Quote from: MPOE-PR on November 20, 2012, 11:11:45 PM

Quote from: dooglus on November 20, 2012, 07:23:57 PM

Code:

after 1000000 martingale plays, bet 5330214, profit -77550. won -0.0145 per unit bet
after 1000000 martingale plays, bet 5338031, profit -96823. won -0.0181 per unit bet
after 1000000 martingale plays, bet 5347483, profit -123551. won -0.0231 per unit bet
[...]

I imagine what SRoulette is talking about is the "actual" house edge, ie your first martingale example "reduced" the house edge to 1.45%.

Yes, but the 3rd one "increased" the house edge to 2.31%... It's just as likely to increase it as it is to decrease it. Unless you don't run enough trials in the simulation. If the maximum bet was 3 million times the minimum bet, and you only run 1 million plays then it's pretty likely that the player will win, since he'll only bust out once every 3 million plays. That still doesn't change the house edge. Even if you only run the simulation for 10 plays the house edge is still the same.

Here's a simulation which runs 1 million spins, and uses martingale betting with a max_bet of 3 million and min_bet of 1. It runs the simulation 50 times over. In most of the 50 runs the player is up after 1 million spins, but if you watch the "over all" house edge, it gets closer and closer to 2% the longer the simulation runs:

Code:

after 1000000 martingale plays, bet 11457710 (avg 11.46), profit 488962. won 0.0427 per unit bet ( 0.0427 over all)
after 1000000 martingale plays, bet 17008465 (avg 17.01), profit -3704311. won -0.2178 per unit bet (-0.1130 over all)
after 1000000 martingale plays, bet 11017225 (avg 11.02), profit 489021. won 0.0444 per unit bet (-0.0690 over all)
after 1000000 martingale plays, bet 13868162 (avg 13.87), profit 489052. won 0.0353 per unit bet (-0.0419 over all)
after 1000000 martingale plays, bet 13020328 (avg 13.02), profit 489568. won 0.0376 per unit bet (-0.0263 over all)
after 1000000 martingale plays, bet 10977479 (avg 10.98), profit 490197. won 0.0447 per unit bet (-0.0163 over all)
after 1000000 martingale plays, bet 10019905 (avg 10.02), profit 490701. won 0.0490 per unit bet (-0.0088 over all)
after 1000000 martingale plays, bet 13910161 (avg 13.91), profit 489703. won 0.0352 per unit bet (-0.0027 over all)
after 1000000 martingale plays, bet 14831702 (avg 14.83), profit 489618. won 0.0330 per unit bet ( 0.0018 over all)
after 1000000 martingale plays, bet 14752718 (avg 14.75), profit -3704070. won -0.2511 per unit bet (-0.0267 over all)
after 1000000 martingale plays, bet 15026345 (avg 15.03), profit 489887. won 0.0326 per unit bet (-0.0206 over all)
after 1000000 martingale plays, bet 17972262 (avg 17.97), profit 489708. won 0.0272 per unit bet (-0.0153 over all)
after 1000000 martingale plays, bet 17064824 (avg 17.06), profit -3704042. won -0.2171 per unit bet (-0.0344 over all)
after 1000000 martingale plays, bet 10081844 (avg 10.08), profit 490436. won 0.0486 per unit bet (-0.0300 over all)
after 1000000 martingale plays, bet 11156499 (avg 11.16), profit 489897. won 0.0439 per unit bet (-0.0259 over all)
after 1000000 martingale plays, bet 12150884 (avg 12.15), profit 489752. won 0.0403 per unit bet (-0.0221 over all)
after 1000000 martingale plays, bet 12385808 (avg 12.39), profit 491262. won 0.0397 per unit bet (-0.0188 over all)
after 1000000 martingale plays, bet 13666944 (avg 13.67), profit -3704202. won -0.2710 per unit bet (-0.0331 over all)
after 1000000 martingale plays, bet 10932079 (avg 10.93), profit 490997. won 0.0449 per unit bet (-0.0297 over all)
