seed 20260821, edge 1%
  target       rounds  win rate   theory   EV/bet  longest lose streak
    1.01    2,000,000  98.0236% 98.0198% -0.9962%                    3
     1.1    2,000,000  90.0042% 90.0000% -0.9954%                    7
     1.5    2,000,000  66.0062% 66.0000% -0.9907%                   12
       2    2,000,000  49.5052% 49.5000% -0.9896%                   23
       3    2,000,000  33.0755% 33.0000% -0.7737%                   37
       5    2,000,000  19.7944% 19.8000% -1.0280%                   54
      10    2,000,000   9.8864%  9.9000% -1.1355%                  114
      20    2,000,000   4.9694%  4.9500% -0.6130%                  237
      50    2,000,000   1.9706%  1.9800% -1.4725%                  639
     100   20,000,000   0.9880%  0.9900% -1.1955%                 1331
    1000   20,000,000   0.0979%  0.0990% -2.0550%                 8940

$100 bankroll, $1 flat bets, cap 2,000 rounds — 50,000 sessions per target
  target busted<cap  median rounds (busted only)  alive@500  alive@2000  ever 2x bank
     1.5       1.1%                         1777     100.0%       98.9%         0.01%
       2       6.3%                         1592     100.0%       93.7%         0.91%
       5      32.8%                       1120.0      97.3%       67.2%        20.74%
      10      50.3%                          790      86.4%       49.7%        37.39%
     100      83.0%                          200      36.8%       17.0%        41.39%

Martingale at 2x target: $1 base, double after loss, $100 bankroll, 500-round sessions x 100,000
  wiped out (cannot cover next doubled bet): 85.55%
  finishers: 14.45%, median end balance $352.00

rounds until a multiplier first appears (10,000 trials each)
  >=    10x: median 7.0 rounds, mean 10
  >=   100x: median 69.0 rounds, mean 100
  >=  1000x: median 710.5 rounds, mean 1,013

total simulated rounds: 475,353,972