{ "id": "P071", "slug": "leaderboard", "key": "P071-leaderboard", "title": "Leaderboard", "summary": "A small league: games give points and move Elo ratings, worked out in whole numbers with an exact 400th root; the standings rank players level on points the five usual ways - competition, modified competition, dense, ordinal and fractional.", "entry": "main.eml", "ui": "terminal", "readme": "# P071 - Leaderboard\n\nA small league. A game gives 3 points for a win and 1 each for a draw,\nand moves both players' Elo ratings. The standings show the five usual\nways to rank players who are level on points. The program can also say\nwhat a game between two players is worth before it is played. It starts\nwith seven players, three of them level on 7 points.\n\n- `main.eml` - the menu, the standings table, recording games, and new\n players\n- `ranking.eml` - the five rankings, and Elo in whole numbers\n\nHow each part works:\n\n- Rankings, for the scores 9, 7, 7, 7, 4, 4, 1:\n - competition, \"1224\": 1 + how many scores are higher, as in the corpus\n case `rank-with-ties` - 1, 2, 2, 2, 5, 5, 7;\n - modified competition, \"1334\": how many scores are at least this one -\n 1, 4, 4, 4, 6, 6, 7;\n - dense, \"1223\": 1 + how many different scores are higher, also from\n the corpus case - 1, 2, 2, 2, 3, 3, 4;\n - ordinal, \"1234\": level players in the order they joined;\n - fractional: the average of the places level players share, from the\n competition rank to the modified one - 1, 3, 3, 3, 5.5, 5.5, 7.\n- Elo: A's expected score against B is E = 1 / (1 + 10^((B - A)/400)),\n and A's rating moves by K x (score - E) with K = 32, rounded to a whole\n number, halves away from zero; B moves by the opposite.\n- 10^(d/400) is worked out without floats: d = 400 k + r, and\n floor(10^(12 + r/400)) is the whole number y with\n y^400 <= 10^(4800 + r) < (y + 1)^400, found by halving the range from\n 10^12 to 10^13. That is 12 correct digits. The expected score (shown to\n a tenth of a percent) and the change are then exact divisions of whole\n numbers. Against 60-digit decimals, every rating difference from -3000\n to 3000, with every result, comes out the same; no change there comes\n within 0.0001 of a half, far more than the method's error.\n\nWhat is checked: menu choices 1 to 5; players who are in the league, and\nnot the same player twice; a result of A, B or draw; a new name of\nletters, up to 10, not already used; a starting rating from 100 to 3000.\nAn empty answer cancels.\n\nSessions: `sessions/basic.in` gives:\n- the standings: Ben, Chloe and Dev level on 7, Eli and Fay on 4;\n- what Ana against Gus is worth: 78.0%, so a win gains only 7 and a loss\n costs 25;\n- Dev beating Ana (+22 each way), and Ben drawing with Chloe (+1 to Ben,\n the lower rated);\n- the new standings, Hana joining at 1500, and what Hana against Ana is\n worth.\n\n`sessions/bad-input.in` gives:\n- menu choices 0 and x;\n- an unknown player, a player against themselves, and the result \"win\",\n then a cancel;\n- a name already taken and \"Ana Lee\"; ratings 50, 3001 and abc, then a\n cancel;\n- a cancelled question.\n\nBuilt on the verified corpus case `rank-with-ties` (competition and dense\nranking by counting, so ties need no special case).\n", "modules": [ { "name": "main.eml", "eml": "# P071 leaderboard: a small league. Games give points (3 for a win, 1 each\n# for a draw) and move Elo ratings; the standings show the five usual ways\n# to rank players who are level on points.