A Rebuy ? for Math Majors
 

I have basic math skills. But, I definitely lack the ed. to come up with a formula to guide rebuy purchases. Please note, this is not a strategy request. I am looking for a specific formula that would offer a "general guideline" to purchases based on the following: Buy-In,Rebuy Amount, Field, Prize Pool. Possibly, players presumed advantage over field, historical success rate. Any other factors I am not thinking of???

Some examples:

10+1 rebuy with a field of 1,100, 1st place prize of 12k, field advantage of 70%, historical cashes.

100+9 rebuy with a field of 145, 1st place average 13,000, 20% field advantage, historical cashes.

I think there is a sensible formula to be found. What got me thinking about this was playing a 10 rebuy and spending $71 (1-entry 5 rebuys 1 addon) with a very weak field (weak A's calling early pos all-ins etc.) Vs. spending the equivalent 100 plus9 of entry/rebuys/addon and then playing against a smaller, yet much stronger field.

There may be mittigating factors that prevent the creation of an equation. I apologize in advance if that is the case. But, I remain optimistic that there may be a way.

Thank you for any help you may be able to offer.

Re: A Rebuy ? for Math Majors
 

Er. maybe i'm slow this morning, but i don't get what you want the formula to solve/show.

Re: A Rebuy ? for Math Majors
 

I'm also a bit of a mathie but am also a little confused. The variable is going to be estimated field advantage, right? Slide er up and down and see what kind of rebuy investment you should/can justify (or hit optimally)? These are the two unknowns, I think for your historical success rate you'd want to use general MTT roi% b/c I don't think anyone can get near enough to significant numbers within a specific buyin (or even total MTTs played). Bleh, just some more thoughts. Where is sirio when you need him.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
see what kind of rebuy investment you should/can justify

[/ QUOTE ]


I'm pretty sure i won't be able to clearly say this, but each rebuy investment shouold be viewed independantly, so whatever your 'total investment' is, shouldn't mean crap. And if it was right for you to buyin in the first place, unnless it's a crazy turbo, it would be right for you to rebuy when you go broke.

Still confused as to what the question is.

Re: A Rebuy ? for Math Majors
 

This is probably heresy on these boards, but I think logically you maximize your ROI (assuming you are a winning player) by never rebuying when you go broke during a rebuy.

Let's say you've been playing for 15 minutes, push your 3000 chips with your AK, then lose it all. Now let's say you have only $31 left in your account. Are you better off spending $20 to rebuy now (with an extra $10 for the add-on), or are you better off waiting until tomorrow? Clearly, you are better off waiting until tomorrow, since you will have 60 minutes to build your stack tomorrow, as opposed to only 45 minutes today.

My point is that I often hear that you should not play these events unless you can rebuy, which I think is wrong. If you are short on funds and want to play and time is not a factor, then allocating $31 per tournament (original buy-in, rebuy at start, add-on at end of hour) seems to me to be a fine strategy (assuming you don't play more conservatively during the rebuy period because you are afraid of busting out).

However, if you are trying to maximize your amount of winnings per day (as opposed to maximizing your ROI), then of course you will want to rebuy when you go broke.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
This is probably heresy on these boards, but I think logically you maximize your ROI (assuming you are a winning player) by never rebuying when you go broke during a rebuy.

Let's say you've been playing for 15 minutes, push your 3000 chips with your AK, then lose it all. Now let's say you have only $31 left in your account. Are you better off spending $20 to rebuy now (with an extra $10 for the add-on), or are you better off waiting until tomorrow? Clearly, you are better off waiting until tomorrow, since you will have 60 minutes to build your stack tomorrow, as opposed to only 45 minutes today.

My point is that I often hear that you should not play these events unless you can rebuy, which I think is wrong. If you are short on funds and want to play and time is not a factor, then allocating $31 per tournament (original buy-in, rebuy at start, add-on at end of hour) seems to me to be a fine strategy (assuming you don't play more conservatively during the rebuy period because you are afraid of busting out).

However, if you are trying to maximize your amount of winnings per day (as opposed to maximizing your ROI), then of course you will want to rebuy when you go broke.

[/ QUOTE ]

I totally disagree.

The point of rebuys, and the best way to maximize your ROI is by trying to accumulate chips.

If you go all in for 3K 10 minutes into a rebuy, I bet you get two callers w/ decent hands. Your AK is no longer a favorite, but it was probably +EV to push it anyway.

