finished 6-7-8 in one go several times.

Also done the same on other different other combos (4-8-10 and various others).

All in my game history.

Cheers,
M.

Has anyone calculated the probability of winning the game on your first turn?

[Romain672]

Has anyone calculated the probability of winning the game on your first turn?

It's really hard to do properly. You need to decide which numbers to goes on, when to stop (are you trying 3+0 or 0+3? Or 2+1? 1+2? Are you trying to do one number or move up your tokens?).

[Jellby]

I can tell you it's > 0, though.

[euklid314]

It's really hard to do properly. You need to decide which numbers to goes on, when to stop [...]

Yes, impossible to calculate. But we don't have to worry about stopping. Since we want to win in first(!) move we start with nothing and roll the dice till we finish 3 columns or fail.

Since this is not a very good strategy, lets first assume we only try it if we start columns 6,7,8 in the first 2 rolls. Let us assume we have advanced only one step each on 6,7,8.

Rolling at least one of 6,7,8 is 92%. If we do not fall we need at most 32 rolls (because we need to advance 10+12+10 steps) to win the game. Because of double steps (7+7, etc) it will go much faster.

Rolling 32 times and always needing at least one of 6,7,8 is no problem. It will happen 6.9% of all tries. Even succeeding 55 times in a row without falling has a probability of more than 1% (who is not surprised?).

The problem starts as soon as we have finished one of the columns and have only 2 open columns and, finally, having finished 2 columns and having only 1 column open. One needs to simulate that, a calculation is too difficult.

But if you manage to advance the 3 numbers as evenly as possible the time you are limited to 2 or 1 number may not be too long...

Perhaps the probabilty of finishing 6,7 AND 8 in one go is above 1%. I am absolutely sure that it is above 0.1%. Less unlikely as one would assume.

If it is our ONLY goal to finish the game first move, we can try this method with ANY starting columns. With columns 4,6,8 we of course have better chances as with columns 2, 5, 11. But we will NEVER stop (independent of our starting rolls) and will always try to advance the unlikely numbers first and advance as evenly as possible otherwise. With such a tactic we should get a win in a stretch of 200-500 games...

[zoomboom]

Extremely difficult does not equal impossible!

I guess laying out all the possibilities in an organized enough way is what is most difficult. And maybe making sure the chosen strategy is detailed enough to precisely cover all scenarios, and can be proven to be the best strategy.

[dino_2000_22]

I have not played this game enough to say it is broken, but from my limited experiences I have seen that the more experienced players always seem to get to choose between 5-9 and very rarely roll any other numbers.

Usually on my first roll I never roll a 5-9 and have to choose between 2,3,4,10,11,12 which makes it very tough to continue rolling.