bankroll requirements for short stack theory

I know that most people recommend 15-20x the buyin for nl, but is this based on the max buyin or the actual amount that you buy in at (which would be the minimum if you are using the short stack strategy from GSIH)?

[Ed Miller]

[ QUOTE ]
I know that most people recommend 15-20x the buyin for nl, but is this based on the max buyin or the actual amount that you buy in at (which would be the minimum if you are using the short stack strategy from GSIH)?

[/ QUOTE ]

Ok, I see this question a LOT. Here's the deal:

Bankroll requirements are determined by winrate and variance. The higher your variance the bigger the bankroll you'll need. That's obvious.

But the LOWER your winrate, the bigger the bankroll you'll need, and they are roughly inversely proportional. I don't remember the exact math (I'm sure someone will chime in with it), but I generally think of it as if you halve your winrate, you roughly double your bankroll requirement.

In limit, "good" players will tend to have similarish winrates. In a $3-$6 game, maybe 1.5-3BB/100 or something like that is typical. Since winrate and variance (which usually doesn't change drastically from winning player to winning player either, despite what some readers of SSH might say) can often be nailed down to a "one size fits most" range, we can begin to talk about "standard bankrolls" for limit.

Obviously, these are gross estimates, and any particular player might have a bankroll requirement much different. Indeed, a bankroll requirement is meaningless for a losing player. But it makes some sense to talk about a "standard bankroll" for a winning limit player.

No limit is another ball of wax. The winrate of an expert could be five times that of a modest winner. Variance also depends greatly on your style, buy-in size, and caliber of opponents you play... and it differs more than it would for limit players. So the notion of a "one size fits most" bankroll for no limit is basically nonsense. Every player is, indeed, quite different.

Having said that, the GSIH style is prescribed enough that one could probably nail down a reasonable bankroll requirement within 50% or so. I haven't done it... doing so would require a fairly accurate winrate and variance measurement in typical games.

But don't think it makes any sense to compare El Diablo's bankroll requirement to the GSIH strategy's requirements. They are hugely different, and I wouldn't even want to begin to estimate how different they are.

[mosquito]

My experience (maybe 40K hands, not a huge sample) has shown negative downward fluctuations of 7 buyins (short stack, of course). I suspect a BR of 20 short buyins should be plenty, but don't have a statistical basis for saying so. This would be for typical games at 25NL at Party, or a similar game. Tighter games may have a smaller fluctation based on very limited experience, zero statistical basis for this observation.

[jasonHoldEm]

(From pg 45 of GTAOT, I hope I'm getting this right)

Mason gives a formula to calculate a "no-risk" bankroll, basically you need to calculate the point at which the largest possible deficit can occur:

N = [ (3*std dev)/ (2*Winrate)]^2

and then you plug that number into the BR forumula

BR = (winrate)(N) - (3)(std dev)(N)^1/2

(Assuming my math is right and assuming I'm understanding correctly what mason is saying...both of which might be big assumptions /images/graemlins/smile.gif ... ) If we use a winrate of 2bb and a std dev of 20bb (which seem to be reasonable based on my limited expereince with the strategy) you'd get an N of 225, and a "no risk" BR of 450 (so the 20 buy-in rule would be 400 and pretty close to the result we get). Naturally if your winrate or std dev are higher/lower you'd need to adjust, but the 20 buy-in "rule" seems reasonable.

If someone has more concrete numbers for winrate and stddev please feel free to chime in (and feel free to double check my math).

J

EDIT: wait, I confused myself...2bb and 20bb are refering to "big bets" (i.e. the way pokertracker calculates them) so the result is actually 450 big bets (900x the big blind which would be 45 buy-ins)....I think? Yeah...I'm pretty sure. hmmm... /images/graemlins/confused.gif

RE-EDIT: Yeah, that's right (if you plug 4 and 40 you get 900). I'm going to bed before I embarass myself further.

[pokernicus]

I've toyed with the short-stack system a few times. It's not hard to go through something like ten (short) buy-ins in a given session. I know since I did that once. /images/graemlins/smile.gif However, this was at the UB $0.50/$1 game, and I was four tabling.

I did use the short-stack system at Empire while clearing a bonus (this was at the $0.10/$0.25 level), and I think I dipped to being maybe one or two buy-ins behind before surging and making a nice profit (again, I was four tabling). My experience is that the short-stack system seems to work better at $0.10/$0.25 than it does at maybe $.50/1.

Please bear in mind, though, that I don't have nearly enough hands for a statistically meaningful sample size.

Nonetheless, my limited experience suggests that it's safer to have more buy-ins for the short-stack strategy than you might have for a typical NLHE bankroll. (This is primarily because you'll often be getting your entire stack in the middle every time you enter a hand.) But, also keep-in-mind that a typical NLHE buy-in is around 3-5 times what you buy-in for with short-stack play. So, in an absolute sense (i.e., number of dollars), a short-stack bankroll will likely be smaller. In a relative sense (i.e., number of buy-ins), you might need more buy-ins for a short-stack strategy than for a regular (whatever that means!) strategy.

[Rudbaeck]

Well, you can calculate it fairly well. By some bizarre act of statistics the GSIH win rate/standard deviation ends up looking alot like a very good limit players.

I got something like 6bb/100 win rate and a 36bb/100 standard deviation. bb = big blind.

If we plug these into BruceZ's formula for bankroll (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Number=207100&page=&view=&sb=5&o =&fpart=all&vc=1) using a 0.1% risk of ruin we get:

B = -(36^2/12)*ln(0.001) = -108*ln(0.001) = 746bb.

