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Wordle may seem like a word game, but really it’s a mathematical one. Rather than debate the best opening word, why not calculate it with information theory?
Many thanks to Tran Nguyen for all her help with this video…in particular, for inspiring the graphs showing the entropy of different opening words. And also many thanks to Jason Liszka for open-sourcing his Wordle-solving code, which I hacked mercilessly to do the calculations for this video!
You can find the table of the optimal opening words according to this method below:
The best opening words
| easy mode | hard mode | all words | common words | all words | common words | rank | word | turns to win | word | turns to win | word | turns to win | word | turns to win |
|---|---|---|---|---|---|---|---|---|
| 1. | REAST | 3.604 | TRACE | 3.625 | TRAPE | 3.805 | TRACE | 3.840 |
| 2. | TRACE | 3.608 | CRANE | 3.635 | PRATE | 3.808 | SLATE | 3.841 |
| 3. | CRANE | 3.610 | ROAST | 3.638 | SALET | 3.811 | LEAST | 3.846 |
| 4. | CARLE | 3.611 | SLATE | 3.640 | LEANT | 3.812 | LEANT | 3.850 |
| 5. | TORSE | 3.613 | TRICE | 3.641 | REAST | 3.814 | TRAIN | 3.851 |
| 6. | RANCE | 3.614 | CRATE | 3.642 | TRACE | 3.815 | PRATE | 3.852 |
| 7. | SALET | 3.614 | SLANT | 3.648 | CRANE | 3.816 | SLANT | 3.852 |
| 8. | SLATE | 3.616 | STARE | 3.648 | LEAST | 3.818 | CRATE | 3.854 |
| 9. | SNARE | 3.617 | LEAST | 3.651 | SLATE | 3.827 | CRANE | 3.855 |
| 10. | CRATE | 3.620 | PRATE | 3.653 | CRATE | 3.829 | TALES | 3.857 |
| 11. | LEAST | 3.620 | REACT | 3.654 | CARET | 3.829 | TRIPE | 3.862 |
| 12. | TRONE | 3.620 | CORSE | 3.655 | CARLE | 3.829 | SPATE | 3.863 |
| 13. | CARET | 3.621 | CADRE | 3.655 | TRICE | 3.829 | PLATE | 3.864 |
| 14. | ROAST | 3.621 | TRADE | 3.656 | PRASE | 3.830 | TRICE | 3.864 |
| 15. | CARTE | 3.621 | TRAIN | 3.657 | SLANE | 3.832 | DEALT | 3.866 |
| 16. | ROSET | 3.621 | DEALT | 3.657 | PEART | 3.832 | TRIES | 3.866 |
| 17. | PRASE | 3.622 | SNARE | 3.657 | ARTEL | 3.833 | TRAIL | 3.867 |
| 18. | TRINE | 3.622 | LANCE | 3.657 | RESAT | 3.834 | STALE | 3.868 |
| 19. | TOILE | 3.623 | CARET | 3.658 | TRADE | 3.835 | CRAPE | 3.870 |
| 20. | TRICE | 3.623 | STALE | 3.660 | PARSE | 3.835 | TRADE | 3.870 |
| 21. | SLART | 3.625 | SLICE | 3.660 | REIST | 3.836 | LANCE | 3.870 |
| 22. | PARSE | 3.625 | STORE | 3.660 | CARTE | 3.838 | CLEAT | 3.871 |
| 23. | TRADE | 3.626 | SCALE | 3.661 | REACT | 3.838 | CARET | 3.873 |
| 24. | SOREL | 3.627 | TRIPE | 3.662 | CARSE | 3.838 | TRIAL | 3.873 |
| 25. | STARE | 3.627 | STILE | 3.664 | SETAL | 3.839 | CREST | 3.875 |
| 26. | RAINE | 3.628 | TRAIL | 3.664 | TORSE | 3.839 | SCALE | 3.875 |
| 27. | SLANE | 3.628 | LEANT | 3.664 | TRINE | 3.840 | PLANE | 3.876 |
| 28. | REACT | 3.631 | TEARS | 3.666 | SLART | 3.841 | REACT | 3.877 |
| 29. | CARSE | 3.633 | SAINT | 3.667 | TEALS | 3.841 | LEARN | 3.883 |
| 30. | PEART | 3.634 | SPATE | 3.668 | TRIES | 3.841 | NACRE | 3.884 |
| 31. | REIST | 3.634 | RAISE | 3.669 | EARNT | 3.844 | PEARL | 3.884 |