\nimport ranking\n\ndef trim(s):\n 0 => i\n len(s) => j\n while i < j and s[i] == \" \":\n i + 1 => i\n while j > i and s[j - 1] == \" \":\n j - 1 => j\n return s[i:j]\n\ndef number(s):\n # A whole number of up to 4 digits, or -1.\n if len(s) == 0 or len(s) > 4:\n return -1\n 0 => n\n for c in s:\n if not (c >= \"0\" and c <= \"9\"):\n return -1\n n * 10 + int(c) => n\n return n\n\ndef is_name(s):\n if len(s) == 0 or len(s) > 10:\n return False\n for c in s:\n if not ((c >= \"a\" and c <= \"z\") or (c >= \"A\" and c <= \"Z\")):\n return False\n return True\n\ndef pad(s, n):\n while len(s) < n:\n s + \" \" => s\n return s\n\ndef lpad(s, n):\n while len(s) < n:\n \" \" + s => s\n return s\n\ndef find(players, name):\n for i in [0:len(players) - 1]:\n if players[i][0] == name:\n return i\n return -1\n\ndef signed(n):\n if n > 0:\n return \"+\" + str(n)\n return str(n)\n\ndef percent(permille):\n # 640 -> \"64.0%\"\n 0 => whole\n permille => r\n while r >= 10:\n r - 10 => r\n whole + 1 => whole\n return str(whole) + \".\" + str(r) + \"%\"\n\ndef by_points(players):\n # Indices in table order: most points first; level players keep the\n # order they joined the league.\n [0] * len(players) => out\n for i in [0:len(players) - 1]:\n i => out[i]\n for i in [1:len(out) - 1]:\n out[i] => x\n i - 1 => j\n while j >= 0 and players[out[j]][1] < players[x][1]:\n out[j] => out[j + 1]\n j - 1 => j\n x => out[j + 1]\n return out\n\ndef standings(players):\n [0] * len(players) => pts\n for i in [0:len(players) - 1]:\n players[i][1] => pts[i]\n \"player points rating 1224 1334 1223 1234 fractional\" ^0\n for i in by_points(players):\n (pad(players[i][0], 12) + lpad(str(players[i][1]), 6) + lpad(str(players[i][2]), 8) + lpad(str(ranking.competition(pts, i)), 7) + lpad(str(ranking.modified(pts, i)), 6) + lpad(str(ranking.dense(pts, i)), 6) + lpad(str(ranking.ordinal(pts, i)), 6) + lpad(ranking.fractional(pts, i), 12)) ^0\n \"1224 competition: level players share the better rank, and the ranks after them are skipped.\" ^0\n \"1334 modified competition: level players share the worse rank. 1223 dense: no rank is skipped.\" ^0\n \"1234 ordinal: level players in the order they joined. Fractional: the average of the places they share.\" ^0\n\ndef ask_player(players, prompt):\n while True:\n trim(input(prompt)) => name\n if name == \"\":\n return -1\n find(players, name) => i\n if i >= 0:\n return i\n (\"Nobody called \" + name + \" is in the league.\") ^0\n\ndef game(players):\n ask_player(players, \"player A> \") => a\n if a == -1:\n \"Cancelled.\" ^0\n return players\n while True:\n ask_player(players, \"player B> \") => b\n if b == -1:\n \"Cancelled.\" ^0\n return players\n if b != a:\n while True:\n trim(input(\"result (A, B or draw)> \")) => r\n if r == \"\":\n \"Cancelled.\" ^0\n return players\n -1 => s2\n if r == \"A\" or r == \"a\":\n 2 => s2\n elif r == \"B\" or r == \"b\":\n 0 => s2\n elif r == \"draw\":\n 1 => s2\n if s2 >= 0:\n players[a] => pa\n players[b] => pb\n ranking.elo(pa[2], pb[2], s2, 32) => e\n (\"Before the game \" + pa[0] + \" (\" + str(pa[2]) + \") was expected to score \" + percent(e[0]) + \" against \" + pb[0] + \" (\" + str(pb[2]) + \").