Romes

Joined: Jul 22, 2014
• Posts: 4123
March 16th, 2017 at 9:25:23 AM permalink
Quote: ZenKinG

...I think the problem people are missing here is exactly what Grosjean said. The numbers 'fix' themselves in the denominator and NOT the numerator. What happens is just because you won 5k quickly in 5 hours where you should have won only 500, it doesnt mean you're all of a sudden now going to hit a losing streak to make up for it. What happens is that your wins will continue to hit the \$500 EV mark consistently enough to 'dilute' the sample size overtime and thus ending you with the original 100k EV.

Take a 50/50 quarter for example. You might flip 100 heads and 20 tails. The gamblers fallacy argument is that tails will eventually hit a 'streak' to make up for those 80 lost tails and that is purely incorrect. What happens is you start hitting the 50/50 EV and it 'dilutes' the sample size enough to where now the overall results will = 50/50...

You're trying to reconcile the apples and oranges being discussed.

With the coin flip... If you flip 90 heads and 10 tails in the beginning, that's just variance. AS you continue to get more flips and move towards the long run your ups and downs will be "random variance" from that one particular point in time. However, on the grand scale of "The Long Run" (let's say 100,000,000 flips) your numbers WILL balance out to 50/50. The TWO effects this has is 1, as you said, it dampens the previous variance spike (that 90-10 spike now doesn't look like a spike at all), and 2 you will SPREAD OUT OVER THE COURSE OF 100,000,000 FLIPS see more up and down spikes that will "correct" (hate using that word) the data as you described. You will NEVER be "expected" to win or lose more/less, but over the long run these tiny infractions will balance out. Basically, the math will work itself out so long as it's a true random coin flip.

Read my post above, with the images... I'm saying the same thing yet another way.
Playing it correctly means you've already won.
AxelWolf
Joined: Oct 10, 2012
• Posts: 12606
March 16th, 2017 at 1:01:59 PM permalink
Quote: ZenKinG

Quote: TomG

Disagree. Given enough time, Expected Profits will converge with actual profits. Consider this scenario: someone who has an Expected Profit of \$100 per hour. In the first hour of play they earn \$100,000. Then every hour thereafter they earn \$100. What is their hourly rate after x number of hours? Once x gets big enough it will eventually be \$100.00.

Obviously none of us will be able to play cards for 100 million hours. But it does show a few things:
-we can enjoy our big wins for exactly what we won even with the understanding we will regress to the mean, because:
-we can regress to the mean without under-performing. And also:
-given the flimsy nature of these ideas it could just be ZenK searching for any excuse not to further his career

TomG has it right and it's basically what Grosjean said as well. You're never expected to be 'due' for a loss if you have an edge regardless if you had positive flux or negative flux. The EV is always the same per session. If you have a \$100 an hour play, your EV every session is \$100 an hour and you're 'expected' to make that \$100. Of course that almost never happens but for theoretical purposes that's how it works and you're 'expected' to make that \$100.

I think the problem people are missing here is exactly what Grosjean said. The numbers 'fix' themselves in the denominator and NOT the numerator. What happens is just because you won 5k quickly in 5 hours where you should have won only 500, it doesnt mean you're all of a sudden now going to hit a losing streak to make up for it. What happens is that your wins will continue to hit the \$500 EV mark consistently enough to 'dilute' the sample size overtime and thus ending you with the original 100k EV.

Take a 50/50 quarter for example. You might flip 100 heads and 20 tails. The gamblers fallacy argument is that tails will eventually hit a 'streak' to make up for those 80 lost tails and that is purely incorrect. What happens is you start hitting the 50/50 EV and it 'dilutes' the sample size enough to where now the overall results will = 50/50.

Hope this makes sense. I believe I have it right now.

It is what it is. Less talking, more playing.
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
mamat
Joined: Jul 13, 2015
• Posts: 363
March 16th, 2017 at 4:24:44 PM permalink
Here's a simpler summary of misleading EV.

(1) In 100,000,000 hands, you are only expected to see 4,000 zero-crossings (for a Bernoulli coin flip, sqrt(n/6.28)).
Chances are you are in a 25,000 hand hot-streak (or cold-streak) and won't be at EV....either order (10,000) units up or o(10,000) units down.

EV compared to wins vs. total money bet will tend to coverage,
but most of us live in a world with real dollars. o(10,000) units up/down for \$25 units is +/- \$250,000 above or below EV,
which is sizable for most people.

We mostly don't care that in 100 million hands, we have bet \$2.5 billion...and that \$250,000 is 0.01%.

(2) If you record your daily bankroll and project your future bankroll from the "peaks" or the "lows"...using EV from those points, chances are those projections will not be as good as ones from the center.

It's how you draw the "observation point" for calculating future bankroll.
jerijerr
Joined: Mar 19, 2017