The Myth of 20 Buyins and ROR

[Orlando Salazar]

People who say you only need 20 Buyins in NL/PL games are technically mistaken. I ran some randomization funtions in excel to prove that aggression factor will play a significant roll in Risk of Ruin. To know the number of buyins necessary for a game, you'll also need to know the average pot size. If the average pot is 1/20 of your BR, then its highly unlikely that inherent variance will even let a good player (+EV) be a long term winner. You wont go broke in consecutive all ins, but you will be broke. This shows how important pot control is when you only have a marginal edge and limited buyins.
Aggressive Example
$1000 Bankroll
always 1/20th of it in play
When random number (double) is >=.5, hero wins Bankroll*(1/20)*(1 + 1.5%)
When hero loses, hero loses Bankroll*(1/20)*(1 - 1.5%)
After simulating 11,000 scenarios about 27 of 30 will have much less than the $1,000 they started with. When playing on 80 buyins (basically having average pot be 1/80th of Bankroll) only 4 or 5 of 30 will have less than 1k. In both examples, a player has a decent and positive expectation on each scenario. 30 end scenario bankrolls below ($ at 11k hands):

20 BuyIns
$0.32
$0.06
$234.27
$0.04
$0.04
$0.29
$11.66
$34,782.72
$14.24
$0.02
$1.74
$1.43
$3.18
$86.17
$142.08
$0.02
$2,337.06
$3.88
$1.93
$5.79
$94,557.10
$0.58
$38.72
$0.01
$0.11
$191.80
$0.09
$11.66
$286.14
$63.84

80 BUYINS
$3,443.33
$589.47
$1,986.78
$2,088.63
$12,632.37
$1,889.89
$23,015.81
$5,136.56
$4,421.17
$4,205.58
$13,960.74
$336.81
$243.36
$2,037.06
$629.18
$12,016.36
$678.18
$7,288.79
$1,435.56
$4,886.08
$2,749.64
$1,986.78
$6,118.77
$25,436.05
$33,486.10
$1,937.73
$1,331.85
$4,312.03
$5,399.88
$275.76

I know most poker situtations are not 50/50, but they average out to that. Feel free to repeat and critique my experiment.