I think your bankroll requirements have to be pretty high. I say this because the only person I know who is winning with the short-buy system plays 12+ tables.

[Ed Miller]

[ QUOTE ]
I think your bankroll requirements have to be pretty high. I say this because the only person I know who is winning with the short-buy system plays 12+ tables.

[/ QUOTE ]

What does the number of tables have to do with the required bankroll?

[SuitedSixes]

With a gigantic sample size (more than 250k hands at 25NL) I require $420 for a 1% ROR. I always play, at least, 16 tables.

[Rudbaeck]

[ QUOTE ]
What does the number of tables have to do with the required bankroll?

[/ QUOTE ]

When I decided to use Kelly betting while 'starting over' with shorthanded play all the way back down from 0.5/1 it did make a difference. I had to adjust my bankroll up to be able to buy in on six tables. /images/graemlins/wink.gif

[PLOlover]

[ QUOTE ]

What does the number of tables have to do with the required bankroll?

[/ QUOTE ]

Using the extreme example to disprove idea, it is easy to see that if you play 100 tables you would need a larger bankroll. Of course, in practice, this may not apply.

[pokernicus]

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I think your bankroll requirements have to be pretty high. I say this because the only person I know who is winning with the short-buy system plays 12+ tables.

[/ QUOTE ]

Huh? This doesn't make sense -- whether a strategy is +EV is independent of the number of tables played simultaneously. If it's profitable when 12-tabling, then it'll be profitable when single tabling (though it might take you longer to earn the same amount of money).

[Scotch78]

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What does the number of tables have to do with the required bankroll?

[/ QUOTE ]

I don't know about SNGs, but for ring play it can make a huge difference. As an 8-tabler I need 200BB just to sit and play, so if I used the generic 300BB rule I'd have to drop tables during large downswings.

Scott

[Dazarath]

[ QUOTE ]
Using the extreme example to disprove idea, it is easy to see that if you play 100 tables you would need a larger bankroll. Of course, in practice, this may not apply.

[/ QUOTE ]
This is an extreme case and it's not quite addressing the standard misconception a lot of people have.

There's been quite a few threads on this subject, and the misconception is that playing more tables increases your variance. The thing is, your variance per hour (or per amount of time), but your variance per 100 hands does not.

In theory, if you play the same multi-tabling as you do single-tabling, then the bankroll requirements are exactly the same for a given winrate, standard deviation, and desired risk of ruin.

In reality, changing the number of tables also changes your winrate. Most of us could not 100-table without dropping our winrate into the red. You could also argue that a 4-tabler could choose the 4 juiciest tables available, whereas an 8-tabler would be forced to sit down on the 4 next juiciest tables, which would lower one's BB/100. The bankroll requirements do change, not because of a change in variance, but because of the inevitable change in winrate.

There's also the so-called "ADD" internet players who claim that their winrate actually increases when going from 1 table to 4 tables because the "boredom" would cause them to play hands they otherwise would've folded. I'm probably one of these people. /images/graemlins/smile.gif

[Rudi]

What happens when sites won't let you buy-in for the 25BB for a short stack strategy and the minimum buy-in is a medium stack of 50BB?

The bankroll would need to be adjusted upwards yet again, I think.

[ptmusic]

[ QUOTE ]
What happens when sites won't let you buy-in for the 25BB for a short stack strategy and the minimum buy-in is a medium stack of 50BB?

The bankroll would need to be adjusted upwards yet again, I think.

[/ QUOTE ]

Actually, in that case you can't properly do the short stack system, which is predicated on the strategy of getting all your chips in and decisions made before the turn. 50bb won't let you do that, unless you raise so much preflop that you drive everyone away.

So when I was playing the short stack system, I avoided those sites that wouldn't let me buy-in short. I also avoided the sites which had a large minimum add-on requirement (for those times when my stack dwindled down below 15bbs due to the blinds).

[Zim]

Those who were winning with the shortstack strategy claimed win rates between 3 and 5 PTBB/100 hands. With a standard deviation of between 18 and 21PTBB.

We'll go in the middle then, and say 4PTBB/100 hands, and an SD of 20.

Thus, for a full Kelly bankroll (13% ROR) ..

(20)^2/4= 100 PTBBs or about $50 at your typical $25NL Party game.

Now that's at 13% ROR which is a little swingy for most people ... if we double that stake, we can reduce ROR down to 1.69% (.13x.13)

Thus, $100 should give us 20 buy-ins of about $5 with a ROR of less than 2%.

So ... yah, what everyone has been saying. 15-20 buy-ins should do you fine.

If you are a winning player.

I've recently experimented shortstacking PL. After 3000 hands, ten-tabling, I'm dead even ... but it is interesting.

Best,
Zim

[Rudi]

Based on ptmusic's response, I need to find a sight that will let me buy-in for 25BB.

What sites let you buy-in for the 25BB? And what limits are those, since I'd like to start at $0.01/$0.02?

[Matt Ruff]

[ QUOTE ]
What sites let you buy-in for the 25BB? And what limits are those, since I'd like to start at $0.01/$0.02?

[/ QUOTE ]

Party, Paradise, Full Tilt, and Ultimate Bet will let you buy-in for 25BB, although I think only UB has penny tables.

Pokerstars' minimum buy-in is 20BB at the .05/.10 and higher. At the .01/.02, it's 50BB.