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Can Someone Dumb Down 'Expected Value' for Me?

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TheDillon__

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Ahoy there!

So I stumbled across this article from Forever Jobless today - and I can't seem to wrap my head around the idea (I'm still waiting for my coffee to cool off.)

Can someone dumb it down a bit for me?
 

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Vigilante

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What do you struggle to understand?

Do you not understand the math? The general concept? How to apply it?

I personally thought he broke it down pretty nicely and the math all made sense to me. Applying it and making it intuitive is a lot harder, which I would understand, but I don't think I could explain the math or concepts better than the article did. It was pretty comprehensively written.
 

G-Man

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TLDR, but it looks like it's just and un-discounted future value calculation.

Value each possible outcome.
Multiply value of each possible outcome by relative probability.
Add.
 

ChrisJHarrington

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Basic mathematics.

You have a 30% chance of making $100 or a 70% chance of losing $50.

(.3*100)+(.7*-50) = -$5.

The expected value of this game is -$5. Your average score, if you continue to take the 30% chance to win $100, will net you a -$5 return.
 

Jon L

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if you take risks that have better than even odds of success over and over, you will end up coming out ahead in the long run. You will also do better than someone that doesn't take calculated risks. (There's more to it than this, but this is, in a nutshell, is what he's saying.)

This is what casinos do ... we are their calculated risk. They know that some people might win more than they spend, but overall, the casino makes the money, the customers don't.
 

Jonathan Polley

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Ahoy there!

So I stumbled across this article from Forever Jobless today - and I can't seem to wrap my head around the idea (I'm still waiting for my coffee to cool off.)

Can someone dumb it down a bit for me?
I could be wrong on this, but I think it works pretty much the same way it does in an online casino if you are bonus bagging. (A practice now much harder and barely worth while)

Lets say you put $100 down as a deposit and the casino matches that deposit and gives you $100 as a bonus. You now have $200 dollars in your account. The only problem is that it is locked there until you have wagered 20x your original deposit.

You can wager on any game. It could be a complete game of chance such as the slot machines where you could blow all your cash in a few minutes and walk away with nothing. Or you could win big. In short you are actually gambling and the Expected Variance (the amount of money you expect to earn within a distribution curve) is huge.

But if you play blackjack (and follow perfect strategy) and wager $1 a hand for 2000 hands you can expect to lose about $15 but still have $175 dollars in your account that you can now withdraw. The EV (Variance on how much you will lose or win) is very small as this is a safe strategy. And it can be easily predicted with maths.
If you decide that playing 2000 hands of blackjack will take too long then you could wager $5 a hand. The EV will be much larger as you are playing fewer hands and wagering more. Random chance has a bigger effect. You could end up losing all of your deposit and come away with nothing. Or you could end up making more money thanks to your risky strategy. But the variance from the mathmatically predicted outcome is likely to be larger.


Source: I used to earn about a thousand dollars a month at online casinos by taking advantage of their sign up offers before they got wise to the practice and made it much harder to game them
 

eliquid

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Raoul Duke

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Maybe these can help. Reading about something, helps me learn. Actually hearing it explained by the originator, helps me even more. This might be the case with you as well.

 
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TheDillon__

TheDillon__

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Nobody liked this yet?

It was by far the single most awesome/best response to a question ever on this forum
Haha, agreed. My human ability to be oblivious strikes me once again. Thank you @Vigilante.
 
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TheDillon__

TheDillon__

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Maybe these can help. Reading about something, helps me learn. Actually hearing it explained by the originator, helps me even more. This might be the case with you as well.

Welp, there goes my afternoon. Thanks friend!
 

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amp0193

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TLDR, but it looks like it's just and un-discounted future value calculation.
It's not TL, and DR should stand for Definitely Read that shit.

That article is one of the best on the internet, as far as I'm concerned.


It changed my world when I read it 3 years ago. It's worth making it to the end.
 
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TheDillon__

TheDillon__

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It's not TL, and DR should stand for Definitely Read that shit.

That article is one of the best on the internet, as far as I'm concerned.


It changed my world when I read it 3 years ago. It's worth making it to the end.
It seems very lucrative! I'm not sure why I'm having a hard time comprehending. I'm going to spend my day with this to ensure I can get a handle on the concept.
 

amp0193

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It seems very lucrative! I'm not sure why I'm having a hard time comprehending. I'm going to spend my day with this to ensure I can get a handle on the concept.

You have a 3 sided die. It looks like a pyramid.

2 sides say "Win $1".
1 side says "Lose $1".


Should you roll the die?


If you roll it one time, you might lose a $1.

However, if you roll it 100 times, you're guaranteed to come out ahead. Way ahead.


Make decisions that have a greater than 50% chance of success (while taking into account the magnitude of those decisions), over and over, and you will come out ahead.


Don't be afraid of risk, if there is a huge upside to taking that risk, and a reasonable chance of success. You might fail this time, but you'll win in the long run.
 

G-Man

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It's not TL, and DR should stand for Definitely Read that shit.

That article is one of the best on the internet, as far as I'm concerned.


It changed my world when I read it 3 years ago. It's worth making it to the end.
The presidential website story made it worth the read. I guess thinking like this is so much a part of my job that I don't see the revelation... it's definitely super important though.
 

ksc23

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Here's a demo of how to calculate the EV of purchasing a lottery ticket:

Expected profit from lottery ticket

A basic grasp of probability is a prerequisite to understanding EV.

A couple of things I'd add are:

- Higher probability does not equal Higher EV
- An important property of EV is that it is additive. The EV of 10 different decisions is the sum of the individual EVs of each decision.
- EV does not correlate to an ACTUAL outcome, it's the AVERAGE expected value over a number of trials (if interested look up variance and standard deviations)

It's been a while since I've seen 'expected value'... the word brings up memories of many nights playing poker :)
 

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