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November 6, 2018 14:43
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Unfair coin tosses\n", | |
"\n", | |
"Copyright Allen Downey 2018\n", | |
"\n", | |
"[MIT License](https://opensource.org/licenses/MIT)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# Configure Jupyter so figures appear in the notebook\n", | |
"%matplotlib inline\n", | |
"\n", | |
"# Configure Jupyter to display the assigned value after an assignment\n", | |
"%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", | |
"\n", | |
"import numpy as np" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here's a puzzle from [a recent FiveThirtyEight post](https://fivethirtyeight.com/features/how-far-would-you-go-to-rig-a-coin-flip/):\n", | |
"\n", | |
">Coin flips are a handy way to determine a winner — if the goal is to give two people an equal chance of winning. But sometimes it’s not. Suppose Anna and Barry aren’t interested in equity. All they have is a fair coin marked heads and tails. How can they devise a game that gives Anna a 1 in 3 chance of winning? What about a 1 in 4 chance? What about a 1 in 5 chance?\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Solution\n", | |
"\n", | |
"The key to the solution is to take advantage of Pascal's triangle. If you toss `n` coins, the number of heads, `k`, follows a binomial distribution. The relative probabilities of the totals `k = 0...n` are the coefficients in Pascal's triangle.\n", | |
"\n", | |
"Here's a function that uses `np.convolve` to generate the rows of Pascal's triangle." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def pascal(n_rows):\n", | |
" a = [1]\n", | |
" yield(a)\n", | |
" \n", | |
" for i in range(n_rows):\n", | |
" a = np.convolve(a, [1,1])\n", | |
" yield(a)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"[1]\n", | |
"[1 1]\n", | |
"[1 2 1]\n", | |
"[1 3 3 1]\n", | |
"[1 4 6 4 1]\n", | |
"[ 1 5 10 10 5 1]\n" | |
] | |
} | |
], | |
"source": [ | |
"for row in pascal(5):\n", | |
" print(row)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The third row is [1 2 1], which indicates that if we flip two coins, the chance of getting 1 head is twice the chance of getting 0 or 2 heads. So if we want to give Anna a 1/4 chance of winning, we could toss two coins: if we get 0 heads, Anna wins; otherwise Barry wins.\n", | |
"\n", | |
"More generally, we can toss `n` coins and choose\n", | |
"\n", | |
"1. A set of totals where Anna wins,\n", | |
"2. A set of totals where Barry wins, and maybe\n", | |
"3. A leftover set where we have to toss again.\n", | |
"\n", | |
"For example, if Anna should win `1/3` of the time, we could toss `2` coins; Anna wins if we get `0` heads, Barry wins if we get `1`, and we have to toss again if we get `2`.\n", | |
"\n", | |
"The chance that we have to try again is `1/4`, so the expected number of attempts is `4/3`. Each attempt requires 2 coins tosses, so the expected number of flips is `8/3`.\n", | |
"\n", | |
"For each desired probability, we can search for the process that yields the desired outcome with the minimum expected number of flips." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"I'll start with a function that yields all combinations from a set." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from itertools import combinations\n", | |
