from markov_chain, 1000m, no headstart

gistfile1.txt

1000 miners
1.0 blocks per round on expectation
headstart: 0

For alpha = 0.02
5 rounds back, atkr wins: 0.0113342524641
15 rounds back, atkr wins: 4.63649472687e-06
25 rounds back, atkr wins: 2.648025576e-09
35 rounds back, atkr wins: 1.65634798923e-12
45 rounds back, atkr wins: 1.08201408329e-15
55 rounds back, atkr wins: 7.25175542826e-19
65 rounds back, atkr wins: 4.94327263821e-22
75 rounds back, atkr wins: 3.41051928154e-25
85 rounds back, atkr wins: 2.37433138008e-28
95 rounds back, atkr wins: 1.66456706778e-31

For alpha = 0.04
5 rounds back, atkr wins: 0.0172003720307
15 rounds back, atkr wins: 2.2271159937e-05
25 rounds back, atkr wins: 3.92682622688e-08
35 rounds back, atkr wins: 7.55058734662e-11
45 rounds back, atkr wins: 1.51438185184e-13
55 rounds back, atkr wins: 3.11447410118e-16
65 rounds back, atkr wins: 6.51285245837e-19
75 rounds back, atkr wins: 1.37822006294e-21
85 rounds back, atkr wins: 2.94261426099e-24
95 rounds back, atkr wins: 6.32637460407e-27

For alpha = 0.06
5 rounds back, atkr wins: 0.0244569305589
15 rounds back, atkr wins: 7.42145508601e-05
25 rounds back, atkr wins: 3.01656617243e-07
35 rounds back, atkr wins: 1.3342308034e-09
45 rounds back, atkr wins: 6.1510968412e-12
55 rounds back, atkr wins: 2.90686906312e-14
65 rounds back, atkr wins: 1.39655344432e-16
75 rounds back, atkr wins: 6.7889600144e-19
85 rounds back, atkr wins: 3.32955055526e-21
95 rounds back, atkr wins: 1.64419605494e-23

For alpha = 0.08
5 rounds back, atkr wins: 0.0332333586701
15 rounds back, atkr wins: 0.000201395345284
25 rounds back, atkr wins: 1.61561371322e-06
35 rounds back, atkr wins: 1.40795934928e-08
45 rounds back, atkr wins: 1.2781742309e-10
55 rounds back, atkr wins: 1.18910565558e-12
65 rounds back, atkr wins: 1.12445789161e-14
75 rounds back, atkr wins: 1.07581765441e-16
85 rounds back, atkr wins: 1.03835045412e-18
95 rounds back, atkr wins: 1.00905835272e-20

For alpha = 0.1
5 rounds back, atkr wins: 0.0436478865232
15 rounds back, atkr wins: 0.000475779542585
25 rounds back, atkr wins: 6.80026863783e-06
35 rounds back, atkr wins: 1.05426820685e-07
45 rounds back, atkr wins: 1.70169846648e-09
55 rounds back, atkr wins: 2.81402968255e-11
65 rounds back, atkr wins: 4.72935888159e-13
75 rounds back, atkr wins: 8.04097276703e-15
85 rounds back, atkr wins: 1.37910807764e-16
95 rounds back, atkr wins: 2.3814236545e-18

For alpha = 0.12
5 rounds back, atkr wins: 0.0558044583947
15 rounds back, atkr wins: 0.00101397275419
25 rounds back, atkr wins: 2.39560781235e-05
35 rounds back, atkr wins: 6.13006304945e-07
45 rounds back, atkr wins: 1.63221702361e-08
55 rounds back, atkr wins: 4.45129964386e-10
65 rounds back, atkr wins: 1.23354857546e-11
75 rounds back, atkr wins: 3.45793447962e-13
85 rounds back, atkr wins: 9.77761627404e-15
95 rounds back, atkr wins: 2.78341872482e-16

