Would You Quit, or Not?

This is a thought I've had for a long time that I'd like to discuss. It sparked just a bit in the VP thread about cycling 4 of a kinds... but I'll rephrase for this thread. I'm really hoping to hear from Mike, and our great math minds, as I feel this poses a good theoretical discussion and would love their feedback.

Generic Scenario - Say you have a time constrained AP play, albeit a day, week, etc. You figure out that for this play, if you play it the fastest/best you can for the time it's allowed that your EV should be X, plus or minus SD. So let's say you're 1/5th the way through the play, and you're running great... Up X + SD. You know from the math that this is basically the best you could possibly do on this play, so continuing to play any more would (in theory) just bring you back more towards EV.

This crosses near a fine line of "the gamblers fallacy" I assure you I'm aware, but it always makes for a fun theoretical discussion. It's like saying I'm gonna play 1,000,000 hands of blackjack with an average edge of 1% and a $100 avg bet. So after 1,000,000 hands I'll expect to make $1,000,000. Let's say in the first 200,000 hands you're up $1,500,000... Let's also assume you're never playing the game of blackjack again when you hit 1,000,000 hands (like when promotions run out). The "long run" numbers state that even with your standard deviations by the time you hit 1,000,000 hands you're going to be DOWN from where you are now. So why would you keep playing?

It's a double edged sword:
1) You're playing with a 1% advantage, starting right now, so why couldn't you make more money?
2) You're looking at the LONG RUN of the play, in which all of your individual sessions are from the same bankroll, making it essentially 1 big long session.

I'll try to sum it up, but again, I'll pose 2 more arguments. Let's say you're playing the same VP promotion the OP was. If you cycle through all 13 different quads you get a bonus. Pass the fine tune details (which you can see in that thread if you really want) the OP's EV was about 40/hour. IF this had been a 24 hour promotion (it's not, but this is an example) then the OP could have said "My EV for the ENTIRE promotion, playing all 24 hours, is $960 plus or minus some SD." So, my question is again... If the OP is lucky enough to hit a royal, or hell 2, in the first few hours and he's now up about $2500... Why on Earth would you keep playing? Some responded with "It's still an advantage, why not?" But I say... You figured your EV for the 24 period. This is essentially 1 big session and you're up way over your EV and SD... playing more will only result in putting more hands in, aligning you more and more towards your previously calculated EV. Thus, you'll LOSE money if you keep playing, even if the play has an advantage!

Question Time
1) In the blackjack example, after 200,000 hands if you're up 1.5 million... Would you continue to play? Remember after 1,000,000 hands you're never playing blackjack again.

2) In the VP example, assuming the 24 hour promotion... If you're up $2500 in the first 3 hours due to some right side variance, would you continue to play?

Assuming that it would necessarily swing the other way is just as much Gamblers Fallacy as assuming that, if you were down, you would necessarily eventually catch up. AP is AP.

tl-dr will try to read later, but ...

I wonder if you are hung up on one fallacy, and that is that 'regression to the mean' relates to actual dollars of EV, whereas in practice it only means the percentages will fall into line.

[# 1]so if you are up [or down] $1.5 million you can expect the cards to have no knowledge of this! If you have a 1% advantage, then for another 800,000 hands, you probably will add to it. However most likely your results will fall more in line with normal expectations by percentage. I've made this comment in the past on some of your postings, but I'm not sure you have seen it.

#2] I need to read this and will comment if I can

Quote: Romes

This is a thought I've had for a long time that I'd like to discuss. It sparked just a bit in the VP thread about cycling 4 of a kinds... but I'll rephrase for this thread. I'm really hoping to hear from Mike, and our great math minds, as I feel this poses a good theoretical discussion and would love their feedback.

Generic Scenario - Say you have a time constrained AP play, albeit a day, week, etc. You figure out that for this play, if you play it the fastest/best you can for the time it's allowed that your EV should be X, plus or minus SD. So let's say you're 1/5th the way through the play, and you're running great... Up X + SD. You know from the math that this is basically the best you could possibly do on this play, so continuing to play any more would (in theory) just bring you back more towards EV.

