Short buy ? BR = Full Buy?

warrantofice · #1 10-28-2007, 02:13 PM

So my brothers friend is some raging drunk and he seems to think that you need a small bankroll if you short buy into a cash game. Let my clear that up. Bankroll for full buyins at 25nl is 600 dollars, he says its exactly the same if you buy in for $25 at 50nl since you have the same number buy-ins.
I know this dead beat alcy is wrong, whats my proof, i used varaniace just want a solid case to get this gin sipper to be quiet.

oyvindgee · #2 10-28-2007, 04:54 PM

You need empirical evidence that the std is higher with one of the options. Then just do a ROR calculation.

pzhon · #3 10-30-2007, 08:50 AM

He is wrong. This is a common mistake. The mathematics of bankroll management is more complicated than just using a fixed number of buy-ins regardless of the size.

An expert who buys in short tends to have less of an advantage on average when all of the money goes in, and he tends to get all-in more frequently. Higher stakes games also tend to be tougher. The net result may be that an expert would win slightly more $/hour by buying in for 50 BB in a game of twice the stakes, but would need many more short buy-ins than full buy-ins.

TNixon · #4 10-30-2007, 04:41 PM

Another way of looking at it:

The variance of a situation is dependent on the average pot size, and the average pot is measured in units of big blinds, not dollars. Given similar play, the average pot size, in big blinds, is going to be similar, no matter what the stakes are. If the average pot at $.5/$1 NL is $7, then the average pot at $5/$10 is going to be $70, but they're both 7 big blinds.

So, playing $25 at .5/1 is obviously lower variance than playing $100 at .5/1 (you are short, meaning you'll put more chips in more marginal situations, but the average pot size is the same, and you're only risking 1/4 as much, so the potential gains and losses are much smaller), but playing $25 at .5/1 is higher variance than playing $25 at .25/.5. (you're short, the average pot is twice the size, and you're risking just as much)

And higher variance, of course, means you need a deeper bankroll to cover.