\") ^0\n 0 => ga\n 0 => gb\n if s2 == 2:\n 3 => ga\n elif s2 == 0:\n 3 => gb\n else:\n 1 => ga\n 1 => gb\n [pa[0], pa[1] + ga, pa[2] + e[1]] => players[a]\n [pb[0], pb[1] + gb, pb[2] - e[1]] => players[b]\n (pa[0] + \" \" + signed(e[1]) + \" to \" + str(pa[2] + e[1]) + \", \" + pb[0] + \" \" + signed(0 - e[1]) + \" to \" + str(pb[2] - e[1]) + \".\") ^0\n return players\n \"Type A, B or draw.\" ^0\n \"A player cannot play themselves.\" ^0\n\ndef join(players):\n while True:\n trim(input(\"name> \")) => name\n if name == \"\":\n \"Cancelled.\" ^0\n return players\n if not is_name(name):\n \"Type a name of letters, up to 10.\" ^0\n elif find(players, name) >= 0:\n (name + \" is in the league already.\") ^0\n else:\n while True:\n trim(input(\"starting rating (100 to 3000)> \")) => s\n if s == \"\":\n \"Cancelled.\" ^0\n return players\n number(s) => r\n if r >= 100 and r <= 3000:\n (name + \" joins on 0 points, rated \" + str(r) + \".\") ^0\n return players + [[name, 0, r]]\n \"Type a whole number from 100 to 3000.\" ^0\n\ndef odds(players):\n ask_player(players, \"player A> \") => a\n if a == -1:\n \"Cancelled.\" ^0\n return\n while True:\n ask_player(players, \"player B> \") => b\n if b == -1:\n \"Cancelled.\" ^0\n return\n if b != a:\n players[a] => pa\n players[b] => pb\n ranking.elo(pa[2], pb[2], 2, 32) => win\n ranking.elo(pa[2], pb[2], 1, 32) => draw\n ranking.elo(pa[2], pb[2], 0, 32) => loss\n (pa[0] + \" (\" + str(pa[2]) + \") is expected to score \" + percent(win[0]) + \" against \" + pb[0] + \" (\" + str(pb[2]) + \").\") ^0\n (\"For \" + pa[0] + \": a win \" + signed(win[1]) + \", a draw \" + signed(draw[1]) + \", a loss \" + signed(loss[1]) + \".\") ^0\n return\n \"A player cannot play themselves.\" ^0\n\n[\n [\"Ana\", 9, 1620],\n [\"Ben\", 7, 1555],\n [\"Chloe\", 7, 1580],\n [\"Dev\", 7, 1490],\n [\"Eli\", 4, 1450],\n [\"Fay\", 4, 1530],\n [\"Gus\", 1, 1400],\n] => players\n\n\"== Leaderboard ==\" ^0\n\"A small league: 3 points for a win, 1 each for a draw, and Elo ratings with K = 32.\" ^0\nTrue => running\nwhile running:\n \"\" ^0\n \"1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\" ^0\n trim(input(\"choice> \")) => choice\n if choice == \"1\":\n standings(players)\n elif choice == \"2\":\n game(players) => players\n elif choice == \"3\":\n odds(players)\n elif choice == \"4\":\n join(players) => players\n elif choice == \"5\":\n False => running\n else:\n \"Pick a number from 1 to 5.\" ^0\n\"Bye.\" ^0\n", "python": "import ranking\n\ndef trim(s):\n i = 0\n j = len(s)\n while i < j and s[i] == \" \":\n i = i + 1\n while j > i and s[j - 1] == \" \":\n j = j - 1\n return s[i:j]\n\ndef number(s):\n if len(s) == 0 or len(s) > 4:\n return -1\n n = 0\n for c in s:\n if not (c >= \"0\" and c <= \"9\"):\n return -1\n n = n * 10 + int(c)\n return n\n\ndef is_name(s):\n if len(s) == 0 or len(s) > 10:\n return False\n for c in s:\n if not (c >= \"a\" and c <= \"z\" or c >= \"A\" and c <= \"Z\"):\n return False\n return True\n\ndef pad(s, n):\n while len(s) < n:\n s = s + \" \"\n return s\n\ndef lpad(s, n):\n while len(s) < n:\n s = \" \" + s\n return s\n\ndef find(players, name):\n for i in range(0, len(players)):\n if players[i][0] == name:\n return i\n return -1\n\ndef signed(n):\n if n > 0:\n return \"+\" + str(n)\n return str(n)\n\ndef percent(permille):\n whole = 0\n r = permille\n while r >= 10:\n r = r - 10\n whole = whole + 1\n return str(whole) + \".