This crosses near a fine line of "the gamblers fallacy" I assure you I'm aware, but it always makes for a fun theoretical discussion. It's like saying I'm gonna play 1,000,000 hands of blackjack with an average edge of 1% and a $100 avg bet. So after 1,000,000 hands I'll expect to make $1,000,000. Let's say in the first 200,000 hands you're up $1,500,000... Let's also assume you're never playing the game of blackjack again when you hit 1,000,000 hands (like when promotions run out). The "long run" numbers state that even with your standard deviations by the time you hit 1,000,000 hands you're going to be DOWN from where you are now. So why would you keep playing?

It's a double edged sword:
1) You're playing with a 1% advantage, starting right now, so why couldn't you make more money?
2) You're looking at the LONG RUN of the play, in which all of your individual sessions are from the same bankroll, making it essentially 1 big long session.

I'll try to sum it up, but again, I'll pose 2 more arguments. Let's say you're playing the same VP promotion the OP was. If you cycle through all 13 different quads you get a bonus. Pass the fine tune details (which you can see in that thread if you really want) the OP's EV was about 40/hour. IF this had been a 24 hour promotion (it's not, but this is an example) then the OP could have said "My EV for the ENTIRE promotion, playing all 24 hours, is $960 plus or minus some SD." So, my question is again... If the OP is lucky enough to hit a royal, or hell 2, in the first few hours and he's now up about $2500... Why on Earth would you keep playing? Some responded with "It's still an advantage, why not?" But I say... You figured your EV for the 24 period. This is essentially 1 big session and you're up way over your EV and SD... playing more will only result in putting more hands in, aligning you more and more towards your previously calculated EV. Thus, you'll LOSE money if you keep playing, even if the play has an advantage!

Question Time
1) In the blackjack example, after 200,000 hands if you're up 1.5 million... Would you continue to play? Remember after 1,000,000 hands you're never playing blackjack again.

2) In the VP example, assuming the 24 hour promotion... If you're up $2500 in the first 3 hours due to some right side variance, would you continue to play?

The way you've written the situations makes them totally different due to the utility of money argument for me. If I had won $1.5MM in any game I would stop, because that plus my current assets is enough for me to live on for the rest of my life. So, monetary goals achieved, time to hit early retirement.

$2500 is not nearly the same thing.

Quote: ThatDonGuy

Assuming that it would necessarily swing the other way is just as much Gamblers Fallacy as assuming that, if you were down, you would necessarily eventually catch up. AP is AP.

So you're admitting that you will balance out towards EV, in the end... Thus begs the question, if you're up an exceptional amount you know you're just going to go back towards EV, just as if you were down a lot... Only if you're up you don't want to go towards EV, and if you're down you DO want to go towards EV. So when you're up (enough), why keep playing?

Quote: odiousgambit

...[# 1]so if you are up [or down] $1.5 million you can expect the cards to have no knowledge of this!...

But, they do. Your blackjack bankroll, EV's, expectations are all built around your blackjack play being "one big session." I suppose it's more as you put it, regression to the mean. By the end of the 1 million hands math tells us you WILL BE DOWN from where you are now. This isn't the gamblers fallacy, this is math saying "hey, you've been really lucky thus far, but over the course of the long run, that's going to balance out."

It's the same thing if you're 2 SD out to the left after 200,000 hands... What would any pro say? Play through it. You're having bad variance but by the time you're 1,000,000 hands in, you're going to be more in line with your EV as variance will have less of an effect. Thus, if you're up 1.5 million, you should stop playing as you'd expect to move towards variance and therefore lose money on the way to the long run (from where you are now).

You can only look at your expectation, variance, etc. based on where you are right now -- not where you started at hands = 0. Anything that has happened means absolutely nothing.

Assuming it's a promotion worth playing, then I would keep playing if I'm up a lot, all things being equal (heat isn't an issue, I'm still happy with my hourly EV, etc.). Although I will say, if I'm playing something that isn't good (i.e.: low edge)...having fun may be a more significant factor than making EV...and I may throw in a stop loss (quit) point, because I don't wanna lose all my f%*!@$ing money. And if I get up a significant enough amount, I may increase that stop loss point.

I'm not saying I win because of stupid money management systems or nothing.


For the promotions I know you're playing...I don't think you should ever quit because your losing or winning, assuming it's +EV / no heat issues / etc.

It's no different then stopping and coming back at a later time.

