Quote

It's not as simple as that though.

If you both invest 100 BTC, and a whale constantly bets to win the max profit, and loses, then the 1% guy wins more than 4 times that of the 0.25% guy:

A ( p/l) B ( p/l) roll max ratio
-------- (------) -------- (------) -------- ------ --------
100.2500 (0.2500) 101.0000 (1.0000) 200.0000 1.2500 4.000000
100.5006 (0.5006) 102.0100 (2.0100) 201.2500 1.2606 4.014981
100.7519 (0.7519) 103.0301 (3.0301) 202.5106 1.2714 4.030050
101.0038 (1.0038) 104.0604 (4.0604) 203.7820 1.2822 4.045206
101.2563 (1.2563) 105.1010 (5.1010) 205.0642 1.2931 4.060451
101.5094 (1.5094) 106.1520 (6.1520) 206.3573 1.3042 4.075785
101.7632 (1.7632) 107.2135 (7.2135) 207.6614 1.3153 4.091208
102.0176 (2.0176) 108.2857 (8.2857) 208.9767 1.3265 4.106721
102.2726 (2.2726) 109.3685 (9.3685) 210.3033 1.3379 4.122325
...
127.4046 (27.4046) 262.5266 (162.5266) 387.0141 2.9170 5.930639
127.7231 (27.7231) 265.1518 (165.1518) 389.9311 2.9438 5.957197
128.0424 (28.0424) 267.8033 (167.8033) 392.8749 2.9708 5.983919

After 100 or so whale losses, the 1% guy's profit is almost 6 times that of the 0.25% guy. His share of the bankroll keeps increasing relative to the more timid guy.

The converse is also true. If the whale wins, then the 1% guy loses less than 4 times as much as the 0.25% guy, and after around 100 whale wins has lost around 3 times as much as the 0.25% guy. His share of the bankroll keeps decreasing relative to the more timid guy.

A ( p/l) B ( p/l) roll max ratio
-------- (------) -------- (------) -------- ------ --------
99.7500 (-0.2500) 99.0000 (-1.0000) 200.0000 1.2500 4.000000
99.5006 (-0.4994) 98.0100 (-1.9900) 198.7500 1.2394 3.984981
99.2519 (-0.7481) 97.0299 (-2.9701) 197.5106 1.2289 3.970050
99.0037 (-0.9963) 96.0596 (-3.9404) 196.2818 1.2184 3.955206
98.7562 (-1.2438) 95.0990 (-4.9010) 195.0633 1.2081 3.940449
98.5093 (-1.4907) 94.1480 (-5.8520) 193.8552 1.1979 3.925778
98.2631 (-1.7369) 93.2065 (-6.7935) 192.6574 1.1878 3.911192
98.0174 (-1.9826) 92.2745 (-7.7255) 191.4696 1.1777 3.896691
97.7724 (-2.2276) 91.3517 (-8.6483) 190.2919 1.1678 3.882275
97.5279 (-2.4721) 90.4382 (-9.5618) 189.1241 1.1579 3.867943
...
78.4426 (-21.5574) 37.7237 (-62.2763) 116.7439 0.5776 2.888855
78.2464 (-21.7536) 37.3464 (-62.6536) 116.1662 0.5733 2.880154
78.0508 (-21.9492) 36.9730 (-63.0270) 115.5929 0.5691 2.871500

In this example, you're setting the max bet to 1% of the total bankroll (20,000 on the first roll). But this is wrong! The .25% people are willing to risk .25% of their 10,000, or 25. The 1% people are willing to risk 1% of their 10,000, or 100. The max bet on the first roll is 125, not 200.

Oleander

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