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]