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README.md
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README.md
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# 3d6rl-vs-4d6dl
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# 🎲 3d6 Re-roll Lowest 🆚 4d6 Drop Lowest 🎲
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A python script to generate results on rolling dice implementing a quantum number generator ([qrng.anu.edu](http://qrng.anu.edu.au/)) as source of randomness.
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**Thanks** to [@philvuchetich@bsd.network](https://bsd.network/@philvuchetich) for the help and pointers making this work.
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## How to use this script
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Install the random generator
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````shell
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pip3 install quantumrandom
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````
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Run the script
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````shell
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./bin/3d6rl-vs-4d6dl.py
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````
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## Method Explanation
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### 4d6DL
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Roll 4 six-sided dice and drop the lowest result.
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- Using only 6 sided dice roll a set of 4 dice.
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- Remove the lowest result from the set.
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- Add the three remaining dice and note the total sum.
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### 3d6RL
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Roll 3 six-sided dice and re-roll the lowest result.
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- Using only 6 sided dice roll a set of 3 dice.
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- Re-roll the lowest dice.
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- If the result is higher keep the use this value instead.
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- Add the three dice together and note the total sum.
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## Thesis
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The result average for both methods (4d6DL and 3d6RL) should be close, if not the same. And tend towards equality the more the two methods it are tested.
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This script generates results sets using a digital version of the above mentioned methods, ideally the more sets used the closer to zero the difference should be.
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## Results
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The results for 10.000 where 4d6DL rolled 0.20500% more than 3d6RL, using 100.000 3d6rl with 0.02133%, and finally 1.000.000 samples 4d6DL again with 0.01322% difference.
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### Result sample
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```
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$ ./bin/3d6rl-vs-4d6dl.py
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3d6 Re-roll Lowest - 1000000 samples
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Distribution (result : times)
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3 : 776
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4 : 3093
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5 : 7667
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6 : 16344
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7 : 29745
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8 : 47978
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9 : 70516
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10 : 93752
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11 : 114493
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12 : 128574
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13 : 132726
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14 : 122853
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15 : 101249
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16 : 72396
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17 : 41686
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18 : 16152
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67.99701% (12239462 of 18000000).
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4d6 Drop Lowest - 1000000 samples
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Distribution (result : times)
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3 : 813
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4 : 3181
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5 : 7796
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6 : 16136
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7 : 29519
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8 : 47601
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9 : 70463
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10 : 93906
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11 : 114615
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12 : 128518
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13 : 132829
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14 : 123235
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15 : 101007
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16 : 72473
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17 : 41851
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18 : 16057
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68.01023% (12241841 of 18000000).
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4d6dl rolled more by 0.01322%
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```
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A python script to generate results on rolling dice implementing a quantum number generator as source of randomness.
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@ -0,0 +1,60 @@
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#! /usr/bin/python3
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import random
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import quantumrandom # pip3 install quantumrandom
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sample = 1000000
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die_min = 1
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die_max = 6
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max_amount = (die_max * 3) * sample
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qseed = quantumrandom.get_data(); # get seed from quantum API
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quantum_os_rand = random.SystemRandom(qseed[0])
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dist_rl, dist_dl = {}, {}
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i, rl_total, dl_total = 0, 0, 0
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def roll():
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#return random.randint(die_min, die_max) # bad: Pseudo-random
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#return random.SystemRandom().randint(die_min, die_max) # better: OS random
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return quantum_os_rand.randint(die_min, die_max) # good: OS with Quantum seed
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#return quantomrandom.randint(die_min, die_max) # amazing: Slow, try 10 samples max
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def drop_lowest(arr):
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arr.remove(min(arr))
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return arr
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def reroll_lowest(arr):
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arr.sort()
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old_roll = arr.pop(0)
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new_roll = roll()
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if old_roll <= new_roll:
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arr.append(new_roll)
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else:
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arr.append(old_roll)
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return arr
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while i < sample:
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rl_set = sum(reroll_lowest([roll(), roll(), roll()]))
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rl_total += rl_set
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dist_rl[rl_set] = dist_rl.get(rl_set, 0) + 1
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dl_set = sum(drop_lowest([roll(), roll(), roll(), roll()]))
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dl_total += dl_set
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dist_dl[dl_set] = dist_dl.get(dl_set, 0) + 1
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i += 1
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p_rl, p_dl = ((100 / max_amount) * rl_total), ((100 / max_amount) * dl_total)
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print("3d{:d} Re-roll Lowest - {:d} samples\nDistribution (result : times)".format(die_max, sample))
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for attribute, value in dict(sorted(dist_rl.items())).items():
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print('{:d} : {:d}'.format(attribute, value))
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print("{:.5f}% ({:d} of {:d}).\n".format(p_rl, rl_total, max_amount))
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print("4d{:d} Drop Lowest - {:d} samples\nDistribution (result : times)".format(die_max, sample))
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for attribute, value in dict(sorted(dist_dl.items())).items():
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print('{:d} : {:d}'.format(attribute, value))
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print("{:.5f}% ({:d} of {:d}).\n".format(p_dl, dl_total, max_amount))
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if rl_total < dl_total:
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print("4d{:d}dl rolled more by {:.5f}%".format(die_max, p_dl - p_rl))
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else:
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print("3d{:d}rl rolled more by {:.5f}%".format(die_max, p_rl - p_dl))
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