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Version 2 Algorithm Analysis #5

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Necessary Libraries and Constants"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#https://www.youtube.com/watch?v=F1HA7e3acSI\n",
"#https://www.bustabit.com/play\n",
"#https://bitcointalk.org/index.php?topic=2807542.0\n",
"#https://jsfiddle.net/Dexon95/2fmuxLza/"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import hashlib\n",
"import random\n",
"import string\n",
"import hmac\n",
"import math\n",
"import codecs\n",
"\n",
"# https://www.blockchain.com/btc/block/0000000000000000004d6ec16dafe9d8370958664c1dc422f452892264c59526\n",
"salt505750 = \"0000000000000000004d6ec16dafe9d8370958664c1dc422f452892264c59526\"\n",
"SALT = salt505750"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Get Result and Get Previous Game Function"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"results = [('319aa8124bbcddac2bae8438cfd5e658aeca56d524736739622dfb0a09942b22', 159.93),\n",
"('c64559640b124fa354eaaee31510eaa0f1a5fdd5aa004363b95693e52d274d28',2.36),\n",
"('c263a30ad8820e8c3d46f9a5db3c34d3b081cd349a11367a9fbd52063f17cd34',1.31),\n",
"('a6bb64e83b8efa52524ba526cd036ae17c3ec00b9fbec49b8cd4dc1321d7b4ce',1.09),\n",
"('17612b37d97f0faf0930762a328ab383bd2e107c5cc5c975cc76405f41a4bbc2',1.43)]\n",
"\n",
"\n",
"def get_prev_game(hash_code):\n",
" m = hashlib.sha256()\n",
" m.update(hash_code.encode(\"utf-8\"))\n",
" return m.hexdigest()\n",
"for i in range(len(results)-1):\n",
" assert get_prev_game(results[i][0]) == results[i+1][0]\n",
"print(\"get_prev_game passed\")\n",
"\n",
"def get_result(seed, salt=SALT):\n",
" salt = salt.encode(\"utf8\")\n",
" seed = codecs.decode(bytes(seed, \"utf8\"), \"hex\") #https://tinyurl.com/2bf4dann\n",
" hm = hmac.new(salt, seed, hashlib.sha256)\n",
" h = hm.hexdigest()\n",
" \n",
" r = int(h[:13], 16) # 52 most significant bits as int\n",
" x = r / 2**52 # [0,1)\n",
" x = 99 / (1-x) # [99.0, 4.458563631096791e+17]\n",
" result = math.floor(x) # [99, 445856363109679104]\n",
" return (max(1, result/100))\n",
" \n",
"for res in results[:]: \n",
" assert getResult(res[0]) == res[1], print(f\"\\n\\n{res}: {getResult(res[0])}\")\n",
"print(\"get_result passed\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def sim(numerator=99):\n",
" results = []\n",
" for x in range(0,1000):\n",
" x = x/1000 # [0,0.999]\n",
" x = numerator/(1-x) # [99, 99/(0.001) 99,000]\n",
" result = math.floor(x) # [99, 99000]\n",
" answer = max(1, result/100) # [1, 990]\n",
" results.append(answer)\n",
" return results\n",
" \n",
"game = sim()\n",
"fair = sim(100)\n",
"\n",
"print(\"game\", min(game), sum(game)/len(game), max(game))\n",
"print(\"fair?\", min(fair), sum(fair)/len(fair), max(fair))\n",
"\n",
"if False:\n",
" for g in game:\n",
" print(g)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Collecting All Game Results"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"game_hash = '4fc2f264ea3e0bbf8405f74f0bf354bef946283d6023352f5f8d441d6aaad861' # 29oct2021 Update to latest game's hash for more results\n",
"first_game = \"86728f5fc3bd99db94d3cdaf105d67788194e9701bf95d049ad0e1ee3d004277\" #https://bitcointalk.org/index.php?topic=2807542.0\n",
"\n",
"results = []\n",
"count = 0\n",
"while game_hash != first_game:\n",
" count += 1\n",
" results.append(get_result(game_hash))\n",
" game_hash = get_prev_game(game_hash)\n",
" \n",
"results = np.array(results)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"print(count)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Testing Probability Formula"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# What's the analytical EV of this new algorithm? "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Testing Expected Value Formula"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#realized results from start of game to now \n",
"#confirms a 1% house edge\n",
"multiplier = 1.7\n",
"(results < multiplier).mean() * -1 + (multiplier - 1)*(results >= multiplier).mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualizations"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import seaborn as sns\n",
"sns.set(rc={'figure.figsize':(11.7,8.27)})\n",
"\n",
"plt.hist(results, range=(0, 25))\n",
"plt.title(\"Histogram of Game Results\", fontsize=20)\n",
"plt.xticks(fontsize=15)\n",
"plt.yticks(fontsize=15)\n",
"plt.ylabel(\"Number of Games\", fontsize=15)\n",
"plt.xlabel(\"Multiplier\", fontsize=15)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def calculate_ev(multiplier):\n",
" # This is for the version 1 algorithm, not the version 2.\n",
" return ((1/33) + (32/33)*(.01 + .99*(1 - 1/(multiplier-.01))))*-1 + (multiplier-1)*(1 - ((1/33) + (32/33)*(.01 + .99*(1 - 1/(multiplier-.01)))))\n",
"\n",
"xs = np.linspace(101, 1001, 901) / 100\n",
"ys = [calculate_ev(x) for x in xs]\n",
"y2s = [(results < x).mean() * -1 + (x - 1)*(results >= x).mean() for x in xs]\n",
"\n",
"plt.plot(xs, ys, linewidth=5)\n",
"plt.xlabel(\"Multiplier\", fontsize=15)\n",
"plt.ylabel(\"Expected Value\", fontsize=15)\n",
"plt.xticks(fontsize=15)\n",
"plt.yticks(fontsize=15)\n",
"plt.ylim(-.045, -.000)\n",
"plt.plot(xs, y2s, linewidth=3)\n",
"plt.title(\"Expected Value by Multiplier\", fontsize=20)\n",
"plt.legend([\"(error) Theoretical Results\", \"Actual Results\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Martingale Test"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"negatives = []\n",
"in_a_row = 0\n",
"for multiplier in results:\n",
" if multiplier < 2:\n",
" in_a_row += 1\n",
" else:\n",
" in_a_row = 0\n",
" negatives.append(in_a_row)\n",
"negatives = np.array(negatives)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"for i in range(1, 14):\n",
" print(\"Probability of Losing %d Game(s) in a Row:\"%i, (negatives >= i).mean())"
]
}
],
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