A study on the applicability of martingale using simulations of the coin game - page 4

 
Nikolay Demko:

A misunderstanding of Anti-Martin. Anti-Martin is what?

Is it a lot reduction after a losing trade, or

Is it the opposite position to the trading position under Martin?

we have two binary variables, i.e. 4 options, and only one of them is Martin, presumably the other 3 are Anti-Martin.


That's you have three anti-Martin.
But I have one: opposite to Martin and opposite direction of deal and MM (lot reduction after losing trade).


Alexander Puzanov:

If your anti-martin comes with anti-spread, anti-commission and positive slippage

And the struggle with this trivia is a topic for another branch... Here the comrade tests the question purely on a coin

 

Our previous calculation can be checked by simply running a simulation of 3,153,600 games, let's check what the profit will be:

profit: 157632.60234890878
{ 0 = 788417 , 1 = 393279 , 2 = 196918 , 3 = 99323 , 4 = 49040 , 5 = 24706 , 6 = 12390 , 7 = 6091 , 8 = 3088 , 9 = 1511 , 10 = 796 , 11 = 375 , 12 = 183 , 13 = 100 , 14 = 50 , 15 = 30 , 16 = 17 , 17 = 7 , 18 = 3 , 19 = 1 , 25 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 , 23 = 838860.8125 , 24 = 1677721.625 , 25 = 3355443.25 }
profit: 157674.9023495391
{ 0 = 788781 , 1 = 393239 , 2 = 197561 , 3 = 98682 , 4 = 49031 , 5 = 24882 , 6 = 12329 , 7 = 6136 , 8 = 3051 , 9 = 1483 , 10 = 803 , 11 = 408 , 12 = 199 , 13 = 73 , 14 = 58 , 15 = 16 , 16 = 6 , 17 = 5 , 18 = 5 , 22 = 1 , 27 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 , 23 = 838860.8125 , 24 = 1677721.625 , 25 = 3355443.25 , 26 = 6710886.5 , 27 = 1.3421773 E7}
profit: 157621.90234874934
{ 0 = 788127 , 1 = 393663 , 2 = 197306 , 3 = 98323 , 4 = 49360 , 5 = 24656 , 6 = 12424 , 7 = 6226 , 8 = 3048 , 9 = 1559 , 10 = 777 , 11 = 375 , 12 = 169 , 13 = 105 , 14 = 51 , 15 = 20 , 16 = 17 , 17 = 6 , 18 = 4 , 19 = 2 , 20 = 1 , 21 = 1 , 22 = 2 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 }
profit: 157641.30234903842
{ 0 = 788369 , 1 = 393927 , 2 = 196455 , 3 = 98892 , 4 = 49693 , 5 = 24609 , 6 = 12133 , 7 = 6076 , 8 = 3085 , 9 = 1547 , 10 = 818 , 11 = 385 , 12 = 218 , 13 = 98 , 14 = 51 , 15 = 35 , 16 = 9 , 17 = 3 , 18 = 6 , 19 = 3 , 20 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 }
profit: 157530.60234738886
{ 0 = 786859 , 1 = 393728 , 2 = 197400 , 3 = 98421 , 4 = 49673 , 5 = 24537 , 6 = 12262 , 7 = 6167 , 8 = 3133 , 9 = 1542 , 10 = 799 , 11 = 392 , 12 = 173 , 13 = 110 , 14 = 65 , 15 = 24 , 16 = 18 , 17 = 2 , 19 = 1 , 22 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 }
profit: 157765.30235088617
{ 0 = 788939 , 1 = 395345 , 2 = 196607 , 3 = 98383 , 4 = 49182 , 5 = 24447 , 6 = 12368 , 7 = 6181 , 8 = 3157 , 9 = 1495 , 10 = 767 , 11 = 398 , 12 = 165 , 13 = 116 , 14 = 57 , 15 = 17 , 16 = 14 , 17 = 4 , 18 = 7 , 19 = 1 , 20 = 1 , 21 = 1 , 23 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 , 23 = 838860.8125 }
profit: 157589.70234826952
{ 0 = 787785 , 1 = 393602 , 2 = 197476 , 3 = 98136 , 4 = 49575 , 5 = 24489 , 6 = 12460 , 7 = 6132 , 8 = 3063 , 9 = 1597 , 10 = 791 , 11 = 403 , 12 = 187 , 13 = 98 , 14 = 51 , 15 = 24 , 16 = 14 , 17 = 6 , 18 = 3 , 19 = 4 , 20 = 1 , 22 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 }
profit: 157714.10235012323
{ 0 = 789208 , 1 = 393822 , 2 = 196983 , 3 = 98452 , 4 = 49316 , 5 = 24690 , 6 = 12358 , 7 = 6146 , 8 = 3136 , 9 = 1515 , 10 = 768 , 11 = 371 , 12 = 184 , 13 = 88 , 14 = 43 , 15 = 37 , 16 = 9 , 17 = 5 , 18 = 5 , 19 = 5 , 22 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 }
profit: 157639.90234901756
{ 0 = 788547 , 1 = 394045 , 2 = 196710 , 3 = 98051 , 4 = 49597 , 5 = 24544 , 6 = 12389 , 7 = 6263 , 8 = 3176 , 9 = 1520 , 10 = 768 , 11 = 378 , 12 = 196 , 13 = 109 , 14 = 58 , 15 = 20 , 16 = 18 , 17 = 5 , 18 = 1 , 19 = 1 , 20 = 3 , 21 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 }
profit: 157710.70235007256
{ 0 = 788631 , 1 = 395061 , 2 = 196330 , 3 = 98508 , 4 = 49351 , 5 = 24474 , 6 = 12363 , 7 = 6155 , 8 = 3102 , 9 = 1522 , 10 = 812 , 11 = 414 , 12 = 195 , 13 = 91 , 14 = 44 , 15 = 28 , 16 = 11 , 17 = 8 , 18 = 5 , 19 = 2 , 22 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 }

