Online Poker Forum at Full Tilt Poker

HuJwang · Posted: Thu Nov 30, 2006 5:42 pm Post subject:

i don't know enough aobut statistics to really fully answer that but i do know that the statistical error on an event is equal to the square root of the number of times it has occured.. i'll try to explain what that means

let's say you play 1000 heads up SNG's against an opponent whose skill level is the exact same as yours. so therefore you expect to win 500 times. the square root of 500 is about 22.

the statistical error (also called standard deviation) is a range that a value should fall under 68% of the time. so 68% of the time, in those 1000 matches, you will win between 478 and 522 matches, which is a pretty small percentage error.

two standard deviations covers about 95% of cases. 95% of the time you win between 456 and 544 matches.

now if you played only 100 matches, and expect to win 50. the standard error is the square root of 50 which is 7 matches. 95% of the time you win between 36 and 64. 5% of the time you will win more than 64 OR less than 36 matches.

this 95% is the same number that news reports about polls are talking about. they'll say something like, "Person X is favoured by 58% of likely voters, to within 6 percentage points 19 times out of 20". this means that the 6 is twice the statistical error.

i don't know how useful this is, or whether i explained it very clearly, but maybe it'll be of some interest Razz

deadmoney314 · Posted: Thu Nov 30, 2006 5:54 pm Post subject:

I guess the basic question it looked like Gypsy was trying to ask was already answered, and it is of Risk of Ruin from the first article I linked. I was merely going deeper into the interesting combinations you can add to RoR calculations. The mathematics of life are so much more complex than any theoretical construct.

Here is basic RoR from the article that you can plug your own numbers into:

(SD - WR)
------------- ^n
(SD + WR)

SD = Standard Deviation
WR = Win Rate (if you use per hour for SD make sure it matches for WR)
n = Total bankroll divided by SD

Jobe Gilchrist · Posted: Thu Nov 30, 2006 5:54 pm Post subject:

HuJwang: is that only in an even-chance event? Because obviously, if you were 99% to beat the guy heads-up, the error isn't the square root of 990. How does the calculation change as the probability changes?

deadmoney314 · Posted: Thu Nov 30, 2006 5:56 pm Post subject:

I just realized that we still want to know the probabililty that our recorded win rate is accurate based on number of hands played. Hmmmmmmmm, back to the chalkboard.

fire_eyes_2k · Posted: Thu Nov 30, 2006 9:01 pm Post subject:

Man reading this thread makes me feel pretty stupid, so I'm going to try and make it more complicated... The various formulas presented above by dm & others appear to be adaptations of "basic" game theory (which is anything but basic) however surely the precise model required depends on the game, be it poker, blackjack, no-limit or fixed-limit.

As for the infinite monkeys, infinite typewriters problem, I'm told that they would probably write the complete works of shakespeare in spanish before they did in english or any other language as that has the most economical structure in terms of letters per word/words per sentence/chapter and so on, thus making the compilation shorter. So I can only assume that the necessary sample size would depend on the game, no?

And back to gypsy's can you make the correct decisions at the wsop and go out whilst jamie gold goes on to make the wrong decisions and win...surely this has been proven correct by the success of Gold, Nobles, Molina etc. whilst the pros have generally found the ME much harder to crack the first 75% of the field. And does 'making the correct decisions' refer to cards or opponents, as playing your opponents will be a strategy with much higher variance surely.

Time for a beer.

deadmoney314 · Posted: Thu Nov 30, 2006 9:51 pm Post subject:

deadmoney314 · Posted: Thu Nov 30, 2006 10:13 pm Post subject:

I think I butchered the explanation but this should help Wink

inabunnysuit · Pair Joined: 08 Aug 2005 Posts: 24

Ummm, yer math looks.... unclean. I'm not saying it's wrong, but you're getting fuzzy on where stuff is coming from (sez the pot to the kettle). Realize also that you're probably not playing the same as 100k hands ago (not if you're improving, anyway), and they're not either, so that part of the record is irrelevant. I stole that one from someone else I read tonight.

Try some of these instead. Written for the layman, they're not Fibonacci neat, but clever in their own pretty way.

http://www.math.sfu.ca/~alspach/pokerdigest.html

30 and 38 frame the 'expectation question"

Everyone should read 82.

84 answers the "lucky" question.

Everyone should thank Dr. Alspach.

PS. 25 (and most things involving natural logs) make a great basis for party tricks.