Why would you not continue to play and take +EV situations? It doesn't take 45 minutes to build a stack in the 11r...

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
If you go all in for 3K 10 minutes into a rebuy, I bet you get two callers w/ decent hands. Your AK is no longer a favorite, but it was probably +EV to push it anyway.

[/ QUOTE ] I completely agree and would push AK everytime in this situation, regardless as to whether I intend to rebuy or not.

[ QUOTE ]

Why would you not continue to play and take +EV situations? It doesn't take 45 minutes to build a stack in the 11r...

[/ QUOTE ] My point is that you can build a bigger stack with 60 minutes. So I still say you are maximizing your ROI by not rebuying. But maximizing ROI is not always the best goal.

Re: A Rebuy ? for Math Majors
 

Sorry if my post is not clear. I'm lookig for a formula that could be used to guide the investment. For example, a player like Ozzy87/BigSlick789 could rebuy 20x in the 10+1 for 200 and likely show a very healthy return on his investment.

Whereas the same player, with all due respect, rebuying @ that same rate, will likely show a substantial loss in 100 +9.


I am hoping to be able to plug in the data into an excel sheet and come up with a general guide line to rebuy purchases. Any clearer now??? Please let me know. T

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
Let's say you've been playing for 15 minutes, push your 3000 chips with your AK, then lose it all.Now let's say you have only $31 left in your account . Are you better off spending $20 to rebuy now (with an extra $10 for the add-on), or are you better off waiting until tomorrow?

[/ QUOTE ] This is a bad statement IMO. If you only have $50 in your account you should not be playing rebuys. I also think your decisions in tournaments shouldnt be made based on your BR. The money you buy in with shouldnt matter, Dont play over your BR.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
[ QUOTE ]
Let's say you've been playing for 15 minutes, push your 3000 chips with your AK, then lose it all.Now let's say you have only $31 left in your account . Are you better off spending $20 to rebuy now (with an extra $10 for the add-on), or are you better off waiting until tomorrow?

[/ QUOTE ] This is a bad statement IMO. If you only have $50 in your account you should not be playing rebuys. I also think your decisions in tournaments shouldnt be made based on your BR. The money you buy in with shouldnt matter, Dont play over your BR.

[/ QUOTE ] Of course you want to stay within your bankroll. It was only an example.

Here's something more concrete. The general consensus seems to be that you should have 100X buy-in. So if you have a $3100 bankroll and want to play the rebuys, then smart bankroll management would be to not allow yourself to rebuy beyond the first rebuy at the beginning of the tournament.

My only point is that it is wrong to say that you should not play the rebuys if you are not planning on rebuying. Logically, you maximize your ROI by never rebuying.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
Sorry if my post is not clear. I'm lookig for a formula that could be used to guide the investment. For example, a player like Ozzy87/BigSlick789 could rebuy 20x in the 10+1 for 200 and likely show a very healthy return on his investment.

Whereas the same player, with all due respect, rebuying @ that same rate, will likely show a substantial loss in 100 +9.


I am hoping to be able to plug in the data into an excel sheet and come up with a general guide line to rebuy purchases. Any clearer now??? Please let me know. T

[/ QUOTE ] The number of times you rebuy is unimportant if you are planning on rebuying. The critical variable is how much time is left in the rebuy period.

Everytime you lose your stack, it is like you are starting anew. What you spent before doesn't matter--it's how much time you have left to build a competitive stack.

If you are a great player, perhaps one minute is enough. You are able to be profitable with only 3000 chips in your stack after the rebuy period.

If you are marginal, then you might need the whole 60 minutes for your investment to be profitable.

Re: A Rebuy ? for Math Majors
 

Jcm,

I tend to agree with you, but some rebuy tables are sweeter than others. If there is a maniac at the table pushing every hand, I'm happy to keep rebuying, because I can accumulate more playing 45 minutes against that guy than I can playing an hour at a calmer table tomorrow.

Another thing to consider is the amount of money at the table (which of course has a lot to do with the presence of rebuy maniacs). At a juicy table, it's often worth two buyins to stick around, even if no one is playing especially badly.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
Jcm,

I tend to agree with you, but some rebuy tables are sweeter than others. If there is a maniac at the table pushing every hand, I'm happy to keep rebuying, because I can accumulate more playing 45 minutes against that guy than I can playing an hour at a calmer table tomorrow.

