Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Wordle: Adjust expected_wins for bin size #121

Open
wants to merge 1 commit into
base: main
Choose a base branch
from
Open

Wordle: Adjust expected_wins for bin size #121

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
56 changes: 28 additions & 28 deletions ipynb/Wordle.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -19,9 +19,9 @@
"- Q: What first guess maximizes the number of **guaranteed wins** on the second guess?\n",
"<br>A: `BRUTE` and `CHANT` guarantee you 40 wins (out of 2,315).\n",
"- Q: What first guess maximizes the number of **expected wins** on the second guess?\n",
"<br>A: `FILET` gives you 57.5 expected wins (out of 2,315). \n",
"<br>A: `TRACE` gives you 150 expected wins (out of 2,315). \n",
"\n",
"The probability of winning in two guesses is about 2%, so the answer is: mostly lucky.\n",
"The probability of winning in two guesses is about 6.48%, so the answer is: mostly lucky.\n",
"\n",
"# (2) What is a winning strategy I can memorize?\n",
"\n",
Expand Down Expand Up @@ -176,15 +176,19 @@
"\n",
"def expected_wins(guess):\n",
" \"\"\"The expected number of wins on the 2nd guess (after `guess` first).\n",
" With n words in a bin, you have a 1 / n chance of guessing the right one.\"\"\"\n",
" return sum(1 / n for n in bin_sizes(guess))"
" \n",
" With n words in a bin, you have a 1 / n chance of guessing the right one.\n",
" And the chance of ending up in a bin is n / 2315.\n",
" So, the expected wins is, counter-intuitively, just number of possible bins.\n",
" \"\"\"\n",
" return len(bin_sizes(guess))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we see that `BRUTE` and `CHANT` give the most guaranteed wins (bins of size 1), while `FILET` has the most expected wins (because it has many bins of size 2):"
"Below we see that `BRUTE` and `CHANT` give the most guaranteed wins (bins of size 1), while `TRACE` has the most expected wins (because it breaks down the answers into the most number of bins):"
]
},
{
Expand Down Expand Up @@ -224,16 +228,16 @@
{
"data": {
"text/plain": [
"{'FILET': 57.49225359588394,\n",
" 'PARSE': 57.158766264952895,\n",
" 'DINER': 56.80471418211567,\n",
" 'BRUTE': 55.518562422003676,\n",
" 'METRO': 55.227427161935054,\n",
" 'TRUCE': 55.08315688051648,\n",
" 'TRACE': 54.9442057981406,\n",
" 'EARTH': 54.66697429572324,\n",
" 'TRIED': 54.52412463700236,\n",
" 'STALE': 54.34210156658472}"
"{'TRACE': 150,\n",
" 'CRATE': 148,\n",
" 'SLATE': 147,\n",
" 'PARSE': 146,\n",
" 'CRANE': 142,\n",
" 'STALE': 142,\n",
" 'HEART': 141,\n",
" 'LEAST': 140,\n",
" 'REACT': 140,\n",
" 'CATER': 139}"
]
},
"execution_count": 6,
Expand All @@ -249,7 +253,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we see that `MUMMY` is the worst first guess, by both metrics:"
"Below we see that `MUMMY` is one of the worst first guess, by both metrics:"
]
},
{
Expand Down Expand Up @@ -280,11 +284,7 @@
{
"data": {
"text/plain": [
"{'MUMMY': 10.766462361593344,\n",
" 'QUEUE': 10.939009001096343,\n",
" 'QUEER': 12.173425009634647,\n",
" 'QUEEN': 12.2180304500002,\n",
" 'JAZZY': 13.38489636915653}"
"{'JAZZY': 31, 'FUZZY': 34, 'QUEUE': 35, 'FIZZY': 37, 'MUMMY': 37}"
]
},
"execution_count": 8,
Expand Down Expand Up @@ -534,8 +534,8 @@
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 46.5 s, sys: 14.4 ms, total: 46.5 s\n",
"Wall time: 46.5 s\n"
"CPU times: user 33.8 s, sys: 89 ms, total: 33.9 s\n",
"Wall time: 33.9 s\n"
]
}
],
Expand Down Expand Up @@ -634,8 +634,8 @@
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 972 ms, sys: 5.41 ms, total: 977 ms\n",
"Wall time: 977 ms\n",
"CPU times: user 749 ms, sys: 8.64 ms, total: 758 ms\n",
"Wall time: 757 ms\n",
"\n",
"('DUTCH', 'WOVEN', 'SPRIG', 'BALMY') is a winner\n",
" bin counts: {1: 2117, 2: 88, 3: 6, 4: 1}\n",
Expand Down Expand Up @@ -760,7 +760,7 @@
},
{
"cell_type": "code",
"execution_count": 23,
"execution_count": 21,
"metadata": {},
"outputs": [
{
Expand All @@ -769,7 +769,7 @@
"5.0315334773218146"
]
},
"execution_count": 23,
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
Expand Down Expand Up @@ -799,7 +799,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.6"
"version": "3.9.9"
}
},
"nbformat": 4,
Expand Down