Our calculations turned out to be correct, we see the same profit. But wait, in real life, nothing happens for free, and there is a commission, now let's add not a lot, not a little 1%, and see what remains:

profit: 88822.49086572754
{ 0 = 789162 , 1 = 394784 , 2 = 196963 , 3 = 98538 , 4 = 49499 , 5 = 24317 , 6 = 12326 , 7 = 6065 , 8 = 3140 , 9 = 1531 , 10 = 783 , 11 = 380 , 12 = 175 , 13 = 87 , 14 = 40 , 15 = 22 , 16 = 11 , 17 = 4 , 18 = 6 , 19 = 1 , 21 = 1 , 24 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 , 23 = 838860.8125 , 24 = 1677721.625 }
profit: 123625.2866022763
{ 0 = 786908 , 1 = 394133 , 2 = 197405 , 3 = 98932 , 4 = 49458 , 5 = 24430 , 6 = 12308 , 7 = 6175 , 8 = 3105 , 9 = 1510 , 10 = 786 , 11 = 371 , 12 = 159 , 13 = 95 , 14 = 51 , 15 = 21 , 16 = 10 , 17 = 6 , 18 = 2 , 19 = 5 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 }
profit: 121507.11862347
{ 0 = 790402 , 1 = 393787 , 2 = 196971 , 3 = 99023 , 4 = 49062 , 5 = 24533 , 6 = 12165 , 7 = 6157 , 8 = 3095 , 9 = 1537 , 10 = 783 , 11 = 367 , 12 = 196 , 13 = 100 , 14 = 52 , 15 = 21 , 16 = 13 , 17 = 4 , 18 = 2 , 19 = 1 , 20 = 1 , 21 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 }
profit: 122120.13661360118
{ 0 = 787529 , 1 = 393583 , 2 = 197336 , 3 = 98729 , 4 = 49332 , 5 = 24912 , 6 = 12176 , 7 = 6190 , 8 = 3086 , 9 = 1516 , 10 = 754 , 11 = 398 , 12 = 205 , 13 = 79 , 14 = 36 , 15 = 15 , 16 = 13 , 17 = 7 , 18 = 7 , 19 = 2 , 20 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 }
profit: 122313.38861370487
{ 0 = 788149 , 1 = 394042 , 2 = 197090 , 3 = 98480 , 4 = 49415 , 5 = 24699 , 6 = 12456 , 7 = 6148 , 8 = 3084 , 9 = 1494 , 10 = 757 , 11 = 362 , 12 = 204 , 13 = 87 , 14 = 41 , 15 = 21 , 16 = 10 , 17 = 4 , 18 = 2 , 19 = 1 , 20 = 1 , 21 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 }
profit: 114498.12267213926
{ 0 = 788244 , 1 = 394497 , 2 = 197078 , 3 = 98618 , 4 = 48759 , 5 = 24987 , 6 = 12212 , 7 = 6249 , 8 = 2959 , 9 = 1588 , 10 = 780 , 11 = 407 , 12 = 197 , 13 = 103 , 14 = 38 , 15 = 23 , 16 = 14 , 17 = 6 , 18 = 4 , 19 = 2 , 20 = 3 , 21 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 }
profit: 120198.54263129225
{ 0 = 788848 , 1 = 394688 , 2 = 196769 , 3 = 98486 , 4 = 49361 , 5 = 24837 , 6 = 12348 , 7 = 6030 , 8 = 3042 , 9 = 1507 , 10 = 728 , 11 = 427 , 12 = 167 , 13 = 102 , 14 = 35 , 15 = 28 , 16 = 10 , 17 = 9 , 18 = 5 , 20 = 1 , 21 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 }
profit: 124012.17660451238
