Paul Samuel's article "To Add On or Not"
Part I: http://www.pokerpages.com/articles/a...s/samuel32.htm
Part II: http://www.pokerpages.com/articles/a...s/samuel33.htm

The Poker Pages thread that Marm referenced to:
http://www.pokerpages.com/interactiv...pic.php?t=4809

I was surprised this thread didn't progress as I loved the Samuel article and Marm's argument thought it might not show in the thread. I just thought that it was borderline paralysis via analysis as I stated the Poker Pages thread.

This community could definitely do more with it. Have at it.

I have been crunching some numbers on this topic, but have yet to come up with anything concrete enough to persuade alex. Still working though.

The concept is that if you have a massive stack at the end of the rebuy period in a MTT tournament, there may come a point that adding-on becomes -EV. This becomes true when you spend more buying the add-on than you gain in $EV. It is an example of diminshing returns.

Here is an extreme example. Somehow you manage to gather 9900 of the 10,000 chips in a Winner-take-all rebuy tournament (stupid format, but easy math) after the rebuy and you are the last person to choose to ass-on or not. There is $1000 right now on the prize pool after everybody else has choosen to add-on. Everybody else has made their choice, and your % of chips and the prize pool will not change aside from your add-on. You must now spend $10 to get another 10 chips (Yes, 10 chips, I said an extreme example).

Without adding-on, your $EV is $990 right now (9900/10,000 =99% 99%x$1000=$990). Given the fact that skill is not considered here, your % of total TC in play is considered to be your % chance of winning the event. Similar assumptions are made in deal making, so they can be applied here.

If we add-on, we now have 9910TC of the total 10,10TC (for 99% still, actually 99.00099%. but insigificant amount of increase). The prize pool is now $1010. This makes our EV $999.90. ($1010 x 99%)

We have now spent $10 to gain $9.90 increase in EV, therefor creating a -EV situation. We are actually losing $ by adding-on here. We have lost $0.10. Not much, but still an avoidable loss.

Ok, This little example I just pulled outa my arse shows me that the math I have been exploring is actually correct, but I just wasn't testing it with extreme enough numbers to get the results I was looking for. Heres what I have been messing around with, comments welcome. THESE ARE FOR WINNER TAKE ALL EVENTS ONLY! For now at least. The Math to do EV for multiple payout structures becomes VERY complicated VERY quickly. I am showing this stuff for example only.

If we let E represent our $EV for the event if we don't add-on, and we let E' (E prime) represent our $EV to add-on, and D is the amount of money spent on the rebuy, then when E' - E < D then it is -EV to add-on.

Let:
P is the total Prize Pool,
T is the total number of chips in play
A is the amount of chips we recieve for the add-on
D is still the amount spent on the add-on
S is the amount of chips currently in our stack

E = P(S/T)
E' = (P+D)[(S+A)/(T+A)]

E is simple enough, Stack divided by total TC times Pool. in E' we need to add our cost to the prize pool (P+D) and the add-on to both our stack (S+A) and to the total TC (T+A). They are the same formula, just one is with the add-on.
Therefore:

(P+D)[(S+A)/(T+A)] - P(S/T) < D

If the total on the left ends up being less than D (on the right), then rebuying is -EV.

I think you are correct in thinking this way, although the situation where it comes up won't happen enough.

I almost entirely agree with Alex.

There are a few exceptions though,

$20 buy in/$20 add on. 100 people left everyone else has already decided to add on or not. avg stack 4000 the blinds will be 50/100, you are the chip leader with 12,000, the add on is 1,000. There is no reason to add on here.

another example is;

$100 buy in/$100 add on, 500 starting chips. 40 peple left avg stack 4800, you have 2700, the blinds will be 100/200. the $100 add on is not worth the risk, you will still need to double up and the extra 500 chips will not buy you many extra hands, you need to double up NOW. I think this would be a -ev play purchasing the add on. if this wasn't an add on tournament you would feel comfortable, not happy but comfortable, with your current situation.

I need to come back and read this when I can think.

Steve, I agree with your examples as they are extreme, though I would add the 10 extra BB's to my stack in your first example.

The second example has the add on as a SB. That would be retarded. I measure my stack in a tourney with the others, but your stack in proportion to the blinds at such an early stage has a very heavy weight attached to it. Even as a below average stack, if I have 50-60 blinds due to the structure or whatever, I feel good and can play my game. Will I get callers that wouldn't normally call because they're playing their stack? Yes. But, there's still no rush to "make something happen."

Originally Posted by bonchkid

I think you are correct in thinking this way, although the situation where it comes up won't happen enough.

What Bonch said is my main point. EV depends on constants, not coincedences. I'm not talking about ifs and in these extreme examples, I wouldn't rebuy. But rebuy tournaments are very competitive and a lot of chips are in play. You need those chips.

I would refuse an add on only if I possessed a higher percentage of the chips in play than the percentage of people left that will not payout and if the add on were a minute chip similar to Steve's second example.

EXAMPLE:
100 man tourney
At the add-on 90 people left
18 payout
I would have to possess 72% of the chips in play after all of the add ons to consider not adding on.

This has never come up therefore I will continue to rebuy.

Another would be if the add on supplied me with less than enough blinds to compete as I stated earlier.

Samuels wrote a good article that we're still talking about and you're crunching hard numbers that don't need to be crunched because I still say that there is no way to quantify someone's chances of placing or winning a NL or PL tourney at such an early stage unless you have an extreme example in which the answer to our "question" is obvious on its face.

In Samuel's example, he has 20% of the chips in play and the tourney pays out 18%. He never says how many people remain in the 50 man tourney. Let's guess 40. 55% of the field needs to go broke before he can make the money and he questions whether to add 4,500 to his 10K stack at the break?!

That's retarded. He can increase his stack my almost 20% to increase his oppurtunity, not odds, not chances to make a profit.

Nothing's nearly a lock or close to a lock when you have 20% of the chips in play while 55% of the existing field still needs to drop fro you to cash, especially when the vast majority of that existing field that are hunting for your chips have increased their firepower to break you by adding 4,500 to their stacks.

That's like our troops leaving their extra bullets in Basra before going to Baghdad.

(Excuse me for that simile if you feel it's disrespectful to our troops because I mean none.)

I agree that samuels article was a little Ego heavy I think he said something like "I feel I am 60% better than the rest of the field" there fore.....

ANd trust me, you won't catch me not adding on, unless of course I feel that I satisfy the equation I stated above And Then I wouldn't care anyways since I'd have such a huge stack though.

One thing to note though, and its not something I addressed in my original post, is that the threshold for S to satisfy E'-E<D goes down as the number of payout spots goes up. In english, the more places that pay, the point of zero return comes quicker. The flipside to that is, for more spots to payout, there has to be a larger number of entrants, therefore is even harder to have a larger enough stack in realtionship to the total number of chips in play to consider not adding-on.

Originally Posted by Marm

I agree that samuels article was a little Ego heavy I think he said something like "I feel I am 60% better than the rest of the field" there fore.....

ANd trust me, you won't catch me not adding on, unless of course I feel that I satisfy the equation I stated above And Then I wouldn't care anyways since I'd have such a huge stack though.

One thing to note though, and its not something I addressed in my original post, is that the threshold for S to satisfy E'-E<D goes down as the number of payout spots goes up. In english, the more places that pay, the point of zero return comes quicker. The flipside to that is, for more spots to payout, there has to be a larger number of entrants, therefore is even harder to have a larger enough stack in realtionship to the total number of chips in play to consider not adding-on.

I concur.