Letter Shuffling Algorithms
Posted: Mon Jul 13, 2020 12:09 pm
I have been experimenting with different ways to generate letters selections and seeing how it affects the average length of the best available word in a letters selection
Algorithm 1: Deduplication vs last letter
If the the next letter in the stack matches the last latter from that stack (counting consonant and vowel stack separately), then with 70% probability, instead of giving out that letter, repeat the process. Stack refreshes when it becomes empty.
Algorithm 2: Deduplication vs last letter + early refill
Same as above, but clear the stack when down to the last 5, with the idea being that the above algorithm gives you too many duplicates at the end of the stack.
Algorithm 3: Deduplication vs last 2 letters + early refill
As above, but apply the deduplication rule if either of the last TWO letters in the stack are the same as the candidate letter
Algorithm 4: Deduplication vs last 3 letters + early refill
As above, but apply the deduplication rule if either of the last THREE letters in the stack are the same as the candidate letter
Algorithm 5: No deduplication
Don't do anything to remove duplicates. (Similar to how co-events with the board game are played, if you assume players can shuffle cards adequately)
Conclusion
- 10000 rounds generated for each algorithm and maxes from those rounds analyzed
- Rounds are picked to be 40% 3V 40% 4V and 20% 5V
- Letters distribution is:
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"B": 2
"C": 2
"D": 6
"F": 2
"G": 3
"H": 2
"J": 1
"K": 1
"L": 5
"M": 4
"N": 8
"P": 4
"Q": 1
"R": 9
"S": 9
"T": 9
"V": 1
"W": 1
"X": 1
"Y": 1
"Z": 1
"A": 15
"E": 21
"I": 13
"O": 13
"U": 5
If the the next letter in the stack matches the last latter from that stack (counting consonant and vowel stack separately), then with 70% probability, instead of giving out that letter, repeat the process. Stack refreshes when it becomes empty.
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Total of 79850.0 avg max 7.985
Max of 4: 8
Max of 5: 169
Max of 6: 1367
Max of 7: 4037
Max of 8: 3703
Max of 9: 716
Total of 76169.0 distinct letters avg 7.6169 distinct letters per selectionSame as above, but clear the stack when down to the last 5, with the idea being that the above algorithm gives you too many duplicates at the end of the stack.
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Total of 79916.0 avg 7.9916
Max of 4: 4
Max of 5: 157
Max of 6: 1359
Max of 7: 3989
Max of 8: 3780
Max of 9: 711
Total of 76353.0 distinct letters avg 7.6353 distinct letters per selectionAs above, but apply the deduplication rule if either of the last TWO letters in the stack are the same as the candidate letter
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Total of 81583.0 avg 8.1583
Max of 4: 4
Max of 5: 121
Max of 6: 1095
Max of 7: 3908
Max of 8: 4066
Max of 9: 806
Total of 78818.0 distinct letters avg 7.8818 distinct letters per selectionAs above, but apply the deduplication rule if either of the last THREE letters in the stack are the same as the candidate letter
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Total of 81940.0 avg 8.194
Max of 4: 4
Max of 5: 109
Max of 6: 1055
Max of 7: 3777
Max of 8: 4238
Max of 9: 817
Total of 79782.0 distinct letters avg 7.9782 distinct letters per selectionDon't do anything to remove duplicates. (Similar to how co-events with the board game are played, if you assume players can shuffle cards adequately)
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Total of 76740.0 avg 7.674
Max of 4: 17
Max of 5: 261
Max of 6: 1693
Max of 7: 4263
Max of 8: 3242
Max of 9: 524
Total of 73016.0 distinct letters avg 7.3016 per selectionConclusion
- Reducing the number of duplicates in the selection appears to increase the max, which I am sure was already a well known thing.
- I'm not aware of the avg letters max on the show over recent years, so it would be interesting to see that and how it compares to the baseline 7.3 score per letters selection with no shuffling. if anybody as that data, hit me up!
- Over an Octorun you'd expect the available max to increase by 41.6 if you compare the harshest algorithm (number 5) with the nicest algorithm (algorithm 4)