\" + str(r) + \"%\"\n\ndef by_points(players):\n out = [0] * len(players)\n for i in range(0, len(players)):\n out[i] = i\n for i in range(1, len(out)):\n x = out[i]\n j = i - 1\n while j >= 0 and players[out[j]][1] < players[x][1]:\n out[j + 1] = out[j]\n j = j - 1\n out[j + 1] = x\n return out\n\ndef standings(players):\n pts = [0] * len(players)\n for i in range(0, len(players)):\n pts[i] = players[i][1]\n print(\"player points rating 1224 1334 1223 1234 fractional\")\n for i in by_points(players):\n print(pad(players[i][0], 12) + lpad(str(players[i][1]), 6) + lpad(str(players[i][2]), 8) + lpad(str(ranking.competition(pts, i)), 7) + lpad(str(ranking.modified(pts, i)), 6) + lpad(str(ranking.dense(pts, i)), 6) + lpad(str(ranking.ordinal(pts, i)), 6) + lpad(ranking.fractional(pts, i), 12))\n print(\"1224 competition: level players share the better rank, and the ranks after them are skipped.\")\n print(\"1334 modified competition: level players share the worse rank. 1223 dense: no rank is skipped.\")\n print(\"1234 ordinal: level players in the order they joined. Fractional: the average of the places they share.\")\n\ndef ask_player(players, prompt):\n while True:\n name = trim(input(prompt))\n if name == \"\":\n return -1\n i = find(players, name)\n if i >= 0:\n return i\n print(\"Nobody called \" + name + \" is in the league.\")\n\ndef game(players):\n a = ask_player(players, \"player A> \")\n if a == -1:\n print(\"Cancelled.\")\n return players\n while True:\n b = ask_player(players, \"player B> \")\n if b == -1:\n print(\"Cancelled.\")\n return players\n if b != a:\n while True:\n r = trim(input(\"result (A, B or draw)> \"))\n if r == \"\":\n print(\"Cancelled.\")\n return players\n s2 = -1\n if r == \"A\" or r == \"a\":\n s2 = 2\n elif r == \"B\" or r == \"b\":\n s2 = 0\n elif r == \"draw\":\n s2 = 1\n if s2 >= 0:\n pa = players[a]\n pb = players[b]\n e = ranking.elo(pa[2], pb[2], s2, 32)\n print(\"Before the game \" + pa[0] + \" (\" + str(pa[2]) + \") was expected to score \" + percent(e[0]) + \" against \" + pb[0] + \" (\" + str(pb[2]) + \").\")\n ga = 0\n gb = 0\n if s2 == 2:\n ga = 3\n elif s2 == 0:\n gb = 3\n else:\n ga = 1\n gb = 1\n players[a] = [pa[0], pa[1] + ga, pa[2] + e[1]]\n players[b] = [pb[0], pb[1] + gb, pb[2] - e[1]]\n print(pa[0] + \" \" + signed(e[1]) + \" to \" + str(pa[2] + e[1]) + \", \" + pb[0] + \" \" + signed(0 - e[1]) + \" to \" + str(pb[2] - e[1]) + \".\")\n return players\n print(\"Type A, B or draw.\")\n print(\"A player cannot play themselves.\")\n\ndef join(players):\n while True:\n name = trim(input(\"name> \"))\n if name == \"\":\n print(\"Cancelled.\")\n return players\n if not is_name(name):\n print(\"Type a name of letters, up to 10.\")\n elif find(players, name) >= 0:\n print(name + \" is in the league already.\")\n else:\n while True:\n s = trim(input(\"starting rating (100 to 3000)> \"))\n if s == \"\":\n print(\"Cancelled.\")\n return players\n r = number(s)\n if r >= 100 and r <= 3000:\n print(name + \" joins on 0 points, rated \" + str(r) + \".\")\n return players + [[name, 0, r]]\n print(\"Type a whole number from 100 to 3000.\")\n\ndef odds(players):\n a = ask_player(players, \"player A> \")\n if a == -1:\n print(\"Cancelled.\")\n return\n while True:\n b = ask_player(players, \"player B> \")\n if b == -1:\n print(\"Cancelled.