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stackdump/tic-tac-toe-expert-system.ipynb

Created December 31, 2024 13:44
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use tic-tac-toe petri-net model to predict win probability
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tic-tac-toe-expert-system.ipynb
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"source": [
"using Petri\n",
"using LabelledArrays\n",
"using Plots\n",
"using OrdinaryDiffEq\n",
"using Accessors\n",
"\n",
"# Define the states (places in Petri net)\n",
"states = [\n",
" :P10, :P11, :P12, :P20, :P21, :P22, :P00, :P01, :P02, :Next,\n",
" :X00, :X01, :X02, :X10, :X11, :X12, :X20, :X21, :X22,\n",
" :O00, :O01, :O02, :O10, :O11, :O12, :O20, :O21, :O22,\n",
" :win_x, :win_o\n",
"]\n",
"\n",
"# get the index of win_x and win_o for plotting\n",
"win_x_index = findfirst(x -> x == :win_x, states)\n",
"\n",
"# Define the transitions (steps in Petri net)\n",
"transitions = LVector(\n",
" X00=(LVector(P00=1), LVector(Next=1, X00=1)),\n",
" X01=(LVector(P01=1), LVector(Next=1, X01=1)),\n",
" X02=(LVector(P02=1), LVector(Next=1, X02=1)),\n",
" X10=(LVector(P10=1), LVector(Next=1, X10=1)),\n",
" X11=(LVector(P11=1), LVector(Next=1, X11=1)),\n",
" X12=(LVector(P12=1), LVector(Next=1, X12=1)),\n",
" X20=(LVector(P20=1), LVector(Next=1, X20=1)),\n",
" X21=(LVector(P21=1), LVector(Next=1, X21=1)),\n",
" X22=(LVector(P22=1), LVector(Next=1, X22=1)),\n",
" O00=(LVector(P00=1, Next=1), LVector(O00=1)),\n",
" O01=(LVector(P01=1, Next=1), LVector(O01=1)),\n",
" O02=(LVector(P02=1, Next=1), LVector(O02=1)),\n",
" O10=(LVector(P10=1, Next=1), LVector(O10=1)),\n",
" O11=(LVector(P11=1, Next=1), LVector(O11=1)),\n",
" O12=(LVector(P12=1, Next=1), LVector(O12=1)),\n",
" O20=(LVector(P20=1, Next=1), LVector(O20=1)),\n",
" O21=(LVector(P21=1, Next=1), LVector(O21=1)),\n",
" O22=(LVector(P22=1, Next=1), LVector(O22=1)),\n",
" X00_X01_X02=(LVector(X00=1, X01=1, X02=1), LVector(win_x=1)),\n",
" X10_X11_X12=(LVector(X10=1, X11=1, X12=1), LVector(win_x=1)),\n",
" X20_X21_X22=(LVector(X20=1, X21=1, X22=1), LVector(win_x=1)),\n",
" X00_X10_X20=(LVector(X00=1, X10=1, X20=1), LVector(win_x=1)),\n",
" X01_X11_X21=(LVector(X01=1, X11=1, X21=1), LVector(win_x=1)),\n",
" X02_X12_X22=(LVector(X02=1, X12=1, X22=1), LVector(win_x=1)),\n",
" X00_X11_X22=(LVector(X00=1, X11=1, X22=1), LVector(win_x=1)),\n",
" X20_X11_X02=(LVector(X20=1, X11=1, X02=1), LVector(win_x=1)),\n",
" O00_O01_O02=(LVector(O00=1, O01=1, O02=1), LVector(win_o=1)),\n",
" O10_O11_O12=(LVector(O10=1, O11=1, O12=1), LVector(win_o=1)),\n",
" O20_O21_O22=(LVector(O20=1, O21=1, O22=1), LVector(win_o=1)),\n",
" O00_O10_O20=(LVector(O00=1, O10=1, O20=1), LVector(win_o=1)),\n",
" O01_O11_O21=(LVector(O01=1, O11=1, O21=1), LVector(win_o=1)),\n",
" O02_O12_O22=(LVector(O02=1, O12=1, O22=1), LVector(win_o=1)),\n",
" O00_O11_O22=(LVector(O00=1, O11=1, O22=1), LVector(win_o=1)),\n",
" O20_O11_O02=(LVector(O20=1, O11=1, O02=1), LVector(win_o=1))\n",
")\n",
"\n",
"# Create the Petri net model\n",
"petri_net = Petri.Model(states, transitions)\n",
"\n",
"# Plot the Petri net graph\n",
"graph = Graph(petri_net)\n",
"\n",
"# Display graphviz graph\n",
"display(graph)\n"
]
},
{
"cell_type": "code",
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"id": "6dc66ca7-c4b7-47bb-8e0e-77ea9881b441",
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"data": {
"text/plain": [
"show_ranked_board (generic function with 1 method)"
]
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"source": [
"\n",
"# Define the time span\n",
"tspan = (0.0, 9.0)\n",
"\n",
"# Define the simulation parameters\n",
"rates = LVector(\n",
" X00=1.0, X01=1.0, X02=1.0,\n",
" X10=1.0, X11=1.0, X12=1.0,\n",
" X20=1.0, X21=1.0, X22=1.0,\n",
" O00=1.0, O01=1.0, O02=1.0,\n",
" O10=1.0, O11=1.0, O12=1.0,\n",
" O20=1.0, O21=1.0, O22=1.0,\n",
" X00_X01_X02=1.0, X10_X11_X12=1.0, X20_X21_X22=1.0,\n",
" X00_X10_X20=1.0, X01_X11_X21=1.0, X02_X12_X22=1.0,\n",
" X00_X11_X22=1.0, X20_X11_X02=1.0,\n",
" O00_O01_O02=1.0, O10_O11_O12=1.0, O20_O21_O22=1.0,\n",
" O00_O10_O20=1.0, O01_O11_O21=1.0, O02_O12_O22=1.0,\n",
" O00_O11_O22=1.0, O20_O11_O02=1.0\n",
")\n",
"\n",
"function solution(input_tuple)\n",
" prob = ODEProblem(petri_net, LVector(input_tuple), tspan, rates)\n",
