Slot Machine RTP Optimization and Symbols Wins Equalization with Discrete Differential Evolution

Efficient Monte Carlo Methods for Multidimensional Modeling of Slot Machines Jackpot

“…The other suitable method is the interlaced digital sequence, producing the five smallest errors, but they are obtained for large values of C, and they are of one order better than the errors produced by the other methods. 2 10 1.6125e-04 5.9472e-03 1.2844e-04 7.2665e-04 1.0475e-03 5.9037e-04 1.0728e-03 2 11 1.9346e-04 1.8509e-03 1.8755e-04 4.0143e-06 5.2541e-04 6.6748e-04 8.3025e-04 2 12 3.4622e-05 5.8246e-04 2.4591e-04 1.5847e-05 9.0208e-04 1.0248e-04 4.4663e-04 2 13 2.7674e-04 1.9345e-04 2.9789e-04 8.5159e-05 1.8386e-04 8.4683e-05 2.8420e-05 2 14 7.8357e-05 2.0888e-06 2.3893e-04 2.6495e-05 2.7664e-04 1.5048e-05 1.3011e-04 2 15 6.8036e-05 6.2652e-06 6.4250e-05 5.9894e-05 4.2919e-05 7.1324e-06 8.6867e-05 2 16 6.7842e-05 5.6128e-06 2.7236e-05 2.0672e-05 4.6293e-05 4.2045e-05 4.2164e-05 2 17 3.4242e-05 2.2065e-05 6.4611e-06 2.7191e-06 3.2974e-05 3.7721e-06 2.9521e-05 2 18 1.3859e-05 1.4018e-05 4.3472e-06 5.2437e-06 3.4679e-05 5.4494e-06 1.9901e-06 2 19 1.0718e-05 6.3245e-06 1.2579e-06 4.8620e-06 4.3226e-05 2.5429e-06 9.4656e-06 2 20 3.5234e-05 2.6706e-06 2.8323e-06 3.3937e-06 8.7798e-06 5.1221e-06 8.2347e-06 2 21 1.0182e-05 1.6646e-06 1.9961e-06 5.3631e-06 1.6481e-05 1.8632e-06 5.9903e-07 2 22 2.2655e-05 3.2259e-07 1.6827e-06 2.4378e-06 2.4166e-06 4.2597e-07 7.2949e-07 2 23 1.7509e-05 3.3866e-07 1.1103e-06 2.1528e-06 2.1024e-05 1.3517e-06 8.3793e-07 2 24 1.6180e-05 1.3048e-07 2.9587e-07 6.1431e-07 9.9364e-06 2.1059e-07 3.7635e-07 2 25 2.1837e-06 1.4345e-07 4.7869e-08 6.7600e-08 4.8745e-06 1.2202e-07 3.5241e-07 2 26 9.3048e-07 8.9044e-08 1.9305e-07 2.4566e-08 8.1265e-07 2.4635e-07 1.3593e-07 2 27 1.9097e-06 1.5722e-07 1.6952e-07 7.3093e-08 3.6900e-06 1.9022e-07 7.1400e-08 2 28 3.1659e-06 2.5281e-07 2.0586e-07 1.3335e-07 4.5442e-06 1.3973e-07 8.8798e-08 2 29 1.7997e-06 2.5890e-07 9.7798e-08…”

“…It makes an impression that the scrambled Halton sequences achieves order of error 1e-9 for both integrals. 11 1.1533e-04 3.7009e-04 1.9943e-04 5.6922e-05 2.2411e-04 6.5545e-04 5.3065e-05 2 12 5.8559e-05 2.4444e-05 2.2240e-04 1.1855e-06 1.1090e-04 2.5692e-04 9.3302e-05 2 13 3.0213e-05 7.7243e-05 1.3250e-05 5.0104e-05 6.3212e-05 1.0417e-04 8.1908e-05 2 14 2.6176e-05 8.8000e-05 1.0513e-05 3.0773e-05 4.3708e-05 3.5951e-05 3.7869e-05 2 15 2.5704e-05 2.2879e-05 6.0667e-06…”

“…It is also noticeable that the former achieves an order of error 1e-9. 11 9.8530e-05 2.1244e-04 1.2350e-04 2.8501e-05 1.0423e-04 6.8519e-04 1.5751e-04 2 12 6.4999e-05 1.4588e-05 1.4909e-04 8.1798e-05 4.0251e-05 3.1762e-04 1.1229e-04 2 13 2.9633e-05 1.0840e-05 3.3027e-05 1.5929e-05 2.6352e-05 9.4241e-05 7.3354e-05 2 14 2.2212e-05 4.6066e-05 2.2826e-05 1.1102e-05 7.2073e-06 2.6834e-05 5.0587e-05 2 15 1.2054e-05 1.8725e-05 1.7282e-06…”

“…An exact formula does not exist-it should be interpreted just as the higher the number, the more volatile the win size. A game has different settings for the RTP level [3,[10][11][12], which often varies between 88% and 96%, but usually is higher than 91-92%. Every RTP level is associated with a different set of reels.…”

Slot Machine RTP Optimization Using Variable Neighborhood Search

“…Furthermore, the algorithm's behavior in the case where special symbols appear in reels (e.g., wild, scatter) is also unknown. e same authors in [5] also proposed a Differential Evolution (DE) algorithm, since the problem of optimal symbols distribution on the reels is discrete and its convergence was found to be faster than GAs. Additionally, they also used Monte Carlo simulations with 1,000,000 separate runs over ten trials for better accuracy in base game.…”