Post
Topic
Board Service Announcements (Altcoins)
Re: Just-Dice.com : Invest in 1% House Edge Dice Game
by
GOB
on 28/09/2013, 17:44:10 UTC
If you pick 0.25% and I pick 1%, then I make (or lose) 4 times as much as you.  Simple as that.  

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


Chriswen, this looks like your scenario C, so looks like you're right!