EV is an ok beginner's way to rank plays but it doesn't take into account variance and bankroll. CE takes into account EV, plus variance and bankroll:
CE = EV - variance/2xBankroll
Example:
FPDW hand: 22299
holding all five returns 15 bets
holding just 222 returns:
deuces: 46/1081 x 200 = 8.511
wrf: 40/1081 x 25 = 0.925
5k: 67/1081 x 15 = 0.930
sf: 108/1081 x 9 = 0.899
4k: 820/1081 x 5 = 3.793
total EV = 15.058
deuces: 46/1081 x (200-15.058)^2 = 1455.470
wrf: 40/1081 x (25-15.058)^2 = 3.657
5k: 67/1081 x (15-15.058)^2 = 0
sf: 108/1081 x (9-15.058)^2 = 3.667
4k: 820/1081 x (5-15.058)^2 = 76.738
total variance = 1540
solve for when CE>15:
15.058 - 1540/2xBankroll > 15
Bankroll > 13,276 bets > 16.6 royals
So, even though just holding 222 is the maxEV play, it's not a Kelly overlay unless your current bankroll exceeds 13,276 bets or 16.6 royals. Gamblers might typically play FPDW with a 5 royal bankroll, so 16.6 royals represents a much larger bankroll (more than 3x) than typical. For a quarter player, 13,276 bets is $16,595.
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Posted by: nightoftheiguana2000@yahoo.com
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