A Rebuy ? for Math Majors

[M.B.E.]

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I think logically you maximize your ROI

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That's where I stopped reading this thread.

[Exitonly]

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.
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[M.B.E.]

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.

[Exitonly]

uh?

EV = ROI

[M.B.E.]

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?

[Exitonly]

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.

[Exitonly]

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

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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.

[DWarrior]

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.

[Exitonly]

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

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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.

[DWarrior]

[ 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.

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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.