Theory EV/SD hours to double:

[doublesnapper]

I currently play 10-20 online or 2 tables of 5-10 simultaneously. I'm trying to guess at my "Hours to Double" my poker bankroll of currently ~6K. My "guess" is at 4.5 BB per hour (playing 2 tables of 5-10 simult., i.e.: $45 per hour).
I read somewhere that EV and SD for a good solid player is 1.5 BB and 12.5 BB at a brick and mortar, so I'm using 1.5 times the speed for online and times 2 because the 2 tables for the EV, but I don't know what to do with the SD figure for 2 tables simultaneously, the only thing I know is that it is LESS than double the SD for 1 table.

My actual figures are higher for the EV and lower for the SD, but I started playing at the micro-limits and many times short handed. That must be the reason, worse players and many more hands per hour.

I would appreciate some advice on calculating my "Hours to Double" figure. Also would appreciate comments on higher limit players' actual EV and SD in bigger games.

One last question: How high is the limit holdem sky?. I.e.: What are the highest games available that still contain "live ones"?. I have no experience of playing other than online.

Thanks in advance.

DoubleSnapper.

Thanks in advance.

[BruceZ]

I read somewhere that EV and SD for a good solid player is 1.5 BB and 12.5 BB at a brick and mortar

That's quite good. A rule of thumb is that SD = 10*EV for B&M. Lower is better. This is meant to apply for higher limits also.


so I'm using 1.5 times the speed for online and times 2 because the 2 tables for the EV, but I don't know what to do with the SD figure for 2 tables simultaneously, the only thing I know is that it is LESS than double the SD for 1 table.

SD for 2 tables is sqrt(2) times what it is for 1 table. Since you are playing 1.5 times as fast as B&M, you are playing 3 times more hands per hour than B&M, so your SD will be sqrt(3) times higher than B&M. For you that is sqrt(3)*12.5 = 21.65 bb.


would appreciate some advice on calculating my "Hours to Double" figure.

If you just want average hours to double, you don't need SD of course. Just divide your bankroll by your win rate per hour. (600 bb) / (4.5 bb/hr) = 133 hours. For the time to double your bankroll with a particular probability, solve this for n:

n*EV - sqrt(n)*SD*x = BR

where EV and SD are for 1 hour
n is the number of hours
BR is bankroll in same units as EV and SD
x is the number of SDs for the probability of doubling

x is from the normal distribution as follows:

84%, x = 1
90%, x = 1.28
95%, x = 1.64

Get other x values from Excel function NORMSINV(p) or a table of the standard normal distribution.

This equation says that even if you are x SDs below the average value of EV*n, you will still have won BR dollars.

Your BR is 600 bb, EV = 4.5 bb, and SD = 21.65 BB, so for a 90% chance of doubling, solve

n*4.5 - sqrt(n)*21.65*1.28 = 600.

That comes out to n = 226. You can solve this by trial and error, or use the goal seek feature in Excel.

The number of hours to be ahead is (x*SD/EV)^2. This comes from solving the above equation for n with BR = 0. You have a 90% probability of being ahead after 38 hours.

[doublesnapper]

Thanks a lot for a very clear explanation Bruce.

What level is the highest limit game, that you know of, that would still be reasonably loose for the 1.5 BB EV to hold for a solid player?. In other words, how high can I aim at with the proper bankroll?.

Best Regards.

DoubleSnapper

[TheLoser]

I have played as high as 100/200, people there are still crazy, and in the really high limits you then get rich people who don't care about the money so the sky really is the limit.

[AliasMrJones]

[ QUOTE ]
x is from the normal distribution as follows:

84%, x = 1
90%, x = 1.28
95%, x = 1.64


[/ QUOTE ]

I understand all of the above, but this. For a standard curve, 1 SD = 68% of outcomes, 2 SD = 95% of outcomes and 3 SD = 99% of outcomes. To get 95% confidence, why don't you use a multiple of 2 rather than the 1.64 you reference above? (and a multiple of 1 for 68% confidence, 3 for 99% confidence based on the % of outcomes each SD multiple represents?) TIA as this has perplexed me since reading your previous excellent post about SD.

[Big Dave D]

I think its unlikely that you will be able to continue to win 4.5 BB/hr for two table play. My feel, based on others empirical evidence, is that a number around 3 BB/hr is more likely.

gl

dd

[doublesnapper]

Thanks for your reply. That's my strong suspicion too. It'd be too easy if one could double on average every 70 hours.

I wonder about the results of solid players in 100-200 games and above. Do they still make 1 to 1.5 BB per hour?.

Best

[Big Dave D]

Not playing that high, Im not sure. I suspect that its very game dependent. For example, online the 50-100 and sometimes the 100-200 is notoriously weak on Ladbrokes. And sometimes you get "fish out of water" scenarios in the Stars game, such as short handed players ending up in a full game and visa-versa.

gl

dd

[BruceZ]

For a standard curve, 1 SD = 68% of outcomes, 2 SD = 95% of outcomes and 3 SD = 99% of outcomes. To get 95% confidence, why don't you use a multiple of 2 rather than the 1.64 you reference above? (and a multiple of 1 for 68% confidence, 3 for 99% confidence based on the % of outcomes each SD multiple represents?)

We want the 1-sided confidence interval here, that is, the probability of being no more than x SDs below the mean. The figures you suggest are for the 2-sided confidence interval, for the proability of being +/- x SDs from the mean. So instead of 68% for +/- 1 SD, for > -1 SD we want 1 - 16% = 84%. 16% is 1 tail. > - 2 SDs would be 1 - 2.5% = 97.5%. 1.64 SDs is +/- 90%, but > -1.64 SDs is 95%.

[AliasMrJones]

[ QUOTE ]
We want the 1-sided confidence interval here, that is, the probability of being no more than x SDs below the mean. The figures you suggest are for the 2-sided confidence interval, for the proability of being +/- x SDs from the mean. So instead of 68% for +/- 1 SD, for > -1 SD we want 1 - 16% = 84%. 16% is 1 tail. > - 2 SDs would be 1 - 2.5% = 97.5%. 1.64 SDs is +/- 90%, but > -1.64 SDs is 95%.

[/ QUOTE ]

OK, thanks. I thought it must have something to do with the no less than (one-sided) aspect. One more question. I have created a spreadsheet that computes # of hours to break even and computes worst case scenario at 10,50,100,200 hours, etc. And, with a bit of calculus, when the max loss occurs and what the max loss will be. But, for fairly typical numbers (SD of 10 BB and 1 BB/hr. win rate) it shows a max loss of about 100 BB. Standard rule of thumb is a bankroll of 300 BB is needed. Why is that?

Also, one of the reasons I began investigating SD, etc. is a recent string of bad cards that took me down about 80 BB. The number of hours and max loss amounts I experienced were almost exactly what my spreadsheet shows I should have seen given my actual numbers as shown in PokerTracker. Perhaps some validation of the theory?

Also, FWIW, in another thread someone mentioned that since SD, win rate, etc. doesn't change your play it isn't worth much. I very much beg to differ. It is crucial to determining what limits to play, bankroll management and, as was the case for me, how to determine when to become concerned (or as was the case for me when not to be concerned) about a losing streak.