Another thing to consider is the amount of money at the table (which of course has a lot to do with the presence of rebuy maniacs). At a juicy table, it's often worth two buyins to stick around, even if no one is playing especially badly.

[/ QUOTE ] I completely agree with you. Very good points.

I don't like to be the maniac during the rebuy period, but sometimes I start acting like the maniac (and showing my hands when everyone folds) if nobody is willing to play the role. Hopefully that wakes everybody up, and I can slow down a bit.

Re: A Rebuy ? for Math Majors
 

Basically, what I am visualizing in my head is a line graph that shows entry/rebuy purchases intersecting with cashes. At some point the number of purchases exceeds the likely cash return. Finding a way to invest optimally for each set of conditions would be very helpful.

Re: A Rebuy ? for Math Majors
 

If you see it in your head, what is the answer?

Re: A Rebuy ? for Math Majors
 

The problem with rebuying after a certain amount of time has passed in my opinion any more then 30 minutes is that even though your edge no matter how big it is can not make up for the fact that the donkies u face now have a good size chip stack why not save the money and play well again when people do not have that larger chip stack

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
Basically, what I am visualizing in my head is a line graph that shows entry/rebuy purchases intersecting with cashes. At some point the number of purchases exceeds the likely cash return. Finding a way to invest optimally for each set of conditions would be very helpful.

[/ QUOTE ] You can't get that kind of graph, because you are thinking about this in the wrong way.

Your question is (or should be): Is it profitable for me to invest $20 in rebuying 3000 chips?

Here are 2 situations: You push 4 of your first 20 hands and lose everytime (let's say that every push was +EV--you are just having a bad run of cards). 10 minutes has passed. Should you invest $20 to rebuy another 3000 chips?

OR

You push only one hand--the 20th you are dealt. 10 minutes has passed. should you invest $20 to rebuy another 3000 chips?

You should see that the answer is the same. It doesn't matter that you invested $80 in one situation and $20 in the other. That is completely irrelevant to the question. You are faced with the question as to whether you should invest another $20, and you have 50 minutes to rebuild your bankroll.

The better way to approach this question is to determine beforehand how much you can invest in the rebuy, and to stick to that.

Re: A Rebuy ? for Math Majors
 

Again, you have to stop thinking of it as a collective investment.

If you drop 100 in a $10 rebuy, that's not a $100 investment, it's 5 seperate $20 investments (counting double rebuys). The outcome of one has no impact on the outcome of the others.

If you're +EV playing it once, you're +EV playing it a second time.
--

jcm made points about the time remaining, but in the bigger rebuys that we're used to (like the 45k) if you're a winning player w/ 3000 chips to start, then you will be w/ 5000 and an hour in. So i don't think time remaining plays a significant role.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
jcm made points about the time remaining, but in the bigger rebuys that we're used to (like the 45k) if you're a winning player w/ 3000 chips to start, then you will be w/ 5000 and an hour in. So i don't think time remaining plays a significant role.

[/ QUOTE ] I probably am making too much of the time factor, for most winning players. But if you have a somewhat limited bankroll, then I think time is an important factor. If you have only 100X buy-ins, the smart thing if you bust out 30 minutes into the tournament is to come back the next day.

Actually sleep is the important factor for me. If I bust out with 10 minutes remaining, I'm giving it up and going to bed.

Re: A Rebuy ? for Math Majors
 

Please understand, this is not about a specific rebuy scenario or a strategy request. Simply a request to see if there is a way to input some relevant data into a model that will produce a result that can be used to guide decisions on investment that yield over an annual period.

Since the factors can be expressed numerically, and since this is about results over time, I know this is possible. I just do not know how to write the math.

Can Anyone write the math?
 

Apparently, rebuy strategy is a hot topic. FWIW, I call multi allins with suited connectors. Unfortunately, my post is not a strat. post.

Can anyone wirte a math formula that would use the factors in my initial post and any other relevant factors I left out?

Thanks!

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
Again, you have to stop thinking of it as a collective investment.

If you drop 100 in a $10 rebuy, that's not a $100 investment, it's 5 seperate $20 investments (counting double rebuys). The outcome of one has no impact on the outcome of the others.

If you're +EV playing it once, you're +EV playing it a second time.

[/ QUOTE ]


What he said...Actually, I find myself thinking that about a lot of your recent posts. Now if I could only start getting your results.

