Some basic questions on winrate probability

Ok I am really trying to understand this probability stuff, so hopefully you guys can help me out. I have questions but I want more than just answers, I want to know HOW you calculate this so I can do it for myself in the future.

First, over the last 90,000 hands I have run at 1.7bb/100(8 tabling, though that doesn't matter). I have a standard deviation of 15.6. I am supposed to put in 40k hands to meet my goal next month. What are the chances I run:

-0bb/100
0-1bb/100
1-2bb/100
2-3bb/100
3-4bb/100
+4bb/100

Now I also had a little over 100,000 hands before this at about 1.5bb/100, but that database is lost. Let's assume my standard deviation was the same, so my total for 200,000 hands is 1.6bb/100. How drastically does this change the answers above?

Thanks for any help in advance

Jonny C

[BruceZ]

[ QUOTE ]
Ok I am really trying to understand this probability stuff, so hopefully you guys can help me out. I have questions but I want more than just answers, I want to know HOW you calculate this so I can do it for myself in the future.

First, over the last 90,000 hands I have run at 1.7bb/100(8 tabling, though that doesn't matter). I have a standard deviation of 15.6. I am supposed to put in 40k hands to meet my goal next month. What are the chances I run:

-0bb/100
0-1bb/100
1-2bb/100
2-3bb/100
3-4bb/100
+4bb/100

Now I also had a little over 100,000 hands before this at about 1.5bb/100, but that database is lost. Let's assume my standard deviation was the same, so my total for 200,000 hands is 1.6bb/100. How drastically does this change the answers above?

Thanks for any help in advance

Jonny C

[/ QUOTE ]

This post (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Board=probability&Number=192 2208&Forum=,All_Forums,&Words=&Searchpage=0&Limit= 25&Main=1921919&Search=true&where=&Name=197&datera nge=&newerval=&newertype=&olderval=&oldertype=&bod yprev=#Post1922208) should tell you everything you need to know to calculate this.

[BigBiceps]

I am too lazy to compute your intervals (I actuallly would have to look up how to do it, because I forgot). Anyhow, here is a basic summary:

n = 2000 (sets of 100 hands)
m = 1.6 (mean big bets won per 100 hands)
s = 15.6 (standard devitions in big bets per 100 hands)

95% CI = m +/- 1.96 (s/sqrt(n))

So 95% of the time your next sample set of hands will be between [0.91 - 2.28] big blinds per hour.

You can easily infer that the chance you will be >3 or <0.5 will be less than 2% each.

All of this is of course assuming that you are playing the same, your opponents are playing the same, and any and all other underlying conditions have not changed.

[BruceZ]

[ QUOTE ]
I am too lazy to compute your intervals (I actuallly would have to look up how to do it, because I forgot). Anyhow, here is a basic summary:

n = 2000 (sets of 100 hands)
m = 1.6 (mean big bets won per 100 hands)
s = 15.6 (standard devitions in big bets per 100 hands)

95% CI = m +/- 1.96 (s/sqrt(n))

So 95% of the time your next sample set of hands will be between [0.91 - 2.28] big blinds per hour.

[/ QUOTE ]

That is the correct 95% confidence interval, but it is big bets per 100 hands, not big blinds per hour, and it doesn't mean that 95% of the time his next sample set of hands will be in that interval. For that to be the case, his win rate would need to be known exactly. What it means is that if his win rate were 1.6 bb/100 hands, then his results would fall in this interval 95% of the time. Most people are misled about the meaning of confidence intervals.

Also, the OP cannot compute the probability that his results will fall in various intervals unless he assumes a particular win rate.