"\n", | |
"def all_combos(s):\n", | |
" n = len(s)\n", | |
" for r in range(1, n+1):\n", | |
" for comb in combinations(s, r):\n", | |
" yield list(comb)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For example, if we take the third row from Pascal's triangle, there are three outcomes, `{0, 1, 2}`, with relative frequencies `[1, 2, 1]`." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"{0, 1, 2}" | |
] | |
}, | |
"execution_count": 5, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"row = np.array([1, 2, 1])\n", | |
"ind = set(range(len(row)))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here are all subsets of the outcomes:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"[0]\n", | |
"[1]\n", | |
"[2]\n", | |
"[0, 1]\n", | |
"[0, 2]\n", | |
"[1, 2]\n", | |
"[0, 1, 2]\n" | |
] | |
} | |
], | |
"source": [ | |
"for comb in all_combos(ind):\n", | |
" print(comb)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Now we'd like to enumerate all partitions of the set into `win` and `lose`, allowing the possiblity of leaving out some outcomes." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def all_partitions(s):\n", | |
" for win in all_combos(s):\n", | |
" rest = s - set(win)\n", | |
" for lose in all_combos(rest):\n", | |
" yield win, lose" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here are the ways to partition `{0, 1, 2}`, and the total relative frequency for each subset." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"[0] [1] 1 2\n", | |
"[0] [2] 1 1\n", | |
"[0] [1, 2] 1 3\n", | |
"[1] [0] 2 1\n", | |
"[1] [2] 2 1\n", | |
"[1] [0, 2] 2 2\n", | |
"[2] [0] 1 1\n", | |
"[2] [1] 1 2\n", | |
"[2] [0, 1] 1 3\n", | |
"[0, 1] [2] 3 1\n", | |
"[0, 2] [1] 2 2\n", | |
"[1, 2] [0] 3 1\n" | |
] | |
} | |
], | |
"source": [ | |
"for win, lose in all_partitions(ind):\n", | |
" print(win, lose, row[win].sum(), row[lose].sum())" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Now we can enumerate the rows of Pascal's triangle and for each set of outcomes, enumerate the partitions.\n", | |
"\n", | |
"For each partition, we compute the odds Anna wins and yield:\n", | |
"\n", | |
"* `expected_coins`: the expected total number of coins we have to toss.\n", | |
"* `n_coins`: number of coins we toss for each attempt\n", | |
"* `win`: set of outcomes where Anna wins\n", | |
"* `lose`: set of outcomes where Anna loses\n", | |
"* `odds`: the odds that Anna wins.\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import math\n", | |
"\n", | |
"def reduce(a, b):\n", | |
" d = math.gcd(a, b)\n", | |
" return a//d, b//d" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from fractions import Fraction\n", | |
"\n", | |
"def enumerate_rows(n_rows):\n", | |
" # loop through the rows of Pascal's triangle\n", | |
" for n_coins, row in enumerate(pascal(n_rows)):\n", | |
" index = set(range(len(row)))\n", | |
" \n", | |
" # loop through ways to partition the outcomes\n", | |
" for win, lose in all_partitions(index):\n", | |
" \n", | |
" # compute the odds Anna wins\n", | |
" numer, denom = row[win].sum(), row[lose].sum()\n", | |
" odds = reduce(numer, denom)\n", | |
"\n", | |
" # compute the expected number of tosses\n", | |
" efficency = Fraction(numer + denom, 2**n_coins)\n", | |
" expected_coins = n_coins / efficency\n", | |
" \n", | |