{ 0 = 790067 , 1 = 393780 , 2 = 197418 , 3 = 98537 , 4 = 49094 , 5 = 24588 , 6 = 12353 , 7 = 6162 , 8 = 3066 , 9 = 1526 , 10 = 735 , 11 = 373 , 12 = 191 , 13 = 99 , 14 = 43 , 15 = 29 , 16 = 13 , 17 = 4 , 18 = 3 , 19 = 2 , 20 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 }
profit: 122983.42060590046
{ 0 = 786979 , 1 = 394002 , 2 = 197291 , 3 = 97998 , 4 = 49489 , 5 = 24802 , 6 = 12214 , 7 = 6223 , 8 = 3200 , 9 = 1551 , 10 = 774 , 11 = 388 , 12 = 213 , 13 = 99 , 14 = 45 , 15 = 25 , 16 = 11 , 17 = 11 , 18 = 3 , 19 = 3 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 }
profit: - 4172302.0854641236
{ 0 = 789930 , 1 = 394339 , 2 = 197224 , 3 = 98052 , 4 = 48951 , 5 = 24853 , 6 = 12473 , 7 = 6051 , 8 = 3077 , 9 = 1546 , 10 = 771 , 11 = 394 , 12 = 167 , 13 = 102 , 14 = 41 , 15 = 24 , 16 = 8 , 17 = 11 , 18 = 8 , 19 = 2 , 31 = 1 }
{ 1 = 0.20000000298023224 , 2 = 0.4000000059604645 , 3 = 0.800000011920929 , 4 = 1.600000023841858 , 5 = 3.200000047683716 , 6 = 6.400000095367432 , 7 = 12.800000190734863 , 8 = 25.600000381469727 , 9 = 51.20000076293945 , 10 = 102.4000015258789 , 11 = 204.8000030517578 , 12 = 409.6000061035156 , 13 = 819.2000122070312 , 14 = 1638.4000244140625 , 15 = 3276.800048828125 , 16 = 6553.60009765625 , 17 = 13107.2001953125 , 18 = 26214.400390625 , 19 = 52428.80078125 , 20 = 104857.6015625 , 21 = 209715.203125 , 22 = 419430.40625 , 23 = 838860.8125 , 24 = 1677721.625 , 25 = 3355443.25 , 26 = 6710886.5 , 27 = 1.3421773 E7, 28 = 2.6843546 E7, 29 = 5.3687092 E7, 30 = 1.07374184 E8, 31 = 2.14748368 E8}

We see that the profit has dipped to 120000, and the problem of exiting the simulation is felt - in some cases, during a drawdown, the loss is not won back as soon as the tested number of games is over. It will be possible to fix this later.

Overall, so far I don't see the benefit. And from a practical point of view, there will be no opportunity (and even a desire, thank God) to increase the account a lot, this is either restrictions in institutions, or just common sense - with a deposit of more than a million dollars in a DC, I think it will simply close)))

So then we will continue testing an increase by two, but with an exit and resignation to a loss after different series of losses in a row (i.e. we increase only x times - one, two, three, etc. and then start again with the initial lot). This will require a slight change in the program.

But first, you can still try to do the same as before, but with a smaller bankroll designed for fewer failures in a row, not 32 as it is now, but let's say 20, 15, 10, 7, 5, 4, 3. And look at the probabilities of occurrence collapse, profit.

