Too Many Aces?

[SlowStroke]

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Post in the statistics thread, and wait until you have at least 10k hands or else people will tell you to wait until you have 10k hands.

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Thanks. I debated where to post this.

The Internet Forum, or Variance, or Small Stakes No Limit, or Probability.

By the way, I've now been dealt 35 AA in 3877 hands.

The heater continues......

[MameFan]

This is all well and good. My question is... does anybody have any stats about AFTER the first two cards. Is the flop distribution normal? Do the turn cards and river cards appear in a random order?

[FastEddie4269]

You got pocket pairs 195 times.

195 divided by 13 (number of possible pocket pairs)= 15
3076 hands divided by 220 = approx 14

Thats not much of a variance. As far as aces popping up disproportionately, I wouldn't think twice about it. There's some poor sap out there who's played 3k hands and only got AA's 7 or 8 times. Just be thankful you aren't him.

[betadecay]

why do you have to rub it in, you JERK!

[01001011]

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Why on earth would you use simulation for this?

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Maybe because it's the easiest way to get a feel for the answer when you are unsure of the math? It's only about 20 lines of code.

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This follow a poisson function with a lambda of 1/221. All of your values should be easily calculated from that.

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What you need is the expected value and the expected standard deviation. I don't see what that has to do with a poisson function. See calculations below.

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And some of you may want to pick up a statistics book if you are saying 4 SD is surely relevant when:
A) Not looking at a normal function
B) Measuring statistical beliefs AFTER knowing the results. You test a hypothesis THEN measure, not measure then make a hypotheisis.

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A) As long as the sample size is big enough, independent events with a constant probability approximates a normal curve. So using standard deviations are perfectly valid. Big enough depends on the probabilities. You can use it when: n*p>5 and n*(1-p)>5, where n is the sample size and p is the probability.

B) If you're uncertain about how likely something that has already happened is, you calculate it. I'm not sure what you mean by "measuring statistical beliefs", but you can certainly find the exact probability. This has nothing to do with hypothesises.

In this case, the calculations work out like this, using the latest data he gave:

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By the way, I've now been dealt 35 AA in 3877 hands.

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p = (4/52*3/51) = 0.004524887

Big enough sample size to approximate a normal curve? Yes, since 3877*p>5 and 3877*(1-p) > 5.

mean = n*p = 3877 * p = 17.543
stddev = sqrt(n*p*(1-p)) = 4.179

(35-17.543)/4.179 = 4.177

4.177 standard deviations away translate to a probability of 0.000015, or one in 67708.

In other words, about as likely as having suited hole cards and flop, turn and river of the same suit. Clearly within the realms of probability, so you can't say anything is wrong with the shuffle based on this.

[Sponger.]

Once I got KK something like 15x in 400 hands. Play long enough and weird stuff happens.

[Our House]

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Once I got KK something like 15x in 400 hands. Play long enough and weird stuff happens.

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Or, get a forum full of enough people who don't even have to play a long time.

[MNpoker]

Pssttt.... Quick lesson on the Poisson function (and how you approximated it)

The possion function is used when event A has a independent random chance of happening with a expected value of X.

First you say we need to find expected value and ignore my 1 / 221.
What do you think 4 / 52 * 3 / 51 =?

Next you go through all this junk to find the ST Deviation.
In a poisson function the Variance = The Mean
(Look at your SD and Mean)17.543 and 4.179
4.179 ^ 2 = 17.46 (or approx 17.543) - So yes your approximation came very close.

Next you find the Z score = 4.177 (or 1 in 67,708 chance)
This is where your analysis sort of falls apart.
You Approximation to the Normal IS TRUE BUT not in the tails. At 4 Standard deviations we are way into the tails.

The actual chance of 35 AA's (or more) in 3,877 hands is 1 in 13,511.

Note: If you are looking at say 2 SD you would be OK with your approach.
Say you want to know the chance of 26 or more AA's in 3877 hands.
Using your approach:
Mean = 3877 / 221 = 17.543
SD = [3877 * 1/221 * (220 / 221) ] ^.5 = 4.179 (same as you did)
Now your Z score is (26 - 17.543) / 4.179 which gives a prob of .0215
Using the Possion (non approximated) you get .02148

Which IS very close, and your method works quite well.


I know you don't seem to trust me on this so feel free to ask someone.
But to say you don't see what is has to do with the poisson function = you don't understand the poisson function.