Re: A Rebuy ? for Math Majors
 

BPA..I think the results of your request wouldnt be worth the effort.

Lets say in a freezeout with n runners, a starting stack of S per runner and a buy in (excluding vig) of b, your equity is (S/nS) x nb = b because everyones skill is equal. This is essentially an ICM value of the total prize pool, where your chances of each prize happens to be equal to everyone elses.

Now lets say because of your skill, you historical equity happens to be 3 buy ins.

The problem is that you can get to that increased equity in a lot of different ways...eg one player may be a survivalist who has an unusually high number of cashes where they are in the middle prize areas and never wins a first prize, or there may be a "win it all" player who has a small incremental advantage for the big prize, but never make it into the money if he doesnt win.

Now when you look at the equity of a rebuy for these 2 players the answers will be very different depending on the situation, despite their "equivalent skill" of 3b equity.

If the redistribution of chips is fairly even and the average is less than 3b, both players probably still have +EV.

However if the redistibution of chips is skewed, so that the majority are in a few players hands the "win it all" player will have a lower EV than the survivalist, because the ratio of the top stacks (that he has to surpass) to his new buyin is greater than the ratio of the average of the other stacks to the survivalists buyin.

In fact the survivalist may actually have increased EV in that situation...in the extreme say the top stack is equal to all of the rebuys plus his original stack plus the buy ins of 1/2 the field that have dropped out. The remaining players have exactly their original stack. The survivalist has 1/2 the field to get through to get to the same prizes he was contending for before, and a rebuy should be very +EV for him.

The win it all player on the other hand has more ground to cover to get to the same chip ratio to the other tcontenders.

Re: A Rebuy ? for Math Majors
 

I am disappointed. But, I respect your position. Thank you for replying.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
I think logically you maximize your ROI

[/ QUOTE ]
That's where I stopped reading this thread.

Re: A Rebuy ? for Math Majors
 

well, he's right in a way.

the first time you buy in to the tournament is when it's most profitable, because you're stack will be average (or above if you double rebuy) and you'll have the entire first hour to accumulate. The longer you wait the shorrter the stack your buying is. So, if you treated it as a freezeout (well, a double rebuy + an addon, but no extra rebuying) it makes sense that you'd have a higher ROI. Since you're playing only in the most favorable conditions.

BUT it's not in a vacuum there are a million things factored in, so it's all pointless. AND the ROI increase from never rebuying woudl be miniscule, and the hourly wage would be retarded.
---

Re: A Rebuy ? for Math Majors
 

You shouldn't even consider ROI when thinking about poker tournaments: that just leads to bad decisions.

You should make the decisions that maximize EV, not ROI.

Re: A Rebuy ? for Math Majors
 

uh?

EV = ROI

Re: A Rebuy ? for Math Majors
 

Suppose you have a choice between two poker tournaments in different cities (your bankroll is easily large enough to enter either one).

The first is a $3,000 buyin and you estimate your ROI would be 75%.

The other is a $10,000 buyin but the field is a bit tougher so you estimate your ROI in that tournament as 60%.

The first one has higher ROI, but the second has much higher EV. Which would you enter?

Re: A Rebuy ? for Math Majors
 

Stacked rebuys (as in, being able to rebuy when you still have chips in front of you at or below starting chip amount) and addons aside, I think you're misunderstanding ROI calculation of rebuys.

If there was a $10+1 tournament where your only option was to rebuy if you went broke (no stacked rebuys or addons) and the rebuy would also be $10+1, rebuying would be the same as putting money down for a different tournament (your $10 added to the prize pool wouldn't make any real difference in a large enough field)

There would, however, be one significant difference: you'd be starting with a stack that's below the average. In that instance it would be a better idea to go into a different tournament instead. However, you wouldn't take the rebuy not because your ROI is based off a $22 investment as opposed to an $11 investment, but because it is -EV to spend the second $11 rebuying as opposed to spending $11 on another tournament.

What affects the EV of rebuys are the fact that sometimes you don't have to pay rake on rebuys and all the strategy changes: starting with a bigger stack, being able to add onto your stack during the tournament, being able to play a tournament where you normally wouldn't be able to (as in, if this was the only tournament around), the psychological effect of having the rebuy cushion for other players, and hte fact that most of the early chips lost will be going to the lucky bad players.