" yield expected_coins, n_coins, efficency, win, lose, odds" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here are the results from tossing one coin or two." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"(Fraction(1, 1), 1, Fraction(1, 1), [0], [1], (1, 1))\n", | |
"(Fraction(1, 1), 1, Fraction(1, 1), [1], [0], (1, 1))\n", | |
"(Fraction(8, 3), 2, Fraction(3, 4), [0], [1], (1, 2))\n", | |
"(Fraction(4, 1), 2, Fraction(1, 2), [0], [2], (1, 1))\n", | |
"(Fraction(2, 1), 2, Fraction(1, 1), [0], [1, 2], (1, 3))\n", | |
"(Fraction(8, 3), 2, Fraction(3, 4), [1], [0], (2, 1))\n", | |
"(Fraction(8, 3), 2, Fraction(3, 4), [1], [2], (2, 1))\n", | |
"(Fraction(2, 1), 2, Fraction(1, 1), [1], [0, 2], (1, 1))\n", | |
"(Fraction(4, 1), 2, Fraction(1, 2), [2], [0], (1, 1))\n", | |
"(Fraction(8, 3), 2, Fraction(3, 4), [2], [1], (1, 2))\n", | |
"(Fraction(2, 1), 2, Fraction(1, 1), [2], [0, 1], (1, 3))\n", | |
"(Fraction(2, 1), 2, Fraction(1, 1), [0, 1], [2], (3, 1))\n", | |
"(Fraction(2, 1), 2, Fraction(1, 1), [0, 2], [1], (1, 1))\n", | |
"(Fraction(2, 1), 2, Fraction(1, 1), [1, 2], [0], (3, 1))\n" | |
] | |
} | |
], | |
"source": [ | |
"for result in enumerate_rows(2):\n", | |
" print(result)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"There are several ways to get `1:1` odds, but the most efficient is to toss one coin once. No surprise there.\n", | |
"\n", | |
"The best ways to get `1:2` odds (so far) is to toss 2 coins, but we might have to try several times, so the expected number of tosses is `8/3`, as in the example above.\n", | |
"\n", | |
"Now we can enumerate the rows of Pascal's triangle and for each effective odds, record the best way to achieve it.\n", | |
"\n", | |
"`best` maps from `odds`, represented by a tuple of integers, to `results`, which is a tuple.\n", | |
"\n", | |
"The elements of `results` are in order so we can use tuple comparison to select the results with the lowest expected number of coin tosses, and the lowest number of tosses per round, as a tie-breaker." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def run_rows(n):\n", | |
" absent = (np.inf,)\n", | |
"\n", | |
" for result in enumerate_rows(n):\n", | |
" odds = result[-1]\n", | |
" t = best.get(odds, absent)\n", | |
" if result < t:\n", | |
" best[odds] = result" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"CPU times: user 6h 1min 48s, sys: 13 s, total: 6h 2min 1s\n", | |
"Wall time: 6h 3min 44s\n" | |
] | |
} | |
], | |
"source": [ | |
"best = {}\n", | |
"%time run_rows(17)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here are the results for odds `1:n`, for various `n`:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 21, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"(1, 1) 1 1 1 [0] [1]\n", | |
"(1, 2) 2 3/4 8/3 [0] [1]\n", | |
"(1, 3) 2 1 2 [0] [1, 2]\n", | |
"(1, 4) 3 5/8 24/5 [0] [1, 3]\n", | |
"(1, 5) 4 3/4 16/3 [0, 4] [1, 2]\n", | |
"(1, 6) 3 7/8 24/7 [0] [1, 2]\n", | |
"(1, 7) 3 1 3 [0] [1, 2, 3]\n", | |
"(1, 8) 6 63/64 128/21 [0, 1] [2, 3, 4, 5]\n", | |
"(1, 9) 4 5/8 32/5 [0] [1, 3, 4]\n", | |
"(1, 10) 4 11/16 64/11 [0] [1, 2]\n", | |
"(1, 11) 4 3/4 16/3 [0] [1, 2, 4]\n", | |
"(1, 12) 9 247/256 2304/247 [0, 2, 9] [3, 4, 5, 6, 7]\n", | |
"(1, 13) 7 49/64 64/7 [1] [2, 3, 4]\n", | |
"(1, 14) 4 15/16 64/15 [0] [1, 2, 3]\n", | |
"(1, 15) 4 1 4 [0] [1, 2, 3, 4]\n", | |
"(1, 16) 7 119/128 128/17 [1] [2, 3, 4, 5]\n", | |