 

New version of the software, if anyone is interested

public class CheckupCoinGame {
        private static final Random RANDOM = new Random();
        private static final int REPETITION = 10;
        private static final long ITERATIONS = 3_153_600;
        private Map<Integer, Integer> series;
        private Map<Integer, Double> bets;
        private double initialBet;
        private static final double MARTIN_KOEFF = 2.0;
        private double profit;
        private double currentBet;
        private static final double COMMISSION = 0.00;
        private static final double MAX_COMMISSION = 5.0;
        private int losingInRow;
        private int failCount;
        private static final int MAX_SERIES = 3;
        
        public CheckupCoinGame(double initialBet) {
                this.initialBet = initialBet;
                series = new HashMap<>();
                bets = new HashMap<>();
                init();
        }
        public void init() {
                series.clear();
                bets.clear();
                profit = 0.0;
                losingInRow = 0;
                currentBet = initialBet;
                failCount = 0;
        }
        public int getLosingInRow() {
                return losingInRow;
        }
        public void printSeries() {
                System.out.println("profit: "+profit+" fails: "+failCount+"("+failCount/(double)ITERATIONS*100.0+"%)");
                System.out.println(series.toString());
                System.out.println(bets.toString());
                System.out.println();
        }
        public void play() {
                profit -= currentBet;
                if(RANDOM.nextBoolean()) {
                        double prize = currentBet*2.0;
                        double commission = prize*COMMISSION;
                        if(commission>MAX_COMMISSION) commission = MAX_COMMISSION;
                        
                        if(series.get(losingInRow)==null) series.put(losingInRow, 1);
                        else series.put(losingInRow, series.get(losingInRow)+1);
                        
                        currentBet = initialBet;
                        losingInRow = 0;
                        profit += prize-commission;
                }
                else {
                        currentBet = currentBet * MARTIN_KOEFF;
                        losingInRow++;
                        if(losingInRow>MAX_SERIES) {
                                currentBet = initialBet;
                                losingInRow = 0;
                                failCount++;
                        }
                        if(bets.get(losingInRow)==null) bets.put(losingInRow, currentBet);
                }
        }
        
        public static void main(String[] args) {
                CheckupCoinGame coinGame = new CheckupCoinGame(0.1);
                for(int i=0; i<REPETITION; i++) {
                        coinGame.init();
                        for(long j=0; j<ITERATIONS; j++) {
                                coinGame.play();
                        }
                        while(coinGame.getLosingInRow()!=0) coinGame.play();
                        coinGame.printSeries();
                }
        }
        
}

Anyway, I have tested, if you put up with losses in any combinations (after 0,2,3,20 - any) - the expectation is always NULL in tests without commission. So there is no advantage at all (unlike the first case).

Here are the results where it is set to increase by a maximum of 3 times:

profit: 1064.4000000010242 fails: 104485(3.313197615423643%)
{0=841720, 1=420343, 2=210167, 3=105689}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: -592.5000000111686 fails: 105469(3.344400050735667%)
{0=840210, 1=420909, 2=210267, 3=104724}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: 89.59999999777897 fails: 105038(3.3307331303906644%)
{0=840330, 1=420664, 2=210097, 3=105375}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: 133.59999999348236 fails: 105075(3.331906392694064%)
{0=841801, 1=420508, 2=210124, 3=105028}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: -9.599999996863112 fails: 105251(3.337487316083206%)
{0=844023, 1=420160, 2=209691, 3=104795}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: 701.9999999914036 fails: 104714(3.320459157787925%)
{0=840924, 1=421350, 2=210704, 3=104752}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: -962.3000000318344 fails: 105685(3.3512493658041604%)
{0=840870, 1=419495, 2=210148, 3=105139}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: 746.2999999787268 fails: 104627(3.3177004058853377%)
{0=840081, 1=420623, 2=210889, 3=105275}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: 716.9999999892076 fails: 104750(3.3216007102993403%)
{0=842449, 1=420843, 2=210046, 3=105082}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}
profit: 788.0999999872712 fails: 104674(3.319190766108574%)
{0=842199, 1=420400, 2=209663, 3=105729}
{0=0.1, 1=0.2, 2=0.4, 3=0.8}

In more than 3 percents there is an unpleasantness.

I do not see any sense to describe something here, and count necessary bankroll, as expectation is zero, with the commission, of course, negative.

 

In cases where you put up with losing - zero expectation applies to any multiplier, be it 2, or any other, I've tried 1.5, 1.75, 3.0. There's no difference, only the bigger the value, the bigger the variance.

