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@t-flora
Created November 1, 2020 18:35
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Naive exploration of the coin challenge
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Task 1\n",
"\n",
"My betting strategy to maximize the amount of money I get after 20 bets is to:\n",
"\n",
"- Partition 60% of the money (\\\\$150 at first) and bet on heads\n",
"- Bet the remaining 40% (\\\\$100 at first) on tails (if that's allowed)\n",
"\n",
"If we can't bet for both outcomes in the next time step, then I would:\n",
"\n",
"- Always bet 40% of the money I have in the purse on heads.\n",
"\n",
"This strategy would be a good way to make positive returns likely, if not maximize them, by each round limiting the maximum downside to 40% of your funds. Those are the odds of losing, and if we can partition money indefinitely (which we wouldn't in the real world), then we will never be ruined, even if hinging on a technicality."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Task 2\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"95.224"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"forty_perc = lambda money: 0.4*money\n",
"\n",
"forty_perc(238.06)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image('9.1PCW_Strategy.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Task 3"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"class CoinGame:\n",
" def __init__(self, bias = 0.6, n_bets = 20, starting_amount = 250):\n",
" self.bias = bias\n",
" self.n_bets = n_bets\n",
" self.wallet = starting_amount\n",
" self.history = [starting_amount]\n",
" \n",
" def run(self, bet_rate = 0.4):\n",
" bet_amount = bet_rate*self.wallet\n",
" for bet in range(self.n_bets):\n",
" \n",
" bet_amount = bet_rate*self.wallet\n",
" \n",
" if self.wallet == 0:\n",
" break\n",
" if np.random.random() <= self.bias:\n",
" self.wallet += 2*bet_amount\n",
" self.history.append(self.wallet)\n",
" else:\n",
" self.wallet -= bet_amount\n",
" self.history.append(self.wallet)\n",
" return self.wallet, self.history"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"64415.97293184987"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n_trials = 10000\n",
"\n",
"bet_results = [CoinGame().run(bet_rate = 0.4)[0] for _ in range(n_trials)]\n",
"np.mean(bet_results)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The 95% confidence interval over the amount of money at the end\n",
"of 20 bets using my strategy is [5.99701388e+01 3.93464081e+05]\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"percentiles = np.percentile(bet_results, [2.5, 97.5])\n",
"print(f'The 95% confidence interval over the amount of money at the end\\nof 20 bets using my strategy is {percentiles}')\n",
"\n",
"logged_res = np.log10(bet_results)\n",
"plt.hist(logged_res)\n",
"# plt.xlim(percentiles)\n",
"plt.xlabel('Log of money in wallet after 20 bets')\n",
"plt.ylabel('Count')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[250,\n",
" 450.0,\n",
" 810.0,\n",
" 1458.0,\n",
" 874.8,\n",
" 1574.6399999999999,\n",
" 2834.352,\n",
" 1700.6111999999998,\n",
" 1020.3667199999999,\n",
" 612.220032,\n",
" 1101.9960575999999,\n",
" 1983.5929036799998,\n",
" 1190.155742208,\n",
" 2142.2803359744003,\n",
" 3856.1046047539203,\n",
" 6940.988288557057,\n",
" 12493.778919402703,\n",
" 7496.267351641622,\n",
" 13493.28123295492,\n",
" 8095.968739772951,\n",
" 14572.743731591312]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"CoinGame().run()[1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Based on these results, I am not convinced mine is a good strategy. For being proportional, a player will never lose everything, and some runs yield extraordinary returns; alas, those would probably have been achieved regardless of the strategy applied."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"604821.2000515601"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bet_results_alt = [CoinGame().run(bet_rate = 0.6)[0] for _ in range(n_trials)]\n",
"np.mean(bet_results_alt)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The 95% confidence interval over the amount of money at the end\n",
"of 20 bets using a 60% bet-rate strategy is [2.30166096e+00 1.92727136e+06]\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"percentiles = np.percentile(bet_results_alt, [2.5, 97.5])\n",
"print(f'The 95% confidence interval over the amount of money at the end\\nof 20 bets using a 60% bet-rate strategy is {percentiles}')\n",
"\n",
"logged_res_alt = np.log10(bet_results_alt)\n",
"plt.hist(logged_res_alt)\n",
"# plt.xlim(percentiles)\n",
"plt.xlabel('Log of money in wallet after 20 bets')\n",
"plt.ylabel('Count')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"199748.13484649657"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bet_results_alt2 = [CoinGame().run(bet_rate = 0.5)[0] for _ in range(n_trials)]\n",
"np.mean(bet_results_alt2)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The 95% confidence interval over the amount of money at the end\n",
"of 20 bets using a 50% bet-rate strategy is [1.5625e+01 1.0240e+06]\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"percentiles = np.percentile(bet_results_alt2, [2.5, 97.5])\n",
"print(f'The 95% confidence interval over the amount of money at the end\\nof 20 bets using a 50% bet-rate strategy is {percentiles}')\n",
"\n",
"logged_res_alt2 = np.log10(bet_results_alt2)\n",
"plt.hist(logged_res_alt2)\n",
"# plt.xlim(percentiles)\n",
"plt.xlabel('Log of money in wallet after 20 bets')\n",
"plt.ylabel('Count')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"rates = np.linspace(0.05, 0.95, 19)\n",
"mean_returns = []\n",
"\n",
"for rate in rates:\n",
" bet_results_rates = [CoinGame().run(bet_rate = rate)[0] for _ in range(n_trials)]\n",
" mean_returns.append(np.mean(bet_results_rates))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(rates, mean_returns)\n",
"plt.ylabel('Mean returns for 10000 trials')\n",
"plt.xlabel('Betting rate')\n",
"plt.xticks(rates[::3])\n",
"plt.show()"
]
}
],
"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": "3.7.8"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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