" sol = solve(prob, Tsit5())\n",
" return sol\n",
"end\n",
"\n",
"function heuristic(input_tuple)\n",
" # Convert the input tuple to a LabelledArray\n",
" sol = solution(input_tuple)\n",
" # Extract win probabilities at a specific time\n",
" time = sol.t\n",
" win_x = sol[win_x_index, :]\n",
" #win_o = sol[28, :]\n",
" index_time = findfirst(t -> t >= 9, time) # Example: t = 9\n",
" win_x_t = win_x[index_time]\n",
" # REVIEW: assume expert system is always X\n",
" # win_o_t = win_o[index_time] \n",
" \n",
" # Return a heuristic score with 3 decimal places\n",
" return round(win_x_t, digits=3)\n",
"end\n",
"\n",
"function apply_move(previous_state, input)\n",
" u1 = deepcopy(previous_state)\n",
" p_key = Symbol(\"P\" * string(input)[2:end])\n",
" move_key = previous_state[:Next] == 0 ? :X : :O\n",
" move_symbol = Symbol(string(move_key) * string(input)[2:end])\n",
" u1 = @set u1[move_symbol] = 1\n",
" u1 = @set u1[p_key] = 0\n",
" u1 = @set u1[:Next] = previous_state[:Next] == 0 ? 1 : 0\n",
" #println(\"------------------- Move: \", input, \" -------------------\")\n",
" #println(u1)\n",
" return u1\n",
"end\n",
"\n",
"function compare_move_outcomes(previous_state)\n",
" # Define the possible moves\n",
" #moves = [:P00, :P01, :P02, :P10, :P11, :P12, :P20, :P21, :P22]\n",
" moves = [:P00, :P01, :P11]\n",
"\n",
" move_labels = Dict(\n",
" :P00 => \"Top Left\",\n",
" :P01 => \"Top Middle\",\n",
" :P02 => \"Top Right\",\n",
" :P10 => \"Middle Left\",\n",
" :P11 => \"Middle Middle\",\n",
" :P12 => \"Middle Right\",\n",
" :P20 => \"Bottom Left\",\n",
" :P21 => \"Bottom Middle\",\n",
" :P22 => \"Bottom Right\"\n",
" )\n",
" \n",
" # Evaluate the heuristic for each possible move\n",
" plot( # Create a plot to compare the outcomes\n",
" legend=:none,\n",
" xlabel=\"Time\",\n",
" ylabel=\"Win Probability\",\n",
" title=\"Value Of First Move\"\n",
" )\n",
"\n",
" for move in moves\n",
" u1 = apply_move(previous_state, move)\n",
" sol = solution(u1)\n",
" time = sol.t\n",
" win_x = sol[win_x_index, :]\n",
" plot!(time, win_x, label=string(move))\n",
" annotate!([(7.2, win_x[end], text(string(heuristic(u1)), 9, 0.4, :left))])\n",
" annotate!([(8, win_x[end], text(move_labels[move], 9, 0.5, :left))])\n",
"\n",
" end\n",
"end\n",
"\n",
"function show_ranked_board(previous_state)\n",
" # Define the possible moves\n",
" moves = [:P00, :P01, :P02, :P10, :P11, :P12, :P20, :P21, :P22]\n",
" \n",
" # Evaluate the heuristic for each possible move\n",
" scores = Dict()\n",
" for move in moves\n",
" u1 = apply_move(previous_state, move)\n",
" score = heuristic(u1)\n",
" scores[move] = score\n",
" end\n",
"\n",
" println(\" -------- Scores -------\")\n",
" # format scores as the tic-tac-toe board\n",
" # display as ascii art of the game\n",
" board = \"\"\"\n",
" | $(scores[:P00]) | $(scores[:P01]) | $(scores[:P02]) |\n",
" | $(scores[:P10]) | $(scores[:P11]) | $(scores[:P12]) |\n",
" | $(scores[:P20]) | $(scores[:P21]) | $(scores[:P22]) |\n",
" \"\"\"\n",
" println(board)\n",
"end"
]
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"id": "e68fc9d1-104d-4116-8b5c-5e60b55e735b",
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{
"name": "stdout",
"output_type": "stream",
"text": [
" -------- Scores -------\n",
"| 1.146 | 1.082 | 1.146 |\n",
"| 1.082 | 1.228 | 1.082 |\n",
"| 1.146 | 1.082 | 1.146 |\n",
"\n"
]
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]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Test the expert system - initial state\n",
"u0 = (\n",
" P10=1, P11=1, P12=1, P20=1, P21=1, P22=1, P00=1, P01=1, P02=1, Next=0,\n",
" X00=0, X01=0, X02=0, X10=0, X11=0, X12=0, X20=0, X21=0, X22=0,\n",
" O00=0, O01=0, O02=0, O10=0, O11=0, O12=0, O20=0, O21=0, O22=0,\n",
" win_x=0, win_o=0\n",
")\n",
"\n",
"compare_move_outcomes(u0)\n",
"show_ranked_board(u0)\n",
"plot!()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "21b4698e-2b1e-484e-acd6-b143378cf161",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.11.2",
"language": "julia",
"name": "julia-1.11"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
@stackdump
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Try running the petri-net model yourself on pflow.xyz

pflow

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