\")\n return\n if b != a:\n pa = players[a]\n pb = players[b]\n win = ranking.elo(pa[2], pb[2], 2, 32)\n draw = ranking.elo(pa[2], pb[2], 1, 32)\n loss = ranking.elo(pa[2], pb[2], 0, 32)\n print(pa[0] + \" (\" + str(pa[2]) + \") is expected to score \" + percent(win[0]) + \" against \" + pb[0] + \" (\" + str(pb[2]) + \").\")\n print(\"For \" + pa[0] + \": a win \" + signed(win[1]) + \", a draw \" + signed(draw[1]) + \", a loss \" + signed(loss[1]) + \".\")\n return\n print(\"A player cannot play themselves.\")\n\nplayers = [[\"Ana\", 9, 1620], [\"Ben\", 7, 1555], [\"Chloe\", 7, 1580], [\"Dev\", 7, 1490], [\"Eli\", 4, 1450], [\"Fay\", 4, 1530], [\"Gus\", 1, 1400]]\nprint(\"== Leaderboard ==\")\nprint(\"A small league: 3 points for a win, 1 each for a draw, and Elo ratings with K = 32.\")\nrunning = True\nwhile running:\n print(\"\")\n print(\"1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\")\n choice = trim(input(\"choice> \"))\n if choice == \"1\":\n standings(players)\n elif choice == \"2\":\n players = game(players)\n elif choice == \"3\":\n odds(players)\n elif choice == \"4\":\n players = join(players)\n elif choice == \"5\":\n running = False\n else:\n print(\"Pick a number from 1 to 5.\")\nprint(\"Bye.\")\n" }, { "name": "ranking.eml", "eml": "# P071 leaderboard - ranking with ties five ways, and Elo ratings worked\n# out in whole numbers.\n\ndef competition(scores, i):\n # Standard competition ranking, \"1224\": 1 + how many scores are higher\n # (the corpus case rank-with-ties). Tied players share the better rank\n # and the next rank is skipped.\n 1 => r\n for s in scores:\n if s > scores[i]:\n r + 1 => r\n return r\n\ndef modified(scores, i):\n # Modified competition ranking, \"1334\": how many scores are at least\n # this one, so tied players share the worse rank.\n 0 => r\n for s in scores:\n if s >= scores[i]:\n r + 1 => r\n return r\n\ndef dense(scores, i):\n # Dense ranking, \"1223\": 1 + how many DIFFERENT scores are higher.\n {} => seen\n 1 => r\n for s in scores:\n if s > scores[i] and not s in seen:\n True => seen[s]\n r + 1 => r\n return r\n\ndef ordinal(scores, i):\n # Ordinal ranking, \"1234\": everyone a different rank; between equal\n # scores, whoever is earlier in the list comes first.\n 1 => r\n for k in [0:len(scores) - 1]:\n if scores[k] > scores[i] or (scores[k] == scores[i] and k < i):\n r + 1 => r\n return r\n\ndef fractional(scores, i):\n # Fractional ranking, \"1 2.5 2.5 4\": tied players share the average of\n # the ordinal ranks they cover - competition rank c to modified rank m,\n # so (c + m) / 2. Returned as text, since it can end in .5.\n competition(scores, i) + modified(scores, i) => t\n 0 => half\n t => left\n while left >= 2:\n left - 2 => left\n half + 1 => half\n if left == 1:\n return str(half) + \".5\"\n return str(half)\n\ndef power(b, e):\n # b ** e for whole numbers, by repeated squaring.\n 1 => out\n while e > 0:\n if e % 2 == 1:\n out * b => out\n b * b => b\n # e is a few thousand at most, far below 2^53, so the float\n # division is exact\n int((e - e % 2) / 2) => e\n return out\n\ndef tenth_power_scaled(r):\n # floor(10^(12 + r/400)) for 0 <= r < 400, exactly: the whole number y\n # with y^400 <= 10^(4800 + r) < (y + 1)^400, found by halving the range\n # 10^12 to 10^13.\n power(10, 4800 + r) => target\n power(10, 12) => lo\n power(10, 13) => hi\n while hi - lo > 1:\n # lo + hi < 2 x 10^13, below 2^53: halving it as a float is exact\n int((lo + hi - (lo + hi) % 2) / 2) => mid\n if power(mid, 400) <= target:\n mid => lo\n else:\n mid => hi\n return lo\n\ndef ten_to(d):\n # 10^(d/400) x 10^12 for a whole d >= 0, to 12 digits: d = 400 k + r.