"(1, 17) 7 63/64 64/9 [1] [2, 3, 4, 5, 6]\n", | |
"(1, 18) 6 19/32 192/19 [0, 6] [1, 2, 4]\n", | |
"(1, 19) 8 25/32 256/25 [0, 1, 8] [2, 3, 4, 6, 7]\n", | |
"(1, 20) 5 21/32 160/21 [0] [1, 2, 4]\n", | |
"(1, 21) 5 11/16 80/11 [0] [1, 2, 4, 5]\n", | |
"(1, 22) 8 23/32 256/23 [1] [2, 3, 5, 6, 7]\n", | |
"(1, 23) 8 3/4 32/3 [1] [0, 2, 3, 4, 6, 8]\n", | |
"(1, 24) 9 475/512 4608/475 [0, 1, 8] [2, 3, 4, 5, 6]\n", | |
"(1, 25) 5 13/16 80/13 [0] [1, 2, 3]\n", | |
"(1, 26) 5 27/32 160/27 [0] [1, 2, 3, 5]\n", | |
"(1, 27) 13 2009/2048 26624/2009 [0, 3] [1, 4, 5, 6, 7, 8, 9, 10, 12, 13]\n", | |
"(1, 28) 6 29/32 192/29 [0, 6] [1, 2, 3, 4]\n", | |
"(1, 29) 11 495/512 512/45 [1, 2] [3, 4, 5, 6, 7, 8]\n", | |
"(1, 30) 5 31/32 160/31 [0] [1, 2, 3, 4]\n", | |
"(1, 31) 5 1 5 [0] [1, 2, 3, 4, 5]\n", | |
"(1, 32) 6 33/64 128/11 [0] [1, 3, 5]\n", | |
"(1, 33) 6 17/32 192/17 [0] [1, 3, 5, 6]\n", | |
"(1, 34) 9 175/256 2304/175 [0, 1] [2, 3, 4, 6, 8, 9]\n", | |
"(1, 35) 6 9/16 32/3 [0] [2, 3]\n", | |
"(1, 36) 6 37/64 384/37 [0] [1, 2, 4]\n", | |
"(1, 37) 6 19/32 192/19 [0] [1, 2, 4, 6]\n", | |
"(1, 38) 12 1287/2048 8192/429 [2] [5, 6, 7]\n", | |
"(1, 39) 9 55/64 576/55 [0, 1, 9] [3, 4, 5, 6, 8]\n", | |
"(1, 40) 17 32759/32768 32768/1927 [2, 3, 4] [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n", | |
"(1, 41) 6 21/32 64/7 [0] [1, 2, 3]\n", | |
"(1, 42) 6 43/64 384/43 [0] [1, 2, 3, 6]\n", | |
"(1, 43) 6 11/16 96/11 [0] [1, 2, 4, 5, 6]\n", | |
"(1, 44) 12 4095/4096 16384/1365 [0, 1, 2, 11] [3, 4, 5, 6, 7, 8, 9, 10]\n", | |
"(1, 45) 12 897/1024 4096/299 [1, 2] [0, 3, 4, 5, 6, 7, 9, 10]\n", | |
"(1, 46) 12 3149/4096 49152/3149 [0, 2] [1, 4, 5, 6, 7, 10, 12]\n", | |
"(1, 47) 6 3/4 8 [0] [1, 2, 3, 5]\n", | |
"(1, 48) 6 49/64 384/49 [0] [1, 2, 3, 5, 6]\n", | |
"(1, 49) 7 25/32 224/25 [0, 7] [1, 2, 3, 4]\n", | |
"(1, 50) 6 51/64 128/17 [0] [2, 3, 4]\n", | |
"(1, 51) 6 13/16 96/13 [0] [2, 3, 4, 6]\n", | |
"(1, 52) 17 127041/131072 131072/7473 [1, 4] [5, 6, 7, 8, 9, 10, 11, 12]\n", | |
"(1, 53) 12 891/1024 4096/297 [2] [4, 5, 6, 7, 8]\n", | |
"(1, 54) 12 1815/2048 8192/605 [2] [4, 5, 6, 7, 8, 10]\n", | |
"(1, 55) 10 21/32 320/21 [0, 1, 10] [3, 4, 6, 7]\n", | |
"(1, 56) 6 57/64 128/19 [0] [1, 2, 3, 4]\n", | |
"(1, 57) 6 29/32 192/29 [0] [1, 2, 3, 4, 6]\n", | |
"(1, 58) 10 649/1024 10240/649 [0, 1] [2, 3, 4, 5, 9, 10]\n", | |
"(1, 59) 15 7275/8192 8192/485 [1, 3, 14] [0, 4, 5, 6, 7, 8, 9, 11, 15]\n", | |
"(1, 60) 10 671/1024 10240/671 [0, 1] [3, 4, 6, 7]\n", | |
"(1, 61) 10 341/512 5120/341 [0, 1] [3, 4, 6, 7, 9, 10]\n", | |
"(1, 62) 6 63/64 128/21 [0] [1, 2, 3, 4, 5]\n", | |
"(1, 63) 6 1 6 [0] [1, 2, 3, 4, 5, 6]\n", | |
"(1, 64) 7 65/128 896/65 [0] [1, 2, 3, 7]\n", | |
"(1, 65) 10 363/512 5120/363 [0, 1] [2, 3, 4, 6, 7, 9]\n", | |
"(1, 66) 10 201/256 2560/201 [0, 1, 10] [2, 3, 4, 5, 7, 8]\n", | |
"(1, 67) 8 17/32 256/17 [0, 8] [1, 2, 4, 6]\n", | |
"(1, 68) 10 759/1024 10240/759 [0, 1] [2, 3, 4, 5, 7, 10]\n", | |
"(1, 69) 13 1365/2048 2048/105 [2] [1, 3, 4, 5, 6, 8, 11]\n" | |
] | |
} | |
], | |
"source": [ | |
"res = []\n", | |
"\n", | |
"for denom in range(1, 70):\n", | |
" result = best[1, denom]\n", | |
" expected_coins, n_coins, efficiency, win, lose, odds = result\n", | |
" print(odds, n_coins, efficiency, expected_coins, win, lose)\n", | |