Basically, if you are going to come up with a formula for how much to spend on a tournament, it shouldn't compute a total amount of money you can spend. Instead, it should analyze each time you have to rebuy to calculate the EV of spending the money on the rebuy versus playing another tournament for the same money instead. If it shows that taking the rebuy is outright -EV, or if you're higher EV going to another tournament, then you should quit; otherwise take the rebuy.

It's more or less a general consensus that you should rebuy all the time. Besides, even if such formula were to be created, the values you'll be inputting into it will not be precise, so the results will have to be calculated with a certain degree of error and I suspect the highest expected value of that error would always be positive.

EDIT: I think ROI is a pretty useless statistic when calculating profitability, it's all about EV and SD.

Re: A Rebuy ? for Math Majors
 

But in the situation we're tlaking about, the buyins are the same. Your EV on the first $20 you put in, is going to be greater than your EV than the second $20 you put in. Because you're going to be entering yourself into a slightly harder situation, the later in the rebuy, ,the more difficult the situation.

Lets say in the 45k your initial double rebuy ($20) is worth $40. If you bust and buy back in, your new double rebuy, isgoing to be worth slightly less than $40. Lets say $39. Now if you only invest the $20 when you're getting the most value for it, or the initial time, then you'll have won more money.

By the same logic, it could make sense to not even take the double rebuy. The first 1500 chips you get are 'worth more' than the second 1500, so if over the long haul you only invested the original $10, i dont see why it wouldn't be more profitable than if you had spent the same amount of $ w/ the double rebuy.

Though, for variance/hourly rate/enjoyment factors, i think double rebuying and such is best. But now i'm not so convinced that it's the most profitable way.

That said, i could just be thinking really funky at the moment.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
EDIT: I think ROI is a pretty useless statistic when calculating profitability, it's all about EV and SD.

[/ QUOTE ]

ROI IS EV. you just have to make sure the units are the same. ROI uses buuyins as the unit (100% = +1 buyin) and EV is typically $ as the unit. Obviously they're not the same when they have different units, so saying that a $10k buyin has a bigger EV beccause you win more money, Meh, it's borderlin true.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
By the same logic, it could make sense to not even take the double rebuy.

[/ QUOTE ]

Thought about this some more, and i feel pretty confident about saying that now. double rebuying/adding on/buying back in when you bust and all is +EV, no doubt. But compared to what? It's +EV compared to not doing anything (this is considering you're a winning player). But's NOT +EV than just waiting and investing your $10 in the next tournament. So if time were of no concern, it would be better to just take the single addon, and that's all.

Method A:
You take the double rebuy, you buy back in when you bust, and you addon.
You make a series of $10 'purchases'.
The initla buyyin you buiy $20 of value for $10.
The doiuble rebuy you buy lets say $18 of value for $10.
The addon you buy $19 of value for $10.

Overall you've spent $30 to get $57.


Method B:
You single buyin to a tournament, if you bust you come back tomorrow. Repeat.

You buy $20 of value for $10.
You buy $20 of value for $10.
You buyy $20 of value for $10.

so now you get $60 for $30.



This all might be realyl common sense, but it's a new way of thinking for me, because i never really questioned the profitability of double rebuying. Because i just knew it was a +EV investment. but not necesarrily the most +EV.


edit:

If what i said is close to true. then even single rebuying, and single rebuying if you bust, is more +EV than double rebuying and double rebuying if you bust.

Re: A Rebuy ? for Math Majors
 

How does anyone account for the times that players with second hour starting stacks are only 5k and go on to win?

I think Cheif911 has won the 10+1 R a couple times with a 5K stack. I personally have gone deep starting hour 2 with 5K stack after multiple rebuys.

Another question: What is the value of your multiple rebuys if the chips you purchased stay on the table? I rebuyed multiple times at a loose table where our table average was 15K+ and I was very happy with my 5K stack because there were soo... many chips available starting the second hour.

The chips you bought through your multiple rebuys are still available too you after the rebuy period although they aren't in your stack yet.

How many times have we cursed the Pstars random table moves when you are sitting with 5k at a loaded table only to me moved to a table with smaller stacks? [img]/images/graemlins/frown.gif[/img]

I think aggressive Multi rebuy maniacs can gain some EV with every rebuy even if they don't have the chips at the end of the hour.