\n 0 => k\n d => r\n while r >= 400:\n r - 400 => r\n k + 1 => k\n return tenth_power_scaled(r) * power(10, k)\n\ndef rounded(n, d):\n # n / d to the nearest whole number, halves away from zero (d > 0).\n 0 => q\n if n < 0:\n return 0 - rounded(0 - n, d)\n 2 * n + d => a\n 2 * d => b\n while a >= b:\n b => m\n 1 => k\n while m + m <= a:\n m + m => m\n k + k => k\n a - m => a\n q + k => q\n return q\n\ndef elo(ra, rb, score2, k):\n # A rated ra plays B rated rb; score2 is A's score doubled (2 win, 1\n # draw, 0 loss). A's expected score is E = 1 / (1 + 10^((rb - ra)/400)),\n # and A's rating moves by k x (score - E), B's by the opposite.\n # Returns [A's expected score in tenths of a percent, A's change].\n if rb < ra:\n elo(rb, ra, 2 - score2, k) => back\n return [1000 - back[0], 0 - back[1]]\n power(10, 12) => one\n ten_to(rb - ra) => x\n # E = one / (one + x); change = k (score2 / 2 - E)\n rounded(1000 * one, one + x) => permille\n rounded(k * (score2 * (one + x) - 2 * one), 2 * (one + x)) => change\n return [permille, change]\n", "python": "def competition(scores, i):\n r = 1\n for s in scores:\n if s > scores[i]:\n r = r + 1\n return r\n\ndef modified(scores, i):\n r = 0\n for s in scores:\n if s >= scores[i]:\n r = r + 1\n return r\n\ndef dense(scores, i):\n seen = {}\n r = 1\n for s in scores:\n if s > scores[i] and not s in seen:\n seen[s] = True\n r = r + 1\n return r\n\ndef ordinal(scores, i):\n r = 1\n for k in range(0, len(scores)):\n if scores[k] > scores[i] or scores[k] == scores[i] and k < i:\n r = r + 1\n return r\n\ndef fractional(scores, i):\n t = competition(scores, i) + modified(scores, i)\n half = 0\n left = t\n while left >= 2:\n left = left - 2\n half = half + 1\n if left == 1:\n return str(half) + \".5\"\n return str(half)\n\ndef power(b, e):\n out = 1\n while e > 0:\n if e % 2 == 1:\n out = out * b\n b = b * b\n e = int((e - e % 2) / 2)\n return out\n\ndef tenth_power_scaled(r):\n target = power(10, 4800 + r)\n lo = power(10, 12)\n hi = power(10, 13)\n while hi - lo > 1:\n mid = int((lo + hi - (lo + hi) % 2) / 2)\n if power(mid, 400) <= target:\n lo = mid\n else:\n hi = mid\n return lo\n\ndef ten_to(d):\n k = 0\n r = d\n while r >= 400:\n r = r - 400\n k = k + 1\n return tenth_power_scaled(r) * power(10, k)\n\ndef rounded(n, d):\n q = 0\n if n < 0:\n return 0 - rounded(0 - n, d)\n a = 2 * n + d\n b = 2 * d\n while a >= b:\n m = b\n k = 1\n while m + m <= a:\n m = m + m\n k = k + k\n a = a - m\n q = q + k\n return q\n\ndef elo(ra, rb, score2, k):\n if rb < ra:\n back = elo(rb, ra, 2 - score2, k)\n return [1000 - back[0], 0 - back[1]]\n one = power(10, 12)\n x = ten_to(rb - ra)\n permille = rounded(1000 * one, one + x)\n change = rounded(k * (score2 * (one + x) - 2 * one), 2 * (one + x))\n return [permille, change]\n" } ], "sessions": [ { "name": "bad-input", "input": "0\nx\n2\nZed\nAna\nAna\nBen\nwin\n\n4\nAna\nAna Lee\nKim\n50\n3001\nabc\n\n3\n\n5\n", "screen": "== Leaderboard ==\nA small league: 3 points for a win, 1 each for a draw, and Elo ratings with K = 32.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 0\nPick a number from 1 to 5.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> x\nPick a number from 1 to 5.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 2\nplayer A> Zed\nNobody called Zed is in the league.