Quote: ROMES

It's like saying I'm gonna play 1,000,000 hands of blackjack with an average edge of 1% and a $100 avg bet. So after 1,000,000 hands I'll expect to make $1,000,000. Let's say in the first 200,000 hands you're up $1,500,000... . The "long run" numbers state that even with your standard deviations by the time you hit 1,000,000 hands you're going to be DOWN from where you are now. So why would you keep playing?

It's a double edged sword:
1) You're playing with a 1% advantage, starting right now, so why couldn't you make more money?
2) You're looking at the LONG RUN of the play, in which all of your individual sessions are from the same bankroll, making it essentially 1 big long session.

I'll try to sum it up, but again, I'll pose 2 more arguments. Let's say you're playing the same VP promotion the OP was. If you cycle through all 13 different quads you get a bonus. Pass the fine tune details (which you can see in that thread if you really want) the OP's EV was about 40/hour. IF this had been a 24 hour promotion (it's not, but this is an example) then the OP could have said "My EV for the ENTIRE promotion, playing all 24 hours, is $960 plus or minus some SD." So, my question is again... If the OP is lucky enough to hit a royal, or hell 2, in the first few hours and he's now up about $2500... Why on Earth would you keep playing? Some responded with "It's still an advantage, why not?" But I say... You figured your EV for the 24 period. This is essentially 1 big session and you're up way over your EV and SD... playing more will only result in putting more hands in, aligning you more and more towards your previously calculated EV. Thus, you'll LOSE money if you keep playing, even if the play has an advantage!

Wtf. I can only assume you are being deliberately silly. If you have a y% edge that doesn't become a negative edge just because you find yourself ahead of where you expected to be just because of luck. You know what regressing to the mean means and you just made it out to be what many fools believe it to be. I hope the plan is to educate those who fall into that trap. Now Axel's point about utility of money is another thing altogether. Voting to play on just the BJ 'cos VP means nothing to me.

Quote: AcesAndEights

...The way you've written the situations makes them totally different due to the utility of money argument for me. If I had won $1.5MM in any game I would stop, because that plus my current assets is enough for me to live on for the rest of my life. So, monetary goals achieved, time to hit early retirement.

$2500 is not nearly the same thing.

This is "life goals aside" they both have the same mathematical conundrum. Would you keep playing, and regress towards your mathematical EV, or would you assume "I still have an advantage why wouldn't I make more money?" and keep playing is the question.

Quote: RS

You can only look at your expectation, variance, etc. based on where you are right now -- not where you started at hands = 0.

Assuming it's a promotion worth playing, then I would keep playing if I'm up a lot, all things being equal (heat isn't an issue, I'm still happy with my hourly EV, etc.)...

But your hourly EV is just a mathematical average that you'll work out to for your expected value over the time of the play. We all know you're not actually making X/hour... as you could lose for 9 hours, then hit big in the last hour and come out to EV. So in reality the first 9 hours was -X/hour but the last hour was 10X/hour.

So if you can mathematically identify that you've hit your 10X/hour in the first hour, why play the rest of the hours that you know will drag you back down towards EV?

There is no question -- you keep playing.

Quote: Romes

Quote: odiousgambit

...[# 1]so if you are up [or down] $1.5 million you can expect the cards to have no knowledge of this!...

But, they do. Your blackjack bankroll, EV's, expectations are all built around your blackjack play being "one big session." I suppose it's more as you put it, regression to the mean. By the end of the 1 million hands math tells us you WILL BE DOWN from where you are now. . . . Thus, if you're up 1.5 million, you should stop playing as you'd expect to move towards variance and therefore lose money on the way to the long run (from where you are now).

Can we have the real Rome's back?? Whoever hacked his account or got him befuddled just pack it in.

Quote: OnceDear

Can we have the real Rome's back?? Whoever hacked his account or got him befuddled just pack it in.

He's starting to sound like Rob Singer!

Quote: RS

There is no question -- you keep playing.

All of the math we've built to believe on (in blackjack for example) is about the long run. The reason we play, the reason the game is beatable, is because we know short term ANYTHING can, and will happen. However, we know in the long run with mathematical certainty that we're going to be at EV X plus or minus SD.

