RANDOM thoughts

[bugstud]

read the mid/high limit DERB thread lately?

[vinyard]

[ QUOTE ]

I understand your point in general, but it's relation to SNG poker is slim at best, complete gibberish at it's worst.

Whatever.

[/ QUOTE ]

[treeofwisdom7]

hey guys interesting post. i have been running very good with a 25% ITM and 10% ROI over 95 games.. i think this is good but is it enuf to tell if im a winning player or not?




AHHHHAAAAHHAAAAAAHAAAAA *do the raptor **GASP** * AHHHHAHHAAAHHHHHHHAAAAA

YOU CAN BE MY BABY IT DONT MATTER IF YOUR BLACK OF WHITE

[SumZero]

I think it was (or at least could become) a more constructive response to "Part-time SnG grinders" (thread link).

I mean even ignoring the amazing drjnightowl there were several posters who have a hard time understanding randomness.

And that isn't surprising seeing people in general have a hard time with probability. And not just random calculations (What are the chances of the flopped four flush giving me the flush be the river?) but especially the intuition to reason properly with math especially under uncertainty (and I think it is funny that Irieguy mentions "Fooled by Randomness" as that is on my queue of books to read and I'll probably get to it after HOH2 and HP6). I mean I post a little in General Gambling/Probability and look at two common questions people ask:

- Why doesn't a Martingale roulette strategy work (bet $1 on black, if you lose double your bet until you win and start over again)?

- The Monty Hall/Let's make a deal problem (choose from 3 doors randomly (one of which has a prize behind it), after you pick the host (who knows what's behind what door) will show you one of the rooms that you didn't pick that has no prize and then offer you to keep your pick or switch to the unpicked and unopened room).

The first is obviously a problem understanding how fast exponential growth is and figuring out how to calculate the expectation in the face of that. And what's worth even when people can't calculate the expectation they can't even inuitively reason why it doesn't work.

The second is but one of many examples that most people just don't get conditional probability and also can't logically reason the answer very well. I have two favorite examples of conditional probability that, when I ask them to many smart people, they can't figure out the right answer (or even worse "figure out" a wrong answer).

Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)

The second one of my questions (and I think I may be cribbing it from "There Are Two Errors in the the Title of This Book*: A Sourcebook of Philosophical Puzzles, Paradoxes and Problems" by Robert M. Martin which is also a fantastic read) ties directly in to what Irieguy was getting at with the coin-flipping analogy (although coin-flipping is a bad analogy because one really can "flip" coins in an unfair way as often coins don't flip but actually wobble which only looks like flipping and one can practice this). But first the question:

Question 2 (a different flavor of the false positive health test question):
Assume that we are on an Island with 100 taxis. On the Island 95 taxis are yellow and 5 taxis are green on the Island. Police know that eyewitnesses are 80% accurate (that is they will correctly identify the color of a taxi 80% of the time and the other 20% of the time they will say that the taxi was the opposite color from what it was - and that this eroor rate is idependent and unrelated to the actual color of taxi). There is a hit and run involving a taxi. The only eyewitness says that the taxi was green. What is the probability that the taxi involved was actually a green taxi?

The very high number of people who think that it doesn't matter if you switch in the Montey Hall problem because it is 50/50 that you'll win or that the answer to question 1 above is 5 or that the answer to question 2 is 80% is astonishing.

So to repharse Irieguy's analogy as it applies to SNG (and this is the important point):

So in SNG land imagine someone has done the heavy lifting of the math and figures out that the chances of a break-even player having a 15% (or better) ROI over 500 SNG is just 20%. Player X just finished 500 SNG and had a 15% ROI. Player X now thinks they are 80% likely to be a winning player. The biggest mistake here is that Player X isn't taking in to account the distribution of the population. The vast majority of SNG players are losing players (for the sake of argument let's say 95%). The average SNG player loses the rake. So player X isn't somehow picked from a uniform distribution that is as likely to be -100% ROI as +100% ROI but rather a distribution centered on -rake ROI that gets drastically less players the further you move from -rake ROI. This is now a conditional probability question just like question 2 above and actually player X is much more likely to be a break-even or losing player currently being misidentified by our "one witness" (the 500 SNG sample) then a true winning player being correctly identified.

Irieguy's secondary point:

"Furthermore, the most successful of the 'skilled professional' group will also be beneficiaries of randomness to a much larger degree than they would like to admit" is worth remembering too (and has Daniel Negreanu's name all over it, for one).

[valejo]

[ QUOTE ]
hey guys interesting post. i have been running very good with a 25% ITM and 10% ROI over 95 games.. i think this is good but is it enuf to tell if im a winning player or not?




AHHHHAAAAHHAAAAAAHAAAAA *do the raptor **GASP** * AHHHHAHHAAAHHHHHHHAAAAA

YOU CAN BE MY BABY IT DONT MATTER IF YOUR BLACK OF WHITE

[/ QUOTE ]

Based on the stated sample, there's 70.5% confidence that you are ROI >= 0.

[jcm4ccc]

[ QUOTE ]

The very high number of people who think that it doesn't matter if you switch in the Montey Hall problem because it is 50/50 that you'll win . . . is astonishing.



[/ QUOTE ]

Oh yes, let's discuss Monty Hall.

Because it is 50/50. Marilyn vos Savant was wrong.

[elrudo]

I think this little essay is brilliant.

However, there is a small flaw in it.
There would be some real lucky flipdonkeys who performed a 'magic 9' yet wouldnt claim to be a pro.

Not that the real pros would notice.
A lucky poker player

[skipperbob]

[ QUOTE ]
I am just trying to make sure there isn't some new nugget of knowledge buried in this one.

[/ QUOTE ]

Irie doesn't dispense knowledge in nugget-sized parcels; it's more like "pixie dust" [img]/images/graemlins/smirk.gif[/img]

[AleoMagus]

[ QUOTE ]
Because it is 50/50. Marilyn vos Savant was wrong.

[/ QUOTE ]

Given her assumptions, she was correct. it is NOT 50/50 if the host always offers the switch.

Regards
Brad S

[AleoMagus]

Very good post.

I actually doubt that many who should be paying attention to this will really get it. Bayesian reasoning is just so counter-intuitive to so many.

Regards
Brad S