The Myth of 20 Buyins and ROR
 

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.

Re: The Myth of 20 Buyins and ROR
 

Said better than me:

The book "The Mathematics of Poker" derives the following formula:

Risk_of_Ruin = exp(-2*WR*BR/SD^2)

Where, WR = win rate in ptBB/100 hands
BR = bankroll in ptBB
SD = your standard deviation in ptBB/100 hands
1 ptBB = one Poker Tracker big bet = 2 big blinds

If you want to know what your bankroll should be for a given risk of ruin ...

BR = -(ln(ROR) * SD^2)/(2 * WR)

for example, if your SD = 60 ptBB/100 hands, your winrate at PLO 25 is 8 ptBB/100 hands and your winrate at PLO 50 is 4 ptBB/100 hands, then for a 1% risk of ruin ...

PLO 25 BR = -(ln(0.01) * 60^2)/(2*8) = 1036 ptBB = approx $500

PLO 50 BR = -(ln(0.01) * 60^2)/(2*4) = 2072 ptBB = approx $2000

Re: The Myth of 20 Buyins and ROR
 

One thing about the 20 buyin recommendation is that it is recommended to move down after a downswing...

If you have $8000, playing 400NL and move down if you hit 15 buyins on a given level, you will have:

5 buyins at 400NL (move down with 6000)
15 buyins at 200NL (move down with 3000)
15 buyins at 100NL (move down with 1500)
15 buyins at 50NL (move down with 750)
30 buyins at 25NL (supposing you can't move down anymore)

That's 80 buyins, so our ROOOOOOOOOOR is alot lower.

Re: The Myth of 20 Buyins and ROR
 

[ QUOTE ]
One thing about the 20 buyin recommendation is that it is recommended to move down after a downswing...

If you have $8000, playing 400NL and move down if you hit 15 buyins on a given level, you will have:

5 buyins at 400NL (move down with 6000)
15 buyins at 200NL (move down with 3000)
15 buyins at 100NL (move down with 1500)
15 buyins at 50NL (move down with 750)
30 buyins at 25NL (supposing you can't move down anymore)

That's 80 buyins, so our ROOOOOOOOOOR is alot lower.

[/ QUOTE ]

No. Everytime the computer bet it effectively moved down, because it never bet more than 1/20 of its roll after the previous hand. If it was up 10 1050 its next risk would be 52.5 and vice versa, you see?

Re: The Myth of 20 Buyins and ROR
 

ok , I see. So in your scenario your number of buyins is constant (20), where as in mine it varies between 15 and 30. I guess we can assume the difference is not too large.

There's one assumption in your scenario that I think is incorrect, which is the average pot size. If you play 100NL 6max, the average pot size is no higher than $20... You're gonna play alot of small pots and a few big pots here and there.