For alpha = 0.14
5 rounds back, atkr wins: 0.0697898137833
15 rounds back, atkr wins: 0.00199232421654
25 rounds back, atkr wins: 7.33743596535e-05
35 rounds back, atkr wins: 2.92233139271e-06
45 rounds back, atkr wins: 1.21038616822e-07
55 rounds back, atkr wins: 5.13320180364e-09
65 rounds back, atkr wins: 2.21177686561e-10
75 rounds back, atkr wins: 9.63918662274e-12
85 rounds back, atkr wins: 4.23706536577e-13
95 rounds back, atkr wins: 1.87498677678e-14

For alpha = 0.16
5 rounds back, atkr wins: 0.0856708138181
15 rounds back, atkr wins: 0.00366183566634
25 rounds back, atkr wins: 0.000200376296765
35 rounds back, atkr wins: 1.18386693204e-05
45 rounds back, atkr wins: 7.26934847793e-07
55 rounds back, atkr wins: 4.56899553056e-08
65 rounds back, atkr wins: 2.91712855025e-09
75 rounds back, atkr wins: 1.88359174135e-10
85 rounds back, atkr wins: 1.22662077503e-11
95 rounds back, atkr wins: 8.04115866138e-13

For alpha = 0.18
5 rounds back, atkr wins: 0.103492087487
15 rounds back, atkr wins: 0.00636052259069
25 rounds back, atkr wins: 0.000496605818944
35 rounds back, atkr wins: 4.17927206352e-05
45 rounds back, atkr wins: 3.65280965717e-06
55 rounds back, atkr wins: 3.2668876094e-07
65 rounds back, atkr wins: 2.9673085918e-08
75 rounds back, atkr wins: 2.72540908884e-09
85 rounds back, atkr wins: 2.52438332039e-10
95 rounds back, atkr wins: 2.35362365203e-11

For alpha = 0.2
5 rounds back, atkr wins: 0.123274065754
15 rounds back, atkr wins: 0.0105204244756
25 rounds back, atkr wins: 0.00113162203786
35 rounds back, atkr wins: 0.00013096035916
45 rounds back, atkr wins: 1.57284536022e-05
55 rounds back, atkr wins: 1.93215889215e-06
65 rounds back, atkr wins: 2.41002353883e-07
75 rounds back, atkr wins: 3.03932079169e-08
85 rounds back, atkr wins: 3.86494429658e-09
95 rounds back, atkr wins: 4.94694854279e-10

For alpha = 0.22
5 rounds back, atkr wins: 0.145011463118
15 rounds back, atkr wins: 0.0166663617954
25 rounds back, atkr wins: 0.00239459311128
35 rounds back, atkr wins: 0.000369420385499
45 rounds back, atkr wins: 5.90949054574e-05
55 rounds back, atkr wins: 9.66490574799e-06
65 rounds back, atkr wins: 1.60454904321e-06
75 rounds back, atkr wins: 2.6928487931e-07
85 rounds back, atkr wins: 4.55651103728e-08
95 rounds back, atkr wins: 7.75969575557e-09

For alpha = 0.24
5 rounds back, atkr wins: 0.168672255861
15 rounds back, atkr wins: 0.0254039049984
25 rounds back, atkr wins: 0.00474230177517
35 rounds back, atkr wins: 0.000948459824607
45 rounds back, atkr wins: 0.000196506212953
55 rounds back, atkr wins: 4.16038178459e-05
65 rounds back, atkr wins: 8.9385464775e-06
75 rounds back, atkr wins: 1.94097211047e-06
85 rounds back, atkr wins: 4.24888372666e-07
95 rounds back, atkr wins: 9.36009720509e-08

For alpha = 0.26
5 rounds back, atkr wins: 0.194197194332
15 rounds back, atkr wins: 0.0373949050695
25 rounds back, atkr wins: 0.00884491982141
35 rounds back, atkr wins: 0.00223594615754
45 rounds back, atkr wins: 0.000584913060386
55 rounds back, atkr wins: 0.00015626807889
65 rounds back, atkr wins: 4.23520412207e-05
75 rounds back, atkr wins: 1.15983938366e-05
85 rounds back, atkr wins: 3.20151732139e-06
95 rounds back, atkr wins: 8.89230324879e-07