Some of the classic multi rebuy players are very good players that do an excelent job of getting those chips back. Some of that may be the "maniac" image that carried over into the second hour. Most of it is probably superior play when the non-rebuy portion of the tourny starts.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
[ QUOTE ]
I think logically you maximize your ROI

[/ QUOTE ]
That's where I stopped reading this thread.

[/ QUOTE ] That's too bad. Because eventually you would have come to this sentence:

[ QUOTE ]
if you are trying to maximize your amount of winnings per day (as opposed to maximizing your ROI), then of course you will want to rebuy when you go broke.

[/ QUOTE ]

My main point was to refute the notion that you should only enter rebuy tournaments if you are planning on rebuying if you go broke. Which I think is just silly and illogical.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
If what i said is close to true. then even single rebuying, and single rebuying if you bust, is more +EV than double rebuying and double rebuying if you bust.

[/ QUOTE ]
That doesn't make sense. I think you are inadvertently assuming that the player's total bankroll is $30, which obviously is preposterous.

If you buy in to a rebuy tournament, then you're already playing it. If you can then take an initial rebuy, which in your example gains $18 of value for $10, it makes no sense at all to say "I'm going to forego that, essentially throwing $8 out the window, because tomorrow I can enter another tournament and get $20 of value for the same $10".

You are confused because you are still thinking in terms of ROI, which is not the same as EV.

Re: A Rebuy ? for Math Majors
 

Well i said that you have to ignore time. EV is unrelated to time spent. So you're not 'throwing away' $8, you're just going to put the $10 to a better use. Think of it as you're playing two seperate tournaments, instead of one and double rebuying.

and, like i said to the other guy.. roi and EV are the same. They both measure your value.


[ QUOTE ]
That doesn't make sense. I think you are inadvertently assuming that the player's total bankroll is $30, which obviously is preposterous.

[/ QUOTE ]

Size of bankroll has nothign to do with the EV of a situation.

Re: A Rebuy ? for Math Majors
 

I don't know any of the math behind any of this. What I do know is that I play the first hour aggressively (sometimes maniacally) and rebuy every time I bust, because I need a giant stack to survive the second hour and go deep. I don't play outside of my bankroll and I don't play if I can't afford to rebuy.
It seems logical to me that playing a rebuy when you can't rebuy puts you at an automatic disadvantage to everyone else in the tournament.
Since my results support this method I will continue to use it.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
[ QUOTE ]
EDIT: I think ROI is a pretty useless statistic when calculating profitability, it's all about EV and SD.

[/ QUOTE ]

ROI IS EV. you just have to make sure the units are the same. ROI uses buuyins as the unit (100% = +1 buyin) and EV is typically $ as the unit. Obviously they're not the same when they have different units, so saying that a $10k buyin has a bigger EV beccause you win more money, Meh, it's borderlin true.

[/ QUOTE ]

ROI and EV are not the same, they're about as different as division and subtraction.

ROI = result/input, EV = result-input

A winning player in a $10,000 tournament will generally have a lower ROI than he would in a $1 tournament because of the vast skill difference of the opponents, but the EV of the $10,000 will be much higher than the EV of a $1.

Same in a cash game, your ROI will decrease, but your EV will increase. Doubling the stakes will not double your hourly rate, but it will increase it enough to be profitable.

Re: A Rebuy ? for Math Majors
 

[ QUOTE ]
Well i said that you have to ignore time. EV is unrelated to time spent. So you're not 'throwing away' $8, you're just going to put the $10 to a better use.

[/ QUOTE ]
But why are you so concerned with "the" $10?

If we are talking about the last $10 in your bankroll, then what you say will make some sense: put it where the EV is highest. But if we are sufficiently bankrolled, then we can spend the $10 on a rebuy today (which is worth $8 of EV) and if we lose that, still spend $10 on tomorrow's tournament (which is worth $10 of EV I think, I forget the numbers in your example).

The point is, this is not an either/or situation. You can do both. If you pass up rebuying today, then you are throwing away $8 of EV (compared to rebuying today, and also entering tomorrow's tournament).

[ QUOTE ]
Think of it as you're playing two seperate tournaments, instead of one and double rebuying.

[/ QUOTE ]
But it isn't two separate tournaments.

[ QUOTE ]
and, like i said to the other guy.. roi and EV are the same. They both measure your value.

[/ QUOTE ]
DWarrior gives a good explanation of why you are wrong on this point.