| 32. | TRAPE | 3.634 | PARSE | 3.670 | STALE | 3.844 | CADRE | 3.885 |
| 33. | HEART | 3.635 | CATER | 3.670 | TALES | 3.844 | STORE | 3.885 |
| 34. | ARTEL | 3.635 | CRAPE | 3.670 | TERAS | 3.844 | CASTE | 3.886 |
| 35. | EARST | 3.635 | PLATE | 3.671 | ALERT | 3.845 | TREAD | 3.886 |
| 36. | RONTE | 3.635 | PLANE | 3.671 | RANCE | 3.847 | ROAST | 3.887 |
| 37. | STALE | 3.635 | SNORE | 3.671 | CATER | 3.848 | ALERT | 3.888 |
| 38. | PRATE | 3.636 | AROSE | 3.672 | STANE | 3.849 | HEART | 3.888 |
| 39. | RAILE | 3.636 | NITRE | 3.672 | ALTER | 3.849 | STARE | 3.888 |
| 40. | TASER | 3.636 | SIREN | 3.673 | TEARS | 3.850 | CORSE | 3.889 |
| 41. | SOARE | 3.637 | TARGE | 3.673 | ROATE | 3.850 | PARSE | 3.889 |
| 42. | STANE | 3.637 | ALTER | 3.674 | SANER | 3.851 | TAPER | 3.891 |
| 43. | TEARS | 3.637 | CREST | 3.674 | LEARN | 3.852 | SNARE | 3.891 |
| 44. | ANTRE | 3.638 | TRIED | 3.674 | TRONE | 3.852 | TRIED | 3.891 |
| 45. | LEANT | 3.638 | CLEAT | 3.675 | ROAST | 3.853 | TEARS | 3.892 |
| 46. | ROATE | 3.638 | TRIAL | 3.676 | STARE | 3.853 | NEARS | 3.892 |
| 47. | TARES | 3.640 | SCARE | 3.677 | HEART | 3.854 | LITRE | 3.892 |
| 48. | AROSE | 3.641 | TREAD | 3.678 | ORATE | 3.854 | STEAL | 3.892 |
| 49. | EARNT | 3.641 | SHALE | 3.678 | TASER | 3.854 | CATER | 3.893 |
| 50. | RAISE | 3.641 | ARISE | 3.679 | LATER | 3.854 | STILE | 3.894 |
| 51. | PARLE | 3.642 | GRATE | 3.679 | EARST | 3.854 | TENOR | 3.895 |
| 52. | RESAT | 3.642 | NACRE | 3.679 | TARES | 3.855 | RINSE | 3.896 |
| 53. | SLIER | 3.643 | TRIES | 3.679 | ROSET | 3.855 | SAINT | 3.896 |
| 54. | STORE | 3.643 | CLEAR | 3.680 | SNARE | 3.856 | SLICE | 3.896 |
| 55. | STIRE | 3.645 | PEARL | 3.680 | STORE | 3.857 | SORTA | 3.897 |
| 56. | PAIRE | 3.648 | ALONE | 3.682 | TOILE | 3.857 | ALTER | 3.897 |
| 57. | CATER | 3.648 | STAIR | 3.682 | SCARE | 3.857 | STAIR | 3.897 |
| 58. | ORATE | 3.649 | ALIEN | 3.682 | PARLE | 3.858 | SIREN | 3.898 |
| 59. | SANER | 3.649 | HEART | 3.682 | ANTRE | 3.859 | RATES | 3.899 |
| 60. | SETAL | 3.649 | LATER | 3.682 | SERAL | 3.859 | SCARE | 3.899 |
| 61. | ARIEL | 3.650 | SPARE | 3.682 | STRAE | 3.859 | SHALE | 3.899 |
| 62. | ALERT | 3.650 | CASTE | 3.683 | RATEL | 3.860 | SNORE | 3.900 |
| 63. | SERAL | 3.651 | ALERT | 3.683 | ALINE | 3.860 | SPARE | 3.901 |
| 64. | ALTER | 3.651 | TALES | 3.684 | ARETS | 3.862 | LATER | 3.901 |
| 65. | SCARE | 3.651 | AISLE | 3.685 | LITRE | 3.862 | NITRE | 3.901 |
| 66. | LIANE | 3.652 | CARES | 3.685 | SOREL | 3.863 | GRATE | 3.902 |
| 67. | RATEL | 3.652 | RINSE | 3.686 | TALER | 3.865 | IRATE | 3.902 |
| 68. | COATE | 3.653 | RATES | 3.686 | ALIEN | 3.867 | CLEAR | 3.903 |
| 69. | STRAE | 3.653 | LEARN | 3.687 | RONTE | 3.868 | PATER | 3.904 |
| 70. | TALER | 3.654 | IRATE | 3.689 | RATES | 3.869 | ALIEN | 3.906 |
| 71. | AISLE | 3.655 | SAUTE | 3.690 | ARIEL | 3.870 | SATED | 3.910 |
| 72. | ALINE | 3.656 | TENOR | 3.690 | REALS | 3.870 | TARGE | 3.911 |
| 73. | ALONE | 3.656 | TAPER | 3.690 | LIANE | 3.872 | ASTER | 3.912 |
| 74. | SAINE | 3.656 | SOLAR | 3.691 | STEAR | 3.872 | CANOE | 3.912 |