For alpha = 0.28
5 rounds back, atkr wins: 0.221499873507
15 rounds back, atkr wins: 0.053320299429
25 rounds back, atkr wins: 0.0156162164442
35 rounds back, atkr wins: 0.00487504428594
45 rounds back, atkr wins: 0.00157295935821
55 rounds back, atkr wins: 0.00051798494003
65 rounds back, atkr wins: 0.000172967767838
75 rounds back, atkr wins: 5.83466481631e-05
85 rounds back, atkr wins: 1.98344298801e-05
95 rounds back, atkr wins: 6.78367092391e-06

For alpha = 0.3
5 rounds back, atkr wins: 0.250467372092
15 rounds back, atkr wins: 0.0738316173287
25 rounds back, atkr wins: 0.0262117949872
35 rounds back, atkr wins: 0.00988959892943
45 rounds back, atkr wins: 0.00385123007338
55 rounds back, atkr wins: 0.00152949488956
65 rounds back, atkr wins: 0.000615656095754
75 rounds back, atkr wins: 0.000250260830157
85 rounds back, atkr wins: 0.000102495181311
95 rounds back, atkr wins: 4.22264026962e-05

For alpha = 0.32
5 rounds back, atkr wins: 0.280961455997
15 rounds back, atkr wins: 0.0994944444296
25 rounds back, atkr wins: 0.0419795672462
35 rounds back, atkr wins: 0.0187617187281
45 rounds back, atkr wins: 0.00864106302283
55 rounds back, atkr wins: 0.00405512253948
65 rounds back, atkr wins: 0.00192769952713
75 rounds back, atkr wins: 0.000925070790159
85 rounds back, atkr wins: 0.000447146366409
95 rounds back, atkr wins: 0.000217374349846

For alpha = 0.34
5 rounds back, atkr wins: 0.31282032749
15 rounds back, atkr wins: 0.130728786478
25 rounds back, atkr wins: 0.0643524178466
35 rounds back, atkr wins: 0.0334323921718
45 rounds back, atkr wins: 0.0178672514676
55 rounds back, atkr wins: 0.00971948226895
65 rounds back, atkr wins: 0.00535230264505
75 rounds back, atkr wins: 0.00297400929884
85 rounds back, atkr wins: 0.00166395709463
95 rounds back, atkr wins: 0.000936096622944

For alpha = 0.36
5 rounds back, atkr wins: 0.345860887213
15 rounds back, atkr wins: 0.167752501389
25 rounds back, atkr wins: 0.0946840233919
35 rounds back, atkr wins: 0.0561743748625
45 rounds back, atkr wins: 0.0342144912547
55 rounds back, atkr wins: 0.0211864503932
65 rounds back, atkr wins: 0.013270291843
75 rounds back, atkr wins: 0.00838247096147
85 rounds back, atkr wins: 0.00532955461896
95 rounds back, atkr wins: 0.00340611854751

For alpha = 0.38
5 rounds back, atkr wins: 0.379881462863
15 rounds back, atkr wins: 0.210534489406
25 rounds back, atkr wins: 0.134043388695
35 rounds back, atkr wins: 0.0893070179141
45 rounds back, atkr wins: 0.0609454811283
55 rounds back, atkr wins: 0.0422252952617
65 rounds back, atkr wins: 0.0295650976266
75 rounds back, atkr wins: 0.0208628619157
85 rounds back, atkr wins: 0.014811129651
95 rounds back, atkr wins: 0.0105655998482

For alpha = 0.4
5 rounds back, atkr wins: 0.414664946139
15 rounds back, atkr wins: 0.258763973078
25 rounds back, atkr wins: 0.182998394517
35 rounds back, atkr wins: 0.134766938037
45 rounds back, atkr wins: 0.101394138499
55 rounds back, atkr wins: 0.0773257263159
65 rounds back, atkr wins: 0.0595307803846
75 rounds back, atkr wins: 0.0461541262781
85 rounds back, atkr wins: 0.0359788493953
95 rounds back, atkr wins: 0.0281696159332

