Oy, help me with some math please
 

I'm just trying to work out something... I'm considering going from playing 4x 2/4 LHE to playing 3x 3/6 LHE.

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Since I'd be dropping to 3/4 the number of tables, but the price of poker goes up by 50%, I'd be looking at 4.5/4, or 1.125x my previous stakes (per hour).

Now, this hardly tells the whole story:

Depending on if the games sped up or slowwed down (hands per hour) at 3/6, I would experience slightly higher or lower stakes, apart from the 12.5% increase.

Rakeback may drop, depending on the average rake per pot difference between the two levels, and the change in game speed.

Oh! I should also point out that if the pots are raked a smaller % at the new level, this will have the effect of increasing the stakes past the 12.5% level also.

However, the math thing that completely boggles me is this:

Assume that I don't get rakeback, assume rake % per pot is the same, and assume that hands per hour is the same...

If my stakes have effectively increased by 12.5%, how much can my bb/100 drop in order for me to make the same amount of absolute money (or, I suppose, how much would my lossrate have to drop for me to lose the same amount of absolute money)?

As a simple example, if my stakes increased by 50% (I went from 2/4 to 3/6 without changing my number of tables) I could afford to drop my bb/100 by 33% and still make the same absolute money. The 1/8th increase in stakes makes it a little harder for me to figure it out, though.

Hmm... maybe 1/12? (half of 8... same ratio as 3:2).

The math that I started with was something like:

112.5/100 = x/100... which of course didn't help. [img]/images/graemlins/smile.gif[/img]

My guess would be 1/12th, as 12:8 is the same ratio as 3:2.

Trying:

112.5/100 * x/100 = 100/100... This gives me X as 8/9ths (i.e. I could drop by 1/9th).

This is pretty cool, as 9-8 = 3-2 (I don't know what the mathematical term is for this, but I would assume "linear"... it works for a 25% increase in stakes and a 20% decrease in winrate (4&5) too!!! Very cool.).

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So, I guess if everything remained equal, you could drop from 4 tables to 3 tables, increase stakes from 2/4 to 3/6, drop your bb/100 from 2 to 1.7777..., and make the same cash.

You would have to put up with, however:

-increased daily variance from the mean win rate, due to smaller sample size

-having larger and longer downswings, due to a decreased edge (bb/100)

Edit: -I would have to have my bankroll increase by 50% (the poker portion of it), despite only increasing the stakes by 12.5%.

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Obviously there would be some good and bad points to this:

-I'm not ready for 3/6, just yet.
-Psychologically it would be more difficult to handle the increased prevalence of downswings, increasing chances of tilt and perhaps deteriorating winrate to the point of making less absolute money.
-less tables makes for better reads and more observation, leading to an increase in skill and experience, if I can apply myself to the observation.

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Anyways, a long post, and kinda meandering, sorry. But could someone check out my math to see if I came to the correct conclusion?

Edit: D'oh. If you did 1.125 * x = 1, you'd be getting there a lot quicker. [img]/images/graemlins/smile.gif[/img]

Re: Oy, help me with some math please
 

Let me give this a try:

Lets say you're averaging 2bb/100 at 2/4 at 4 tables...

$8 at 4 tables = $32

At 3/6, you're looking to make $32 minimum at 3 tables.

32/3 = 10.66

Divide that by the limit you're at, that's

10.66/6= 1.78bb/100 to break even

So your math is correct:)

What about trying to work your way into it if you're really nervous? It sounds like this is the real issue, so why not try 3 tabling at 2/4 and adding a 3/6 as your 4th? Any variance you experience at 3/6 will be offset by your obvious experience at 2/4.

Or, you could go back and look at the variance you experienced going from 1/2 to 2/4 and apply it proportionally, assuming that it is the same jump experience-wise of course and further assuming you have data from the 1/2 limits

Re: Oy, help me with some math please
 

Yes, I also think your math is correct, you could drop you winrate by 1/9th and make the same cash.

I'll try a general formulation of the problem.

We assume that the winrate is after rake and that we play the same number of hands per hour per table at both levels.