after 1000000 martingale plays, bet 16427193 (avg 16.43), profit -3704633. won -0.2255 per unit bet (-0.0417 over all)
after 1000000 martingale plays, bet 13367344 (avg 13.37), profit 489988. won 0.0367 per unit bet (-0.0380 over all)
after 1000000 martingale plays, bet 13025866 (avg 13.03), profit 490218. won 0.0376 per unit bet (-0.0347 over all)
after 1000000 martingale plays, bet 10847957 (avg 10.85), profit 490019. won 0.0452 per unit bet (-0.0318 over all)
after 1000000 martingale plays, bet 10370444 (avg 10.37), profit 489506. won 0.0472 per unit bet (-0.0292 over all)
after 1000000 martingale plays, bet 10868724 (avg 10.87), profit 489922. won 0.0451 per unit bet (-0.0267 over all)
after 1000000 martingale plays, bet 19760611 (avg 19.76), profit 490625. won 0.0248 per unit bet (-0.0238 over all)
after 1000000 martingale plays, bet 17011539 (avg 17.01), profit -3704287. won -0.2178 per unit bet (-0.0329 over all)
after 1000000 martingale plays, bet 15678676 (avg 15.68), profit 490236. won 0.0313 per unit bet (-0.0302 over all)
after 1000000 martingale plays, bet 11410885 (avg 11.41), profit 490113. won 0.0430 per unit bet (-0.0281 over all)
after 1000000 martingale plays, bet 10187641 (avg 10.19), profit 490873. won 0.0482 per unit bet (-0.0261 over all)
after 1000000 martingale plays, bet 11926302 (avg 11.93), profit 489660. won 0.0411 per unit bet (-0.0242 over all)
after 1000000 martingale plays, bet 12854024 (avg 12.85), profit 489676. won 0.0381 per unit bet (-0.0223 over all)
after 1000000 martingale plays, bet 12424968 (avg 12.42), profit 490366. won 0.0395 per unit bet (-0.0206 over all)
after 1000000 martingale plays, bet 10389545 (avg 10.39), profit 490087. won 0.0472 per unit bet (-0.0190 over all)
after 1000000 martingale plays, bet 9595018 (avg 9.60), profit 490334. won 0.0511 per unit bet (-0.0175 over all)
after 1000000 martingale plays, bet 10597612 (avg 10.60), profit 490320. won 0.0463 per unit bet (-0.0161 over all)
after 1000000 martingale plays, bet 10617003 (avg 10.62), profit 490183. won 0.0462 per unit bet (-0.0147 over all)
after 1000000 martingale plays, bet 20010422 (avg 20.01), profit -7899388. won -0.3948 per unit bet (-0.0299 over all)
after 1000000 martingale plays, bet 17397414 (avg 17.40), profit -3704308. won -0.2129 per unit bet (-0.0361 over all)
after 1000000 martingale plays, bet 11776690 (avg 11.78), profit 489688. won 0.0416 per unit bet (-0.0344 over all)
after 1000000 martingale plays, bet 11885588 (avg 11.89), profit 490168. won 0.0412 per unit bet (-0.0327 over all)
after 1000000 martingale plays, bet 13854636 (avg 13.85), profit 490610. won 0.0354 per unit bet (-0.0310 over all)
after 1000000 martingale plays, bet 13588069 (avg 13.59), profit 489521. won 0.0360 per unit bet (-0.0294 over all)
after 1000000 martingale plays, bet 11199192 (avg 11.20), profit 488470. won 0.0436 per unit bet (-0.0280 over all)
after 1000000 martingale plays, bet 10057752 (avg 10.06), profit 489814. won 0.0487 per unit bet (-0.0267 over all)
after 1000000 martingale plays, bet 10454429 (avg 10.45), profit 489967. won 0.0469 per unit bet (-0.0254 over all)
after 1000000 martingale plays, bet 12164250 (avg 12.16), profit 491088. won 0.0404 per unit bet (-0.0241 over all)
after 1000000 martingale plays, bet 15409300 (avg 15.41), profit 489224. won 0.0317 per unit bet (-0.0227 over all)
after 1000000 martingale plays, bet 14511655 (avg 14.51), profit 490205. won 0.0338 per unit bet (-0.0214 over all)
after 1000000 martingale plays, bet 9878573 (avg 9.88), profit 489889. won 0.0496 per unit bet (-0.0204 over all)