Poker Academy $150 Freeroll

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64o

72o is called "The Hammer".

64o is called "The Vannina".

Don't question it.

Collusion

Ever wonder if cheating via collusion happens? How about in live play? Take a look at Jathan's post.

Stacked

I rented Daniel Negreanu's Stacked tonight. It is very pretty, but a little slow. It feels like it could use an editor to remove all the pauses between the dialog and action like they do in the movies. It also has bugs.

I was sitting in a NL chash game. I player before me raised $40 into a $400 pot. I reraised $220. He came over the top for another $30.

I think I'm getting a bit of motion sickness from the camera spinning around the action.

If you are going to add all of those fancy 3D graphics, at least give me the option to sit still in my seat and control what I look at.

And get a faster dealer.

Table Joke #1

Once I thought I had the nuts, but it turned out to be a legume.

The Expensive Business of Punishing Draws

You play in a regular game with a guy named Chasey McChase-Chase. Chasey has a very profitable habit of calling any bet on the flop with a flush draw. You also have an absolutely reliable tell on Chasey where he scratches his right ear everytime is only has a flush draw. So every time you have a hand that beats a flush draw, say one pair or better, you jam and Chasey calls. You know that Chasey gives will give you a lot of money in the long run, but what sort of damage might he do in the short run?

Let's make some simplifying assumptions:
- Chasey only wins when he makes the flush.
- Chasey always wins when he makes the flush.
- Chasey always has nine outs to make his flush.
- Preflop bets are negligible in our calculations.

Let's also assign some real dollar values to this game. At $1/2 both players should be sitting with around $200 (100 big blinds). Since you know the suites of Chasey's cards and your cards, Chasey has two chances to draw one of nine matching suites out of 45 cards. This gives you a 36% chance to lose $200, but a 64% chance to win $200.

In Gambling Theory and Other Topics Mason Malmuth provides some equations that tell you how much you stand to lose given a positive expectation and a standard deviation.

I am going to define some symbols to use in these calculations.

Let X be a set of values and x_i be an element of that set.
Let X² be a set consisting of x_i² for all i.
Let &mu(X) be the mean of a set.
Let &sigma be the standard deviation (this is a standard symbol for this value).
By definition &sigma² is called the variance.

&sigma² = &mu(X²) - &mu(X)²

This is often described as the mean of squares minus the square of the mean.

I could probably write up a more detailed primer on standard deviation if anyone is interested, but for now I am just going to use this definition to calculate the standard deviation of our bet above.

To calculate the mean of squares we square each value and take the average of them all. Let's pretend that we have 100 samples with a perfect distribution of 64 values at +200 and 36 values at -200. &mu(X²) = 0.64*200² - .36*200² = .64*40000 - .36*40000 = 40000.

To calculate the square of the mean we first have to calculate the mean. &mu(X) = (64*200 - 36*200)/100 = .64*200 - .32*200 = +56. You may recognize this as the EV calculation. &mu(X)² = 56² = 3136.

Therefore the variance is 40000-3136=33136 for a standard deviation of 182.

Now let's define some more values:
Let N be the number of times you encounter this situation.
Let UL be the upper limit of your losses to Chasey.
Let K be a "confidence interval". This is the number of "standard deviations" away from the expected value you are measuring. When K=3, there is a 0.3% chance that the actual amount he wins will be more than the amount listed. If K=6 we would say that we have a "six sigma" (6&sigma) confidence interval (which is pretty damn high confidence).

This equation provides the probable maximum amount Chasey can win from you using variance given that he loses 56 on average with a standard deviation of 182.

UL = EV*N + K*&sigma*sqrt(N)

And the results...

	k=1	k=2	k=3
N	32%	4.6%	0.3%
1	126.00	308.00	490.00
5	126.96	533.93	940.89
10	15.53	591.07	1166.60
25	-490.00	420.00	1330.00
50	-1513.07	-226.13	1060.80
95	-3546.08	-1772.17	1.75

Even after 25 times you encounter this situation, there is a very realistic chance that your friend will be up on you for over 650 big blinds! The odds will eventually catch up with him. At three sigmas you break even around the 95th trial. How many hours would you have to play before you can expect this particular move to become +EV? Say that this particular situation occurs once every thirty hands. At two minutes per hand that averages to one chance an hour. You play every week for about 4 hours with Chasey. You might have to suffer bad beats for six months before you finally break even. It could possibly be even longer. Would you be able to keep making this correct play and lose month after month after month? Personally, I do not think I would be able to keep the faith. Actually I am certain that there are already plays like this that I do not make as often as I should for fear of bad beats. Somehow I need to let go of those silly superstitions.

Alan's Rule #3: When in doubt, raise.

It has been a while since I have written about one of my rules. I've been putting this off because I feel like it is kind of smarmy. I had come up with two rules that I was pretty pleased with and decided that I was going to make a set of ten. All of the poker books I was reading said that aggression was a key component of Hold'em strategy and so I decided to tag along.

This is a simple idea that you probably already know. If you think there is a decent chance that you are ahead, you should bet and try to take the pot. Maybe you will get a 2nd or 3rd pair to fold.

I am very guilty of not following this rule in the past month or so. I seem to have turned into a bit of a rock. When I made this rule, I had made a table of the chance that an opponent had paired the board. I used these percentages as guides on how often I should try to take the pot with a high card.

This tables shows the chance that at least one of opponent paired a flop that you missed. This assumes a flat distribution of your opponents hands. You might be able to reduce this if you can narrow your opponents' possible hands.

# opponents	p(top pair)	p(2nd pair+)	p(3rd pair+)
1	0.124884366327	0.241443108233	0.349676225717
2	0.238914585261	0.432231659799	0.586157598184
3	0.342584027135	0.581247270682	0.742895252028
4	0.436386062288	0.696148934214	0.844482981714
5	0.520814061055	0.783490738550	0.908704584407
6	0.596361393771	0.848833623762	0.948183683042
7	0.663521430774	0.896851178567	0.971696969729
8	0.722787542399	0.931429476661	0.985205234176
9	0.774653098982	0.955760952685	0.992650342139

This does not take into account pocket pairs or draws to monsters, but it does provide a very nice rule of thumb for how often your naked ace might actually be ahead.

Things get better if the board is paired.

# opponents	p(trips)	p(offpair)	p(trips+off)
1	0.0841813135985	0.124884366327	0.203515263645
2	0.164662349676	0.238914585261	0.372466571356
3	0.241443108233	0.342584027135	0.511455149129
4	0.314523589269	0.436386062288	0.624654565794
5	0.383903792784	0.520814061055	0.715831594346
6	0.449583718779	0.596361393771	0.788367073267
7	0.511563367253	0.663521430774	0.845276767851
8	0.569842738205	0.722787542399	0.889232231529
9	0.624421831637	0.774653098982	0.922581667198

Remember, a lot of players should be afraid to call with 3rd pair. If you bet against them there is a very good chance you will take the pot. If they figure out what you are doing then even better because then they will start calling down your TPTK with utter crap.