| 75. | ARISE | 3.657 | GLARE | 3.692 | PAIRE | 3.873 | NARES | 3.913 |
| 76. | LATER | 3.657 | SORTA | 3.693 | STIRE | 3.874 | RENAL | 3.913 |
| 77. | IRATE | 3.657 | PATER | 3.694 | RAINE | 3.875 | BLARE | 3.914 |
| 78. | TRIES | 3.658 | STEAL | 3.695 | IRATE | 3.876 | LITER | 3.914 |
| 79. | ALIEN | 3.659 | LITRE | 3.695 | SAUTE | 3.878 | CARES | 3.916 |
| 80. | TEALS | 3.660 | SATED | 3.696 | ALONE | 3.880 | ALONE | 3.921 |
| 81. | TERAS | 3.660 | CANOE | 3.697 | RAILE | 3.880 | THANE | 3.923 |
| 82. | SAICE | 3.661 | SUITE | 3.698 | SHARE | 3.883 | SAUTE | 3.923 |
| 83. | SAUTE | 3.662 | THANE | 3.698 | LARES | 3.884 | LASER | 3.924 |
| 84. | RATES | 3.662 | BLARE | 3.698 | RALES | 3.885 | SOLAR | 3.925 |
| 85. | SHARE | 3.663 | NARES | 3.700 | URATE | 3.885 | HATER | 3.926 |
| 86. | TOISE | 3.663 | SABRE | 3.701 | SLIER | 3.887 | ARISE | 3.927 |
| 87. | LITRE | 3.663 | SHARE | 3.702 | COATE | 3.888 | AISLE | 3.927 |
| 88. | ARETS | 3.666 | LASER | 3.702 | SOARE | 3.888 | RAISE | 3.928 |
| 89. | TALES | 3.666 | HATER | 3.703 | RAISE | 3.889 | GLARE | 3.928 |
| 90. | LEARN | 3.667 | ASTER | 3.704 | LASER | 3.889 | ANISE | 3.930 |
| 91. | URATE | 3.672 | LOSER | 3.705 | TOISE | 3.892 | LOSER | 3.932 |
| 92. | ARLES | 3.674 | ANISE | 3.708 | SAINE | 3.894 | ATONE | 3.934 |
| 93. | REALO | 3.674 | ATONE | 3.710 | ARLES | 3.895 | SABRE | 3.937 |
| 94. | STEAR | 3.674 | RENAL | 3.714 | AROSE | 3.896 | SHARE | 3.940 |
| 95. | REALS | 3.675 | ORIEL | 3.716 | OATER | 3.898 | SUITE | 3.943 |
| 96. | LARES | 3.678 | SHEAR | 3.717 | AISLE | 3.899 | ORIEL | 3.951 |
| 97. | RALES | 3.679 | NEARS | 3.721 | AESIR | 3.902 | AROSE | 3.961 |
| 98. | LASER | 3.683 | ROUTE | 3.724 | ARISE | 3.902 | SHEAR | 3.965 |
| 99. | OATER | 3.684 | LITER | 3.725 | SAICE | 3.908 | ROUTE | 3.974 |
| 100. | AESIR | 3.686 | ROUSE | 3.726 | REALO | 3.909 | ROUSE | 3.978 |
Please see
https://medium.com/@tglaiel/the-mathematically-optimal-first-guess-in-wordle-cbcb03c19b0a
Tyler Glaiel
(Tyler and Glair are both words)
Dec 30, 2021
With RAISE as the first guess, you will average 3.49546 guesses to solve but have that sweet, sweet chance of landing that hole-in-one (1:2315)
This version of the bot finds a solution in 3.49417 guesses on average, and has a worst-case of 5 guesses (meaning, it *always* finds a solution). The ideal first guess using this method is ROATE.
Please review the algorithm you “hacked mercilessly”, you should be able to reproduce or refute the above. And have a look at why you have RAISE in both feasible and unfeasible test words.
easy mode
ROATE 3.638 – not solution set
RAISE 3.641 – not solution set
RAISE 3.669 – potential solution
hard mode
ROATE 3.850 – not solution set
RAISE 3.889 – not solution set
RAISE 3.928 – potential solution
Hi Nick! Thanks for your comment. I think the difference here is that Tyler’s algorithm works slightly differently to this one—the first version scores words based on yellow and green squares, and the second looks just at the size of the solution set and not the entropy, hence they give slightly different results. 🙂