For alpha = 0.42
5 rounds back, atkr wins: 0.449982268844
15 rounds back, atkr wins: 0.311840921713
25 rounds back, atkr wins: 0.24142907049
35 rounds back, atkr wins: 0.19360656318
45 rounds back, atkr wins: 0.158156243263
55 rounds back, atkr wins: 0.130719174291
65 rounds back, atkr wins: 0.108930720992
75 rounds back, atkr wins: 0.0913297924048
85 rounds back, atkr wins: 0.0769374566903
95 rounds back, atkr wins: 0.0650610851241

For alpha = 0.44
5 rounds back, atkr wins: 0.485596140162
15 rounds back, atkr wins: 0.368890585769
25 rounds back, atkr wins: 0.308413317889
35 rounds back, atkr wins: 0.265543586346
45 rounds back, atkr wins: 0.232155714393
55 rounds back, atkr wins: 0.204931308102
65 rounds back, atkr wins: 0.182121593614
75 rounds back, atkr wins: 0.162665085232
85 rounds back, atkr wins: 0.14585663986
95 rounds back, atkr wins: 0.13119767852

For alpha = 0.46
5 rounds back, atkr wins: 0.521264960341
15 rounds back, atkr wins: 0.428802452692
25 rounds back, atkr wins: 0.382219171785
35 rounds back, atkr wins: 0.348703346677
45 rounds back, atkr wins: 0.321896221548
55 rounds back, atkr wins: 0.299333752113
65 rounds back, atkr wins: 0.279768917544
75 rounds back, atkr wins: 0.262469235508
85 rounds back, atkr wins: 0.246961078995
95 rounds back, atkr wins: 0.232916891738

For alpha = 0.48
5 rounds back, atkr wins: 0.556746821514
15 rounds back, atkr wins: 0.490291072069
25 rounds back, atkr wins: 0.460419127817
35 rounds back, atkr wins: 0.439666269631
45 rounds back, atkr wins: 0.423229126141
55 rounds back, atkr wins: 0.409367116509
65 rounds back, atkr wins: 0.397244202225
75 rounds back, atkr wins: 0.386390108663
85 rounds back, atkr wins: 0.376511835027
95 rounds back, atkr wins: 0.367413239586

For alpha = 0.5
5 rounds back, atkr wins: 0.591803504265
15 rounds back, atkr wins: 0.551973531583
25 rounds back, atkr wins: 0.540117431351
35 rounds back, atkr wins: 0.533855509854
45 rounds back, atkr wins: 0.529833560161
55 rounds back, atkr wins: 0.526971629871
65 rounds back, atkr wins: 0.524801512007
75 rounds back, atkr wins: 0.523082974636
85 rounds back, atkr wins: 0.521678395102
95 rounds back, atkr wins: 0.520502514879