" res.append((denom, efficiency, expected_coins))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The fourth line is `(1, 4) 3 5/8 24/5 [0] [1, 3]`, which indicates that if we want odds `1:4`, we should flip `3` coins. Alice wins if we get `0` heads; Barry wins if we get `1` or `3`. `5/8` of the time we are done; the remaining `3/8` we flip again; on average we expect to toss `24/5` coins. " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Let's see what the results look like graphically. Here's efficiency for each value of odds against." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 15, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"odds, effs, coins = np.array(res).T" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 16, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import matplotlib.pyplot as plt" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 17, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.bar(odds, effs)\n", | |
"plt.xlabel('Odds against')\n", | |
"plt.ylabel('Efficiency');" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"And here's the expected number of coin tosses for each value of odds against." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 18, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.bar(odds, coins)\n", | |
"plt.xlabel('Odds against')\n", | |
"plt.ylabel('Expected number of coins');" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We can also visualize the efficiency for all values of odds, not just `1:k`." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 48, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"0.8322632344081823" | |
] | |
}, | |
"execution_count": 48, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"import warnings\n", | |
"warnings.filterwarnings('ignore', category=DeprecationWarning)\n", | |
"\n", | |
"high = 150\n", | |
"z1 = np.full((high, high), np.nan)\n", | |
"for i in range(1, high):\n", | |
" for j in range(1, high):\n", | |
" odds = reduce(i, j)\n", | |
" if odds in best:\n", | |
" result = best[odds]\n", | |
" expected_coins = result[0]\n", | |
" efficiency = result[2]\n", | |
" z1[i, j] = efficiency\n", | |
" \n", | |
"np.nanmean(z1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 49, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 2 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.pcolormesh(zs)\n", | |
"plt.colorbar();" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We can also look at the expected number of coins (clipped at 15)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 50, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"11.949975109420947" | |
] | |
}, | |
"execution_count": 50, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"high = 150\n", | |
"z2 = np.full((high, high), np.nan)\n", | |
"for i in range(1, high):\n", | |
" for j in range(1, high):\n", | |
" odds = reduce(i, j)\n", | |
" if odds in best:\n", | |
" result = best[odds]\n", | |
" expected_coins = result[0]\n", | |
" z2[i, j] = min(expected_coins, 15)\n", | |
" \n", | |
"np.nanmean(z2)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 51, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 2 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.pcolormesh(z2)\n", | |
"plt.colorbar();" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.6.5" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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