HuJwang · Posted: Thu Nov 30, 2006 11:00 pm Post subject:

Jobe Gilchrist · Posted: Thu Nov 30, 2006 11:15 pm Post subject:

Thanks man! All those terms sound familiar from college stats. Time to revisit that stuff, I think.

draginrat · Pair Joined: 01 Apr 2006 Posts: 31

OK, after all that is said and done, I still faill to see where it is relevant.

I suppose in my very own little mind, I could make a case for the "It's a scam" mentality crowd. Except even in my very own little mind, I can't find the logic behind any of these scam theories.

I understand that there are people out there that constantly have a bunch of numbers crunching in the heads, and can most likely give you a statical number of what your chances are with any given pocket cards, and I have no reason to doubt them. The numbers (as I see them) just do not work for me.

I don't believe I can count on most of the amatuer player I play against to play by the "rules". There doesn't seem to be any rhyme or reason why someone plays or doesn't play any given hand. I find it hard to "read" another player in a live game after only a few hands, and impossible on-line.

I have no delusions of being a great poker player. I like to think that I am not a terrible player, but am not quite convinced of that either. I give some thought to how I play, but do not take hours to ponder every move I make at a table, be it B&M, or on-line.

What I can not understand is what I have to believe is my terrible luck. I play very tight. I use to play very tight agressive, but that has not worked for me.

I don't like to lose, but can understand when I lose because I made a bad choice, or just got out played. I do at times go all-in with KK and run head on into AA. Such is poker. Sometimes I will just get a wild hair and try to bluff with 72 off suit, and again run up against AA. Oh well. "my bad". Playing bad poker is not my problem. I don't play bad very often, and when I do, I don't get upset when I get my lunch handed to me. But, my incredable bad luck, (as I see it) really amazes me.

I would say that better than 85% of the time I go "all-in", or call a large or all-in bet, I have the overwhelming dominate hand. KK vs J7 offsuit. or AK suited to A 3 offsuit. 90% of the time, I lose. There are times when 3 or more of us are all-in, I have the dominate hand, and only one othet player is still alive. Only a single card remaining in the deck can save him, (I know from all the other exposed cards) and don't ya know the bastard pulls it.

I do not know how different to play. If I have KK and the flop is KT7, I just can't fold my hand when someone puts me all-in. As is most likely to happen, the other guy is holding 64, and will pull 8 on the turn, and a 9 on the river. Don't know how I can play that differently.

Anyway, I know there is no solution to my problem, just venting a little.

I no longer worry that I can't shuffle chips. I can't see me getting to the final table on WSOP and looking foolish on TV.

Ken Gasbarri

deadmoney314 · Posted: Fri Dec 01, 2006 9:55 am Post subject:

deadmoney314 · Posted: Fri Dec 01, 2006 10:06 am Post subject:

Oh Jobe, if you hadn't figured out the answer to your question already the wikipedia def has the SE for trials that have a probability attached. See link above:

SE = [p(1-p)/n]^0.5

p: probability
n: sample size

JokerStars · Royal Flush Joined: 28 Feb 2006 Posts: 720

The first post sounds like my life story.

(YEAH RUNNING PRETTY BAD Smile

)

griffinlord · Posted: Fri Dec 01, 2006 1:30 pm Post subject:

I won't repeat the formula's for SEs but there is one that needs to be added to the list:

w = t * SE

Where with very large sample t is essentially equal to z, so using a z to approximate, as others have been doing, is fine.

The answer to gypsy's question is, I think, "w" which is the width of the confidence interval estimating your win rate.

We've already established that as the number of hands goes up, the SE decreases and therefore so too does the width of the confidence interval.

Using approximations: when your SE = 1/2 your observed win rate will usually be within +/- 1bb of your actual win rate (z ~ 2). When SE=1/4 your observed win rate will be within +/- .5 of your theoretical win rate.

So, when does SE = 1/2?

When sqrt(n) = 2*SD where n= # of hundreds of hands.

that means n = 4*SD^2 or 4*variance

With SD = 12; n = 4 * 144 or 576 hundreds of hands (57,600 hands)

With SD = 10; n = 4 * 100 or 40,000 hands

The bad news for low limit players is that all the fish increase your variance (SD) meaning that you could be playing for a very long time before you know your win rate with any degree of accuracy.

If your SD = 15 you need 4 * 225 * 100 = 90,000 hands to estimate your win rate to +/- 1bb/100.

But, if you believe that you should be beating the game for 4bb/100 and you have an SD = 15 you may be satisfied if w = 2 which would only require 22,500 hands. As long as your observed win rate over those 22,500 hands was between 2bb/100 and 6bb/100 it is plausible you are a 4bb/100 winner. (Although if your observed win rate is 2bb/100 you could be anywhere between break-even and +4bb/100.)

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