For alpha = 0.52
5 rounds back, atkr wins: 0.626204378921
15 rounds back, atkr wins: 0.612456289407
25 rounds back, atkr wins: 0.618256651131
35 rounds back, atkr wins: 0.62619916113
45 rounds back, atkr wins: 0.634348498764
55 rounds back, atkr wins: 0.642271719861
65 rounds back, atkr wins: 0.649860912235
75 rounds back, atkr wins: 0.657101188665
85 rounds back, atkr wins: 0.66400713715
95 rounds back, atkr wins: 0.67060212397
            5         15            25            35            45            55            65            75            85            95
0.02  0.011334  0.000005  2.648026e-09  1.656348e-12  1.082014e-15  7.251755e-19  4.943273e-22  3.410519e-25  2.374331e-28  1.664567e-31
0.04  0.017200  0.000022  3.926826e-08  7.550587e-11  1.514382e-13  3.114474e-16  6.512852e-19  1.378220e-21  2.942614e-24  6.326375e-27
0.06  0.024457  0.000074  3.016566e-07  1.334231e-09  6.151097e-12  2.906869e-14  1.396553e-16  6.788960e-19  3.329551e-21  1.644196e-23
0.08  0.033233  0.000201  1.615614e-06  1.407959e-08  1.278174e-10  1.189106e-12  1.124458e-14  1.075818e-16  1.038350e-18  1.009058e-20
0.10  0.043648  0.000476  6.800269e-06  1.054268e-07  1.701698e-09  2.814030e-11  4.729359e-13  8.040973e-15  1.379108e-16  2.381424e-18
0.12  0.055804  0.001014  2.395608e-05  6.130063e-07  1.632217e-08  4.451300e-10  1.233549e-11  3.457934e-13  9.777616e-15  2.783419e-16
0.14  0.069790  0.001992  7.337436e-05  2.922331e-06  1.210386e-07  5.133202e-09  2.211777e-10  9.639187e-12  4.237065e-13  1.874987e-14
0.16  0.085671  0.003662  2.003763e-04  1.183867e-05  7.269348e-07  4.568996e-08  2.917129e-09  1.883592e-10  1.226621e-11  8.041159e-13
0.18  0.103492  0.006361  4.966058e-04  4.179272e-05  3.652810e-06  3.266888e-07  2.967309e-08  2.725409e-09  2.524383e-10  2.353624e-11
0.20  0.123274  0.010520  1.131622e-03  1.309604e-04  1.572845e-05  1.932159e-06  2.410024e-07  3.039321e-08  3.864944e-09  4.946949e-10
0.22  0.145011  0.016666  2.394593e-03  3.694204e-04  5.909491e-05  9.664906e-06  1.604549e-06  2.692849e-07  4.556511e-08  7.759696e-09
0.24  0.168672  0.025404  4.742302e-03  9.484598e-04  1.965062e-04  4.160382e-05  8.938546e-06  1.940972e-06  4.248884e-07  9.360097e-08
0.26  0.194197  0.037395  8.844920e-03  2.235946e-03  5.849131e-04  1.562681e-04  4.235204e-05  1.159839e-05  3.201517e-06  8.892303e-07
0.28  0.221500  0.053320  1.561622e-02  4.875044e-03  1.572959e-03  5.179849e-04  1.729678e-04  5.834665e-05  1.983443e-05  6.783671e-06
0.30  0.250467  0.073832  2.621179e-02  9.889599e-03  3.851230e-03  1.529495e-03  6.156561e-04  2.502608e-04  1.024952e-04  4.222640e-05
0.32  0.280961  0.099494  4.197957e-02  1.876172e-02  8.641063e-03  4.055123e-03  1.927700e-03  9.250708e-04  4.471464e-04  2.173743e-04
0.34  0.312820  0.130729  6.435242e-02  3.343239e-02  1.786725e-02  9.719482e-03  5.352303e-03  2.974009e-03  1.663957e-03  9.360966e-04
0.36  0.345861  0.167753  9.468402e-02  5.617437e-02  3.421449e-02  2.118645e-02  1.327029e-02  8.382471e-03  5.329555e-03  3.406119e-03
0.38  0.379881  0.210534  1.340434e-01  8.930702e-02  6.094548e-02  4.222530e-02  2.956510e-02  2.086286e-02  1.481113e-02  1.056560e-02
0.40  0.414665  0.258764  1.829984e-01  1.347669e-01  1.013941e-01  7.732573e-02  5.953078e-02  4.615413e-02  3.597885e-02  2.816962e-02
0.42  0.449982  0.311841  2.414291e-01  1.936066e-01  1.581562e-01  1.307192e-01  1.089307e-01  9.132979e-02  7.693746e-02  6.506109e-02
0.44  0.485596  0.368891  3.084133e-01  2.655436e-01  2.321557e-01  2.049313e-01  1.821216e-01  1.626651e-01  1.458566e-01  1.311977e-01
0.46  0.521265  0.428802  3.822192e-01  3.487033e-01  3.218962e-01  2.993338e-01  2.797689e-01  2.624692e-01  2.469611e-01  2.329169e-01
0.48  0.556747  0.490291  4.604191e-01  4.396663e-01  4.232291e-01  4.093671e-01  3.972442e-01  3.863901e-01  3.765118e-01  3.674132e-01
0.50  0.591804  0.551974  5.401174e-01  5.338555e-01  5.298336e-01  5.269716e-01  5.248015e-01  5.230830e-01  5.216784e-01  5.205025e-01
0.52  0.626204  0.612456  6.182567e-01  6.261992e-01  6.343485e-01  6.422717e-01  6.498609e-01  6.571012e-01  6.640071e-01  6.706021e-01