...So my point is if you hit EV X + SD early in your play, you have math that PROVES you're going to be less than that when you hit the long run.


Real Numbers Example
AvgBet = $100
AvgEdge = 1%
OriginalSD = AvgBet*1.1 = 110

Num Hands	Expected Value	Standard Deviation
1	$1	+-$110
100	$100	+-$1,100
10,000	$10,000	+-$11,000
1,000,000	$1,000,000	+-$110,000

This means, when you hit 1,000,000 hands, you can expect to make $1,000,000 plus or minus $110,000. Forgoing 3SD for now, let's just stick to this because the point is all the same... So the BEST you could mathematically possibly do, after 1,000,000 hands is be at $1,110,000... So if you're up $1.5 million after 200,000... why on Earth would you continue to play when you know you're going to end up with less? Variance shined on you, run with it?


EDIT - Guys, this makes for fun theoretical conversation... I still have my wits about me lol.

Quote: Romes

But your hourly EV is just a mathematical average that you'll work out to for your expected value over the time of the play. We all know you're not actually making X/hour... as you could lose for 9 hours, then hit big in the last hour and come out to EV. So in reality the first 9 hours was -X/hour but the last hour was 10X/hour.

So if you can mathematically identify that you've hit your 10X/hour in the first hour, why play the rest of the hours that you know will drag you back down towards EV?

You can't do that.

Every time I flip a coin, the chances of heads/tails are each 50/50. After 1,000 flips, you expect 500/500. But if the results are 485/515, your expected results at the end of the next 1,000 flip is 985/1015.

You can't be at the 485/515 point after 1k flips, and say because my expectation is 1k/1k for 2k coin tosses, that by the end of the 2k flips I should be at 1k/1k.

Every starting hand of VP, you have a 1 in 40,000 chance of hitting the RF (or whatever it is for that specific game JOB/DDB/DW). After hitting one you don't have to wait 39,999 hands for another.

Quote: RS

You can't do that.

Every time I flip a coon, the chances of heads/tails are each 50/50. After 1,000 flips, you expect 500/500. But if the results are 485/515, your expected results at the end of the next 1,000 flip is 985/1015.

You can't be at the 485/515 point after 1k flips, and say because my expectation is 1k/1k for 2k coon tosses, that by the end of the 2k flips I should be at 1k/1k.

Every starting hand of VP, you have a 1 in 40,000 chance of hitting the RF (or whatever it is for that specific game JOB/DDB/DW). After hitting one you don't have to wait 39,999 hands for another.

Damn auto correct

Quote: RS

...Every starting hand of VP, you have a 1 in 40,000 chance of hitting the RF (or whatever it is for that specific game JOB/DDB/DW). After hitting one you don't have to wait 39,999 hands for another.

Yes, I agree entirely with this... but math tells us we can "expect" to hit one 1 in every 40,000 hands. So if in our first week of playing the game, we hit 100 royals... Then over the next 10 years "the long run" we hit none and low and behold by the time we hit the long run we've come out to the correct math/EV of the game... 1 in 40,000.

This is the same as your coins... by the time we get to 1,000,000 flips, I'm betting it will be 50/50 plus or minus some small SD. So if you flip 350,000 heads in the first 350,000 trials, you know in the next 650,000 trials (with mathematical certainty from standard deviations) that there will be more tails than heads. I'm not saying it'll work out to exactly 50/50, but close enough with a small SD window by that number of trials. In the cases I'm presenting that means more losing than winning.

The math will work out as you get more trials. That's the whole idea for AP's... The more hands you play the less variance plays a part and the more you'll gravitate towards your natural EV. My question again is, if you were LUCKY enough to hit 100 royals in the first week (extreme example I know) why would you continue to keep playing knowing that you're just going to work out to the long run math the more hands you play?

Look at my BJ example above, and tell me why you'd keep playing after 200,000 hands and being up $1.5 million.

REMEMBER this is for defined windows of play, such as a promotion that lasts 1 day only, or blackjack where after 1,000,000 hands you're never playing again, etc.

Just swap to another Plus EV play?

Coins or coons doesn't make a difference. One toss the coon lands on it's head, next toss the coon lands on it's tail, usually.
It is different with cats however, 'cause they are in league with the devil!
And they are waiting for you to die so they can eat you.