\nplayer A> Ana\nplayer B> Ana\nA player cannot play themselves.\nplayer B> Ben\nresult (A, B or draw)> win\nType A, B or draw.\nresult (A, B or draw)> \nCancelled.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 4\nname> Ana\nAna is in the league already.\nname> Ana Lee\nType a name of letters, up to 10.\nname> Kim\nstarting rating (100 to 3000)> 50\nType a whole number from 100 to 3000.\nstarting rating (100 to 3000)> 3001\nType a whole number from 100 to 3000.\nstarting rating (100 to 3000)> abc\nType a whole number from 100 to 3000.\nstarting rating (100 to 3000)> \nCancelled.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 3\nplayer A> \nCancelled.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 5\nBye.\n", "interpreter": "equal" }, { "name": "basic", "input": "1\n3\nAna\nGus\n2\nDev\nAna\nA\n2\nBen\nChloe\ndraw\n1\n4\nHana\n1500\n3\nHana\nAna\n5\n", "screen": "== Leaderboard ==\nA small league: 3 points for a win, 1 each for a draw, and Elo ratings with K = 32.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 1\nplayer points rating 1224 1334 1223 1234 fractional\nAna 9 1620 1 1 1 1 1\nBen 7 1555 2 4 2 2 3\nChloe 7 1580 2 4 2 3 3\nDev 7 1490 2 4 2 4 3\nEli 4 1450 5 6 3 5 5.5\nFay 4 1530 5 6 3 6 5.5\nGus 1 1400 7 7 4 7 7\n1224 competition: level players share the better rank, and the ranks after them are skipped.\n1334 modified competition: level players share the worse rank. 1223 dense: no rank is skipped.\n1234 ordinal: level players in the order they joined. Fractional: the average of the places they share.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 3\nplayer A> Ana\nplayer B> Gus\nAna (1620) is expected to score 78.0% against Gus (1400).\nFor Ana: a win +7, a draw -9, a loss -25.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 2\nplayer A> Dev\nplayer B> Ana\nresult (A, B or draw)> A\nBefore the game Dev (1490) was expected to score 32.1% against Ana (1620).\nDev +22 to 1512, Ana -22 to 1598.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 2\nplayer A> Ben\nplayer B> Chloe\nresult (A, B or draw)> draw\nBefore the game Ben (1555) was expected to score 46.4% against Chloe (1580).\nBen +1 to 1556, Chloe -1 to 1579.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 1\nplayer points rating 1224 1334 1223 1234 fractional\nDev 10 1512 1 1 1 1 1\nAna 9 1598 2 2 2 2 2\nBen 8 1556 3 4 3 3 3.5\nChloe 8 1579 3 4 3 4 3.5\nEli 4 1450 5 6 4 5 5.5\nFay 4 1530 5 6 4 6 5.5\nGus 1 1400 7 7 5 7 7\n1224 competition: level players share the better rank, and the ranks after them are skipped.\n1334 modified competition: level players share the worse rank. 1223 dense: no rank is skipped.\n1234 ordinal: level players in the order they joined. Fractional: the average of the places they share.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 4\nname> Hana\nstarting rating (100 to 3000)> 1500\nHana joins on 0 points, rated 1500.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 3\nplayer A> Hana\nplayer B> Ana\nHana (1500) is expected to score 36.3% against Ana (1598).\nFor Hana: a win +20, a draw +4, a loss -12.\n\n1) standings 2) record a game 3) what a game is worth 4) new player 5) quit\nchoice> 5\nBye.\n", "interpreter": "equal" } ], "builtOn": [ { "slug": "rank-with-ties", "caseId": "122-rank-with-ties", "title": "Ranking with ties" } ], "updated": "2026-10-14" }