X1 = old winrate
X2 = new winrate
Y1 = big bet at old level
Y2 = big bet at new level
T1 = #tables at old level
T2 = #tables at new level

for your new winrate (X2) to be the same as the old (X1) the following must hold:

X2 = X1 * (Y1 * T1) / (Y2 * T2)

In your case, we get

X2 = X1 * (4 * 4) / (6 * 3) = X1 * 8 / 9,

so your new winrate must be 8/9th of you old one.

Re: Oy, help me with some math please
 

[ QUOTE ]

I'll try a general formulation of the problem.

We assume that the winrate is after rake and that we play the same number of hands per hour per table at both levels.

X1 = old winrate
X2 = new winrate
Y1 = big bet at old level
Y2 = big bet at new level
T1 = #tables at old level
T2 = #tables at new level

for your new winrate (X2) to be the same as the old (X1) the following must hold:

X2 = X1 * (Y1 * T1) / (Y2 * T2)



[/ QUOTE ]

Thanks to both of you gentlemen. I'm glad my math was right, but this elegant formula is vastly superior to my "envelope math" attempt at it. [img]/images/graemlins/smile.gif[/img]

Thanks, again.
--Dave.

Re: Oy, help me with some math please
 

[ QUOTE ]

What about trying to work your way into it if you're really nervous? It sounds like this is the real issue, so why not try 3 tabling at 2/4 and adding a 3/6 as your 4th? Any variance you experience at 3/6 will be offset by your obvious experience at 2/4.

Or, you could go back and look at the variance you experienced going from 1/2 to 2/4 and apply it proportionally, assuming that it is the same jump experience-wise of course and further assuming you have data from the 1/2 limits

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That sounds like a decent plan.

I'm not so much concerned about the cash as I am the skill of the players; I've heard that the 3/6 games have gotten hugely harder since the 6-max tables emerged. I should probably play a stint at 0.5/1 and 1/2 6-max first, to figure out how to play better in SH pots. [img]/images/graemlins/cool.gif[/img]

I mean, I'd play 1k/2k, grind all the way there at my current skill, if the players along the way were as bad as they are at the 0.5/1 tables... (That's what I'm saying when I mean that I don't care about the money, not that I'm totally rich or whatever.)

Of course, they aren't, which is why kmore people don't do this for a living.
--Dave.

Re: Oy, help me with some math please
 

i stopped reading when you said "i'm considering going from 4x 2/4 to 3x 3/6"

if you have the bankroll for 3x 3/6 you have the bankroll for 4x 3/6.

if you feel ready to make the jump from 2/4 to 3/6, total table numbers shouldn't ultimately be any different.

if this is a temporary measure until you feel more comfortable at this higher limit... accept it for what it is. doing math to figure out precisely how much money you'll make over a temporary period is, well, pointless. particularly since presumably you're playing less tables to concentrate on continuing to play optimally, and figure out where your game needs adjustment.

also... this is a small stakes question, or a math question, or somewhere else but micro question.

but really, don't bother asking, you're wasting your own time.

Re: Oy, help me with some math please
 

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i stopped reading when you said "i'm considering going from 4x 2/4 to 3x 3/6"

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Ok.

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if you have the bankroll for 3x 3/6 you have the bankroll for 4x 3/6.

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Yep.

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if you feel ready to make the jump from 2/4 to 3/6, total table numbers shouldn't ultimately be any different.


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Uh huh.

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if this is a temporary measure until you feel more comfortable at this higher limit... accept it for what it is. doing math to figure out precisely how much money you'll make over a temporary period is, well, pointless.



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Nice to know what bb/100 you need to hit before taking a paycut, even in the short-term.

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particularly since presumably you're playing less tables to concentrate on continuing to play optimally, and figure out where your game needs adjustment.



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Exactly!

(But also to observe some of the subtle differences in play between 2/4 and 3/6, if any exist.)

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also... this is a small stakes question, or a math question, or somewhere else but micro question.


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It's a math question, not limited by what stake you play. Not sure where to post it. Seems to be more academic posters here than elsewhere.

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but really, don't bother asking, you're wasting your own time.

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Dude, it just depends on what you're interested in, really.

Edit: However, DFA rocks!