Quote: TwoFeathersATL

Just swap to another Plus EV play?...

So you would stop playing this particular AP play because you'd expect your profits to head towards your EV?

Quote: Romes

So you would stop playing this particular AP play because you'd expect your profits to head towards your EV?

Sorry, I don't know how to stop. I'm a degenerate....
Actually, if I hit that 100 Royals in the first week you mentioned, I'd stop long enough for maybe an island trip with H & B.
But I'd be back soon, still a degenerate....

How many SD's is +$1.5M within 200k hands for that? I think you're looking at this as if you can only end at within +/- 1 SD. But surely you can end at +2 or +3 SD's. And if you're already at +4 or +5 SD's (up $1.5M in 200k hands), you're very likely to end above EV,

What's the EV + 1 SD for 200k hands? What about EV + 1 SD for 200,100 hands?

What's EV +/- 1 SD for 800k hands? Essentially, once you're at the 200k hands mark (looking at a graph), if you want to see what your expectations are for the next 800k hands, you got to draw a new graph with EV & SD for only those 800k hands, but starting at the +$1.5M point.

I think 2F-Atlanta is being his usual facetious self. Gotta hand it to him, his posts are a little hard to understand sometimes....but the ones I do understand (i.e.: not super long), are brilliant. I like that -- sorta like the class clown.

You can't just stop playing BJ you have to stop playing evrything with a 1% edge or below.

ALL the games will just blend together and average out if you AP long enough. You will over lose on a 130% play and over win on a .5% play.

IMO If you have a small bankroll and you are playing something kinda risky and you get super lucky. You should stop and find better opportunities that are less risky. This gives you the ability to breath and pay bills while you search. IMO you should play below your bankroll unless you have a steady stream of income.

I'm all for taking small shots at high risk high payoff Advantage plays as long and you don't go off and put yourself in a bad spot so when something good comes up you can't take full action. That will cost you in the long run.

Quote: RS

How many SD's is +$1.5M within 200k hands for that? I think you're looking at this as if you can only end at within +/- 1 SD. But surely you can end at +2 or +3 SD's. And if you're already at +4 or +5 SD's (up $1.5M in 200k hands), you're very likely to end above EV,

What's the EV + 1 SD for 200k hands? What about EV + 1 SD for 200,100 hands?

What's EV +/- 1 SD for 800k hands? Essentially, once you're at the 200k hands mark (looking at a graph), if you want to see what your expectations are for the next 800k hands, you got to draw a new graph with EV & SD for only those 800k hands, but starting at the +$1.5M point.

We treat our blackjack card counting career as one graph. You're stating "I'll just say after winning 1.5 million that I'm starting over, so now I need to know my all new EV for the next 800,000 hands." That's not the case. Your previous hands will be part of your graph either way. You have your EV +- 3SD from when you start to when you reach 1,000,000 hands; same as figuring your EV on a VP promotion/play that you haven't started yet. The play is the play. You can't say "ok the first X hands I got lucky, so I'll pretend to start my bankroll now."

Or are you on to something? ;-)

So if I'm up 1.5 million after 200k hands... you're saying "okay, what's my EV for the next 800,000 hands?"

Num Hands = 800,000... EV = $800,000.... SD = +-$100,000... So I get what you're saying; for the next 800,000 hands you still expect to make $800,000 +- $100,000.

However this fails your previous math now. What's our EV of 1,000,000 hands? We already know, $1,000,000 +- $330,000 (3 SD's).

So you have 1 equation telling you that in the SPAN of your career (from 0 hands to 1,000,000 hands) you're going to lose money from where you are now.
Then you have another equation telling you that in the next 800,000 hands you're going to make another $800,000ish. Which one is right?

If you can constantly re-define your expectations, then what's the point/proof/reliability in stating "I'm about to play blackajck, and after 1,000,000 hands I expect to make $1,000,000 +-$330,000." ?? That would just be hog wash because you could make or lose $1,000,000 in the first few hundred thousand hands and then just re-define your EV.

He called me facetious.
I painted white out over his pink jumpy thing, so there!