I wonder, what if I don't put up with losing, but also try multiplying not by 2.0, and also look at other variations. Intuitively it seems that some multiplication from 1 to 2 should also give results. In general, in the case of 1.5 it is clearly seen that it does not give any advantage, zero. In case of 1.75 it is not so clear at once, either it is zero too or some microscopic advantage (without commission) still exists, I am inclined towards the last option - test of 2 billion games:

profit: 2766267.3014452904 fails: 0(0.0%)
{0=499979571, 1=250013092, 2=124999950, 3=62494015, 4=31247634, 5=15626081, 6=7812455, 7=3906885, 8=1952484, 9=977436, 10=488396, 11=244308, 12=122312, 13=61360, 14=30526, 15=15472, 16=7708, 17=3869, 18=1944, 19=881, 20=496, 21=224, 22=112, 23=62, 24=34, 25=11, 26=7, 27=3, 28=1, 29=1}
{1=0.175, 2=0.30625, 3=0.5359375, 4=0.9378906, 5=1.6413085, 6=2.87229, 7=5.0265074, 8=8.796388, 9=15.393679, 10=26.938938, 11=47.143143, 12=82.5005, 13=144.37589, 14=252.6578, 15=442.15115, 16=773.7645, 17=1354.0879, 18=2369.6538, 19=4146.894, 20=7257.0645, 21=12699.863, 22=22224.762, 23=38893.332, 24=68063.33, 25=119110.83, 26=208443.95, 27=364776.9, 28=638359.56, 29=1117129.2}

Earn2766267 / 2,000,000,000 = 0.0013831335(i.e. 1/10th of a cent at 10 cents bet, that's nothing).

Increases greater than or equal to 2 work, it is clear that at odds 3.0 the necessary bankroll will be needed much more, the expectation is higher.

What else can you think of? Reducing? Some kind of tricky conditions such as "At a drawdown of x we will increase it once until the drawdown is over".

So far I haven't managed to find any benefits from using it, I didn't get my hopes up, I just had to make sure, and it would be strange if it worked, and there was nothing to get resources from, roughly speaking.

 
Stanislav Aksenov:

...

What else can you think of? Decrease? Some kind of tricky condition like "At a drawdown in x increase once until you get out of the drawdown".

So far I have not managed to find any advantages of using it, I did not get my hopes up, I just had to make sure, and it would be strange if it worked, and there was nothing to get resources from roughly.


Can I ask a question about the "psychology" of what's going on...?

I do not understand the persistence with which many try to squeeze profit out of one "component".
Why is not the direction "How could so successfully combine several diverse "components" into a SYSTEM capable of generating profits?" ?..
How much will you use one crankshaft (even if it's the crankshaft from the famous Belarus tractor)?

 

Stanislav Aksenov, what is there to think about?

Everything was calculated a long time ago. Martingale is a workable system, but the profit is too small compared to the required deposit.

It is necessary to set the probability of winning in a single trial (say, 0.6, but it may be less than half), the number of series (say, 100000) and the probability of not losing during all this time (say, 99%).

A simple calculation shows that we have to sustain 18 losses in a row, which means the deposit size has to be equal to 256K initial bets (the total result would be +100K bets with 99% probability and -256K bets with 1% probability).

Give us different conditions - all easily recalculated.

Why make some scary calculations ?

 
George Merts:

Stanislav Aksenov, what is there to think about?

Why make some scary calculations ?


Where are they scary? On the contrary, I strive to show/prove in the clearest possible way, without formulas, from a practical point of view, by experience.

By the way, a series of 18 comes out once in a million, which is a lot less than 1%. A series of 5 in a row happens 0.8% of the time. Why would it amount to +100 bets? The total result will be zero.

 
Stanislav Aksenov:

By the way, a series of 18 comes out once in a million, which is a lot less than 1%.

1% is the probability of leaking all 100,000 episodes.

It's about something else - martingale is about moving frequent small losses into a zone of rare and large losses. And the only possibility to stay in profit with it is to transfer losses to the zone of very seldom losses and to stop trading in time. But in this case the deposit requirement is disproportionately big. And the sense is lost, the owner of such a deposit will find a much more profitable use for it.

 
George Merts:

1% is the probability of losing the entire 100,000 series.

The point is different - martingale is about moving frequent small losses into a zone of rare and large losses. And the only way to stay in profit with it is to transfer losses to the zone of superfrequent ones, and stop trading in time. But in this case the deposit requirement is disproportionately big. And the sense is lost, the owner of such a deposit will find a much more profitable use for it.

Of course, you can open a bakery).
 
George Merts:

1% is the probability of losing the entire 100,000 series.

It's about something else - martingale is about shifting frequent small losses into a zone of rare and large losses. And the only way to stay in the black is to move losses to the zone of superfrequent, and stop trading in time. But in this case the deposit requirement is disproportionately big. And the sense is lost, the owner of such a deposit will find a much more profitable use for it.


That's if you look at it differently, it makes more sense to me to look at profit in dollars, it will tend towards zero if you only count on a series of 18 consecutive losses.

I agree with your conclusion, I have come to exactly the same conclusion.