Oy, help me with some math please

[DavidC]

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]

[lautzutao]

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

[Innocentius]

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.

[DavidC]

[ 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.

[DavidC]

[ 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

[/ QUOTE ]

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.

[ErrantNight]

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.

[DavidC]

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

[/ QUOTE ]

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.

[ QUOTE ]



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


[/ QUOTE ]

Uh huh.

[ QUOTE ]


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.



[/ QUOTE ]

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

[ QUOTE ]


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.)

[ QUOTE ]


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!