Seriously Rome's. Please desist. You, a respected 'maths guy' here are expounding the kind of gamblers falacy crap that we use maths properly to defeat. You devalue the very valuable maths that we employ by (ab)using the formulae out of context. I trust that you are being mischievous. But if you persist, then I will start to doubt your credibility or integrity. Others will too. As IBYA said, you were starting to sound like Rob Singer. Don't, please don't be a Muppet even in jest.

This discussion has had me thinking and I may have an idea...

Idea: You'll never be up enough in the short run, in relation to the long run, to call it quits. There will always be more money to be made.

Math: With blackjack. After 200,000 hands, even with 3SD, the most you could be up is $200,000 + $150,000 = $350,000. And if you're up $350,000... but expect to make $1,000,000 in the long run... then you have more winning to go. That means in your next 800,000 hands, you'd normally expect to make $800,000... and if you hit EV on the head then you'd be up $1,150,000... which would be within your "long run" EV +-SD of $1,000,000 +- $330,000... You'll never be up $1.5 mill in 200k hands, it's mathematically inconceivable.

This works for blackjack, at least... I'm not sure about VP though.

Let's look at the 24 hour VP play again... EV = $40/hour, 24 hour window. So in the 24 hour window you can expect to make $960. I don't know what the SD's are though, and I'm expecting because it's VP they'll be huge (like a couple thousand). So this means, if you get lucky and hit 2 royals (as the op in that thread did) and you're up $2500... your max EV for the play could still be $960 +- $2k, or more like $3,000... so again there's still money to earn?

Thoughts?

Quote: OnceDear

Seriously Rome's. Please desist. You, a respected 'maths guy' here are expounding the kind of gamblers falacy crap that we use maths properly to defeat. You devalue the very valuable maths that we employ by (ab)using the formulae out of context. I trust that you are being mischievous. But if you persist, then I will start to doubt your credibility or integrity. Others will too. As RS said, you were starting to sound like Rob Singer. Don't, please don't be a Muppet even in jest.

I've stated 3 times in the thread that this is for fun theoretical discussion... and that I still have my wits about me. Calm down =P.

Quote: Romes

This is "life goals aside" they both have the same mathematical conundrum. Would you keep playing, and regress towards your mathematical EV, or would you assume "I still have an advantage why wouldn't I make more money?" and keep playing is the question.

YOU DON'T REGRESS TOWARDS YOUR MATHEMATICAL EV

Christ, and you're giving people card counting advice? This forum really is going downhill.

Quote: RS

There is no question -- you keep playing.

Yes, "life goals aside" I agree.

VP is weird, the variance/SD is a little wonky, because of RF's. The distribution curve isn't a regular looking bell curve. It looks like a bell curve but also has a few bumps on the right side, due to hitting a RF.


For instance, playing 1000 hands of $1 denom VP (9/6 JOB). You're much more likely to be up $4000 than you are to being up $2000 (unless you're somehow getting a $2/hand EV). Can be up 4K because of a RF. But it's hard to be up 2k. Either gotta hit like 14 extra 4oaks than expected (you expect 2.5 4oaks in 1k hands)....or maybe 10 extra 4oaks and 2 SF's....etc. Not likely. Or you gotta hit a RF for $4k then run incredibly bad to lose $2k from that $4k. Also, very unlikely.


IMO, best way is to sim a 1k hand session (or however many hands you're gonna play) many many times. And once you gather all that data, you figure out which % of sessions are in the A-B range, B-C range, etc. Then you may know something like "I have an almost 0% chance of losing over $8k, 5% chance of losing 5-8k, 15% chance of losing 3.5-5k....and a 2.5% chance to win 18-21k, and almost 0% chance to win 21k+." Then ask if you're willing to have that kind of variance for the EV you'll be getting, your bankroll is big enough, etc..

Quote: Romes

So if you can mathematically identify that you've hit your 10X/hour in the first hour, why play the rest of the hours that you know will drag you back down towards EV?

Because even as the average gets dragged down more and more total profits keep going up

Which is better: getting lucky on a game with an EV of $50 per hour by winning $10000 for one hour then stopping.

Or, getting lucky like that but playing for another 10000 hours and earning exactly your expected value during that extra time.

In the first example you had an hourly profit of $10000. In the second example your hourly profit was only $51. But in the second example you won an extra $500,000

Quote: Romes

This is the same as your coins... So if you flip 350,000 heads in the first 350,000 trials, you know in the next 650,000 trials (with mathematical certainty from standard deviations) that there will be more tails than heads.

