From 33aadd333edb381efdc19eec490482c8bf92d991 Mon Sep 17 00:00:00 2001
From: tim <timolsoncrypto@gmail.com>
Date: Fri, 24 Oct 2025 01:17:40 -0400
Subject: [PATCH] pool_design.py

---
 research/pool_design.py | 67 ++++++++++++++++++++++++++++++++---------
 1 file changed, 53 insertions(+), 14 deletions(-)

diff --git a/research/pool_design.py b/research/pool_design.py
index c470f80..22a01e2 100644
--- a/research/pool_design.py
+++ b/research/pool_design.py
@@ -8,6 +8,18 @@ import numpy as np
 log = logging.getLogger(__name__)
 
 
+UNISWAP_GAS=115_000
+LMSR_GAS=119_000
+ETH_PRICE=4500
+UNISWAP_GAS_COST=UNISWAP_GAS*ETH_PRICE/1e9
+LMSR_GAS_COST=LMSR_GAS*ETH_PRICE/1e9
+
+LMSR_FEE = 0.000010
+
+print(f'   LMSR gas: ${LMSR_GAS_COST:.2}')
+print(f'Uniswap gas: ${UNISWAP_GAS_COST:.2}')
+
+
 def lmsr_swap_amount_out(
     balances,
     amount_in,
@@ -127,36 +139,63 @@ def lmsr_swap_amount_out(
     return float(amount_out)
 
 
-def main():
-    balance0 = 1_000_000  # estimated from the production pool
+def compare():
+    kappa = 10
+    balance0 = 10_000_000  # estimated from the production pool
     balances = [balance0, balance0]
     X = np.geomspace(1, 10_000_000, 100)
-    Y = [1 -
-         lmsr_swap_amount_out(balances, float(amount_in), 0, 1, 0.000010, 0.8)
-         / amount_in
+    Y = [max(0, 1 -
+             (lmsr_swap_amount_out(balances, float(amount_in), 0, 1, LMSR_FEE, kappa) - LMSR_GAS_COST)
+             / amount_in)
          for amount_in in X]
-    plt.plot(X / balance0, Y, label='LMSR')
+    plt.plot(X, Y, label=f'LMSR {kappa:.2f}')
 
     d = pd.read_csv('swap_results_block_23640998.csv')
     d.columns = ['block', 'price0', 'price1', 'in0', 'out0', 'in1', 'out1']
-    uniswap_slippage = 1 - d.out0 / d.in0 / d.iloc[0].price0
-    plt.plot(d.in0 / balance0, uniswap_slippage, label='CP')
+    uniswap_slippage0 = 1 - (d.out0 - UNISWAP_GAS_COST) / d.in0 / d.iloc[0].price0
+    plt.plot(d.in0, uniswap_slippage0, label='CP0')
+    # uniswap_slippage1 = 1 - (d.out1 - UNISWAP_GAS_COST) / d.in1 / d.iloc[0].price1
+    # plt.plot(d.in1, uniswap_slippage1, label='CP1')
 
     # Interpolate Uniswap slippage to match LMSR x-coordinates
-    interp_uniswap = np.interp(X / balance0, d.in0 / balance0, uniswap_slippage)
+    interp_uniswap = np.interp(X, d.in0, uniswap_slippage0)
     mask = Y < interp_uniswap
-    plt.fill_between(X / balance0, 0, 1, where=mask, alpha=0.2, color='green')
+    plt.fill_between(X, 0, 1, where=mask, alpha=0.2, color='green')
 
     plt.xscale('log')
     plt.yscale('log')
-    plt.gca().xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: '{:.2f}'.format(10000*x)))
-    plt.gca().yaxis.set_major_formatter(plt.FuncFormatter(lambda y, _: '{:.2f}%'.format(y)))
-    plt.xlabel('Input Amount (basis points of initial balance)')
+    plt.gca().xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: '{:g}'.format(x)))
+    plt.gca().yaxis.set_major_formatter(plt.FuncFormatter(lambda y, _: '{:.2%}'.format(y)))
+    plt.xlabel('Input Amount')
     plt.ylabel('Slippage')
     plt.title('Pool Slippages')
     plt.grid(True)
     plt.legend()
     plt.show()
 
+
+def plot_kappa():
+    X = np.geomspace(1, 10_000_000, 100)
+    for kappa in np.geomspace(0.01, 100, 8):
+        balance0 = 1_000_000  # estimated from the production pool
+        balances = [balance0, balance0]
+        Y = [1 -
+             lmsr_swap_amount_out(balances, float(amount_in), 0, 1, 0.000010, kappa)
+             / amount_in
+             for amount_in in X]
+        plt.plot(X / balance0, Y, label=f'{kappa:f}')
+    plt.xscale('log')
+    plt.yscale('log')
+    plt.gca().xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: '{:.2f}'.format(10000*x)))
+    plt.gca().yaxis.set_major_formatter(plt.FuncFormatter(lambda y, _: '{:.2%}'.format(y)))
+    plt.xlabel('Input Amount (basis points of initial balance)')
+    plt.ylabel('Slippage')
+    plt.title('Pool Slippages by Kappa')
+    plt.grid(True)
+    plt.legend()
+    plt.show()
+
+
 if __name__ == '__main__':
-    main()
+    compare()
+    # plot_kappa()