Module 7 · Lesson 33 of 39 · Free
Bankroll rules: buy-ins, moving up and moving down
$1,000 at a $0.25/$0.50 table is 20 buy-ins of $50, the low end of the usual rule of 20 to 40. It sounds like plenty for a small game, yet a player who wins 5 bb per 100 hands still loses all 20 buy-ins about 1 time in 7, from the swings alone. A bankroll rule is how you keep playing through them.
The hand
You have set aside $1,000 for poker, money you can afford to lose, and you want to play cash games, sitting down with 100 big blinds each time.
Predict first
Your rule is 30 buy-ins. What is the highest stake your $1,000 allows?
- $0.25/$0.50
- $0.10/$0.25
- $0.05/$0.10
Show the answer
Answer: $0.10/$0.25
At $0.25/$0.50 a buy-in is 100 × $0.50 = $50, and 30 of them cost $1,500, more than you have. At $0.10/$0.25 a buy-in is $25 and 30 of them cost $750, which you have. $0.05/$0.10 is allowed too, but lower.
Working it out
A buy-in is 100 big blinds: at $0.25/$0.50 that is 100 × 0.50 = $50, and $1,000 holds 1,000 ÷ 50 = 20 of them. Why keep so many? Take a player who wins 5 bb per 100 hands with swings of 100 bb per 100 hands, the example of the Mathematics lesson on risk of ruin. With 20 buy-ins he goes broke at some point about 13.5% of the time, with 30 buy-ins 5%, with 40 buy-ins 1.8%: each 10 more buy-ins divide the risk by about 2.7. With only 10 buy-ins it is 37%. And these figures assume he really wins 5 bb per 100 hands, a strong rate that takes many thousands of hands to prove: with a smaller edge the same bankroll goes broke far more often.
A bankroll is money set aside only for poker, money you can afford to lose: rent, bills and savings are never part of it, and no rule makes them safe. Move up when you have your rule's buy-ins for the next stakes, and move down as soon as you no longer have them for yours. Tournaments swing harder, since only the top 10 to 20% of the field win anything, so tournament players often keep 100 buy-ins or more. No bankroll protects a losing player: at a win rate of zero or less the swings take it all in the end. Every chip in this app is play money, so these habits cost nothing to practice.
Formula
Buy-ins = bankroll ÷ (100 × big blind): 1,000 ÷ (100 × 0.5) = 20. Move down below rule × 100 × big blind
Check your understanding
Your bankroll is $600 and you play $0.10/$0.25 with buy-ins of 100 big blinds. How many buy-ins do you have?
Show the answer
Answer: 24
A buy-in is 100 × 0.25 = $25, and 600 ÷ 25 = 24 buy-ins.
Your rule is 40 buy-ins and you play $0.05/$0.10. Below what bankroll do you move down?
- $400
- $40
- $1,000
Show the answer
Answer: $400
A buy-in at $0.05/$0.10 is 100 × 0.10 = $10, and 40 of them are 40 × 10 = $400. $40 forgets that a buy-in is 100 big blinds; $1,000 is 40 buy-ins of the next stakes, $0.10/$0.25.
Which of these is true?
- A big enough bankroll keeps a losing player going for good
- After a losing run, moving up is the fastest way to win it back
- A winning player with 20 buy-ins can still lose them all
Show the answer
Answer: A winning player with 20 buy-ins can still lose them all
Swings are large next to a small edge: with 20 buy-ins, a player who wins 5 bb per 100 hands still goes broke about 1 time in 7. A losing player goes broke whatever the bankroll, and moving up after losses adds bigger swings to a smaller bankroll.