If you just joined this thread. Romes is being mischievous. The thread is full of him quoting 'Mathematical facts' that are neither mathematical nor facts :o) I wish he'd pack it in, because I expect this won't end well and there will be a lot of misquoted 'facts' and assertions as a consequence.

Quote: AcesAndEights

YOU DON'T REGRESS TOWARDS YOUR MATHEMATICAL EV

Christ, and you're giving people card counting advice? This forum really is going downhill.

What's going downhill is your ability to read 3 and 4 times that this is just a "for fun" theoretical discussion. Perhaps there's an audio version of the forums for you?

And no. What the end all answer is, I'm right, but I'll never be right.

1) If you ever found yourself UP 1.5 million after 200k hands in a 1,000,000 hand run of BJ, you should quit. Why? Because you're about 20 SD's out and the game is clearly not fair. If it's not fair now, they could change it to be not fair against you to, so run with the money before you get in legal trouble or cheated.

2) In a fair game you'll NEVER find yourself up more than 3SD from your EV after a short trial run. Thus, you'll always have "more EV" to earn in your long run because your long run EV will be substantially more than your short term EV, even plus 3 SD.

Example: after 200k hands the best you could be is $350,000... when your EV is $1,000,000 for 1,000,000 hands. Thus you still have plenty more of EV and advantage to take advantage of. You'll NEVER be up 1.5 million at this point.

The correct answer, is to keep playing... I believe ThatDonGuy & RS said it first.

And I'm the one being called names/foolish/etc. Just trying to have a fun theoretical discussion in which very few actually came back with coherent thoughts. Guess I shouldn't post threads that provoke thought and discussion? Jesus people.

Quote: Romes

What's going downhill is your ability to read 3 and 4 times that this is just a "for fun" theoretical discussion. Perhaps there's an audio version of the forums for you?

Romes,
I know you are fooling around. Most others will too. But SOME, some of those who most need your help and knowledge will see you spouting nonsense and either soak it up as knowledge, or else will use it to discredit all your previous sensible advice. I'll get the popcorn, you get the asbestos suit. you started the fire $:o)

Quote: OnceDear

Romes,
I know you are fooling around. Most others will too. But SOME, some of those who most need your help and knowledge will see you spouting nonsense and either soak it up as knowledge, or else will use it to discredit all your previous sensible advice. I'll get the popcorn, you get the asbestos suit. you started the fire $:o)

Thought I could avoid this with the 3-4 "for fun conversation" comments...

Regression to the mean is irrelevant.

Standard Deviations are irrelevant.

You will be assimilated, resistance is futile.

In all seriousness, you should eventually regress to the mean whether that be an average of 1% profit on a particular play or 5% profit on a particular play, but that doesn't mean you quit if your profit is more than that. While you are racking up hands or doing whatever you're doing, yes, your profit margin and scores are fluctuating, but the thing that steadily increases in a known way is coin-in.

If you have the opportunity to take advantage of the same play long enough, or even different plays that yield the same percentage advantage (and you have the bankroll to do so) eventually an expected profit of 1% of your coin-in will exceed even your ACTUAL profit at the time you thought about quitting.

Let's say you hit a Royal Flush and now you're up $1000, but at the time, you were playing with a 1.5% advantage. At the time, your total coin-in was $10,000 and your expected profit was $150. What that means is that at such time that you get to $66,667.50 coin in, your expected profit will now have exceeded your actual profit (at the time you were ahead $1,000) by a little over a penny.

In the meantime, though, you have put through $56,667.50 coin-in at such time that you were already ahead $1,000, therefore, your NEW Expected profit (if you recalculate at the time that you are ahead the grand) is $1,850.0125 on the overall play.

The biggest thing about the concept of Expected Profit is that bankroll starting point is, was and always will be arbitrary.

What I mean is, mathematical Expectation is not actually something that you calculate. It is always there and it, 'Calculates itself,' so to speak. It changes with the result of every hand based on how many plays at that situation you think you're going to get in...which also stops only with death in the cases of most people because you never know when a specific situation will again present itself.

Quote: Romes

Thought I could avoid this with the 3-4 "for fun conversation" comments...

