I guess trying to get back into the swing of playing and posting, I'll run a little math past you folks...

Anyhow, it's been said that a good tournament player can have an ROI of 100% or better, so what does one have to do to get that? (Actually, in SNGs, I think 50% ROI is doing very well, but whatever)

First, let's take the Stars prize structure at an 18-player SNG, which is quite different from a big tourney, which I'll consider later on, and let's take the buy-in as $10+$1. Prize pool is thus $180, with equal graduation depending on placement and payout for 4 places. So, if you make the money with a probability of p with even distribution among any of the 4 top places when you do make the money, what's your ROI?

Every time you make the money, you win an average of 180/4 = 45, but you have to subtract your buy-in of $11. So, the net profit for making the money is on average $34.
And when you don't make the money, you lose $11. So, your EV for the tourney is: p*34 - (1-p)*11 = 45*p - 11. That means your ROI is (45*p - 11)/11, which is just about 4*p - 1. Hence, if your probability of making the money at all is 25%, then you have an ROI of around 0. For an ROI of 50%, you need 4*p - 1 = .5, hence, 4*p = 1.5, mor making the money cut 3/8 of the time. It is worth noting that the seemingly small difference in p here (probability of making the money) makes a HUGE difference in ROI--the difference between a break-even player (winning nothing but losing nothing) and a fairly profitable one. To get 100% ROI, you would need to have 4*p - 1 = 1 or 4*p =2. Hence, you would need to make the money 50% of the time. Again, a boost of 1/8 in making the money cutoff makes a BIG difference in ROI.

Ok, now let's consider a big Stars tourney, also with an enormous simplification. I'll again assume that it's $10+$1 buy-in, but this time with 500 players. Top spot gets 25% of the prize pool, and second gets another 15%, so first and second together get 40% of the pool (this is about right also for somewhat larger and somewhat smaller tourneys). To make this generally applicable, here's where I'm going to simplify to the point of being rather inaccurate. Let's just say that you actually win the tourney with a probability of 1/n and otherwise just lose your buy-in.

Well, when you win, you win $1,250, and otherwise you lose $11. So, Your EV here is (1,250/n) - 11*((n-1)/n) = (1,261 - 11*n)/n. Now, if we want ROI to be 100%, then we would have 1 = (1,261 - 11*n)/(n*11) = (115/n) - 1, or 2*n = 115, hence n = 57.5

So, if you play 57.5 tourneys, win just one and miss all the money in the rest of them, you have the extremely good ROI of 100%. In actuality, of course, you need to win far less to meet this ROI, because you're also going to at least get your buy-in back in some of the others and may make another top place for a very good profit sometimes, too (just not first place).

The conclusion I draw is that in big tourneys, it's worth some (controlled) high risks for the higher spots in the tourney. You don't need to win very often to get an extremely good ROI--quite different in that regard from the SNGs, where you actually do need some pretty high consistency.

Ais,

Some interesting thoughts...you seem to prove that survival is an important focus in SNGs (be they 1 or 2 table), but that focus shifts more toward chip-gathering in a big tourny. Could we further assume that the amount of focus one puts on chip-gathering increases in direct proportion to the size of the tourny? In other words, in a 100-man tourney, you'd be more prone to avoid early risks, whereas in a 1000-man tourney, you'd be more willing to take some chances...right?

-TW

Aisthesis "the stat man"........is BACK!!!!