You thought wrong
$:o)

Good post Mission, and a good explanation.

Thanks Romes!

Quote: ThatDonGuy

Assuming that it would necessarily swing the other way is just as much Gamblers Fallacy as assuming that, if you were down, you would necessarily eventually catch up. AP is AP.

Quote: Romes

So you're admitting that you will balance out towards EV, in the end...

On the contrary - I am saying that you can't make that assumption.

Quote: Romes

Quote: odiousgambit

...[# 1]so if you are up [or down] $1.5 million you can expect the cards to have no knowledge of this!...

But, they do. Your blackjack bankroll, EV's, expectations are all built around your blackjack play being "one big session." I suppose it's more as you put it, regression to the mean. By the end of the 1 million hands math tells us you WILL BE DOWN from where you are now. This isn't the gamblers fallacy, this is math saying "hey, you've been really lucky thus far, but over the course of the long run, that's going to balance out."

Let's get someone involved whose math you respect. This is simply wrong. The way the math works is on the future hands without knowledge of the past hands. It evens out by being normal, not by an accelerated rate of losing money when it's -EV because the cards somehow know they have to "catch up"

Quote:

It's the same thing if you're 2 SD out to the left after 200,000 hands... What would any pro say? Play through it. You're having bad variance but by the time you're 1,000,000 hands in, you're going to be more in line with your EV as variance will have less of an effect. Thus, if you're up 1.5 million, you should stop playing as you'd expect to move towards variance and therefore lose money on the way to the long run (from where you are now).

You should only stop playing for the same reason you would if you broke even, or any other scenario.

Quote: Mission146

Let's say you hit a Royal Flush and now you're up $1000, but at the time, you were playing with a 1.5% advantage. At the time, your total coin-in was $10,000 and your expected profit was $150. What that means is that at such time that you get to $66,667.50 coin in, your expected profit will now have exceeded your actual profit (at the time you were ahead $1,000) by a little over a penny.

In the meantime, though, you have put through $56,667.50 coin-in at such time that you were already ahead $1,000, therefore, your NEW Expected profit (if you recalculate at the time that you are ahead the grand) is $1,850.0125 on the overall play.

Romes is saying that if you were up that $1000 you will still only be up $1000 at full coin-in. I don't think he realizes he disagrees with you

Quote:

The biggest thing about the concept of Expected Profit is that bankroll starting point is, was and always will be arbitrary.

immaterial, I would say

Quote: Romes

So if you flip 350,000 heads in the first 350,000 trials, you know in the next 650,000 trials (with mathematical certainty from standard deviations) that there will be more tails than heads.

What a weird thread. The above quote sums it up quite nicely. Always thought the guy was fishy.

["Fun conversation", eh? I just don't get how making absurd claims like the one above is fun.]

Quote: Canyonero

What a weird thread. The above quote sums it up quite nicely. Always thought the guy was fishy.

["Fun conversation", eh? I just don't get how making absurd claims like the one above is fun.]

Yeah, if you flip heads 350,000 times out of 350,000 trials, I think it's safe to assume that both sides are heads. ;-)

Hey guy's don't ease up just yet, there's blood in the water. 10 more pages of bashing and you may get him to pull a Triple A meltdown.

(AOS/Allen/Ahigh)

Quote: Romes

1) If you ever found yourself UP 1.5 million after 200k hands in a 1,000,000 hand run of BJ, you should quit. Why? Because you're about 20 SD's out and the game is clearly not fair. If it's not fair now, they could change it to be not fair against you to, so run with the money before you get in legal trouble or cheated.

More likely than an unfair game is that you miscalculated your odds. If someone came here saying that they were $1.5 million below expectations what would you think is the most likely reason (assuming they were being honest), that the game was rigged, or that they made an error figuring out the Expected Value?

(also, it's very easy to be UP (or down) $1.5 million while being less than 1 SD away. Just bet $1.5 million per hand).

Quote: Romes

So if you flip 350,000 heads in the first 350,000 trials, you know in the next 650,000 trials (with mathematical certainty from standard deviations) that there will be more tails than heads.

I missed that. So, is the joke that I even took this seriously? Jokes on me and a couple of others?

I keep thinking he is serious, because he always has been before.