rebuy tourneys

[gunbuster]

I was reading an earlier (length) thread on rebuys, and I don't know, but it seems relatively simple to me. As long as you are as good or better a player than the field, it makes sense?

The way I figure it, at the very beginning of a tourney, ignoring the VIG, lets say you pay $1000 for 1000TC. Each TC has a value of $1, assuming I am even w/ the rest of the field. If I'm offered the opportunity to buy more chips right there, they are pretty much the same value right? Now if I'm better than the field, the EV for each TC is slightly more than $1, as I have a better chance of cashing in than the next guy. Therefore, I'm making a gain on each $1 that I'm putting in on the tourney.

That seems to make sense to me.

However, I also worked it from another angle, lets say we were in a 10 person sat with each player of equal skill. On average a player will win 1/10 times. Now what if one player put in a rebuy off the bat, while the others did not. They paid $2K, increasing the prize pool to $11K.

The alternative would be to enter another two satellites at $1K each, each with a 1/10 chance of winning.

By entering two satellites at $1K each w/ a 1/10 chance:
1% of the time, I win both for $20K
18% of the time, I win one for $10K
81% of the time, I lose both for $0
This of course would have to total $2000

The case w/ the rebuy, where I pay $2K to win $11K..
In this case, I need to improve my chances of winning to 18.18% in order to be equivalent to entering a second satellite.

Now here's the question -- given equal skill does having 2K vs 9 players w/ 1K give you enough advantage to maintain the equity? I'm not exactly sure how you'd calculate that ?

[gunbuster]

Never mind the second case, it still works out.

Easiest example is if you make it an extreme. You pay $11K for 11K TC, everyone else pays $1K for 1K TC. You paid $11K to win $20K, so you need to win 55% to make this consistent.

Lets assume everyone goes all-in every hand. With 1K TC, you are going to win 10% of the time, so your EV for the tourney is $1K.

With 11K, you have a 90% chance of losing the first hand. After which, you'll be heads up w/ the remaining player for a 50/50 shot. .9 * .5 = .45 -- 45% chance of losing which translates to a 55% chance of winning. EV of your $11K comes out to.. $11K.

So there it goes, rebuy is goot, unless you are bad.

[Greg (FossilMan)]

The issue that throws people off is the diminishing value of chips in a big stack.

In your examples, the event was a satellite, winner-take-all, so there is no diminishing value. But, in a tourney that plays multiple winners, it is true that once you have a very large stack, the average value of a chip in your stack is LOWER than the average value of a chip in the stack of somebody else who has a short stack. While many people have read about this concept in 2+2 books, and understand it, what they don't understand is that this effect does not become of any significance until you are either in or near the money, OR if still far from the money you have a really, really big stack. In a typical rebuy/addon event, when making your rebuy addon decisions, you are still far from the money and it is very rare for your stack to be so big that chips in it are worth noticeably less than average.

Another issue that throws people off is return on investment, or ROI. They buyin for $100, get T100, and run it up to T500. They then get a chance to take a add-on where they pay $100 to get T200. They then reason that they paid only $100 for their current stack of T500, so it would dilute their ROI if they bought just T200 more for the same $100. Of course, they're right. However, their logic is fuzzy. The issue isn't ROI, but EV. If they pay $100 for an extra T200, will their total EV increase by more or less than $100? That's the question, and the answer should be MORE, unless they are a far below average player. Assuming average skill, the answer is a strong MORE, they are paying $100 for chips worth an average of probably $120-150 (depending upon rebuy prices, number of rebuys, number of addons, etc.). That's something like $20-50 of EV, which is very large for a tournament that is going to cost you in the range of $200-500 to play.

I wonder if this thread will turn into another length one or not?

Later, Greg Raymer (FossilMan)

[SossMan]

Greg,
Thanks for the obligatory once a week add-on/rebuy answer. Have you made a word file to cut and paste from yet? [img]/images/graemlins/tongue.gif[/img]

-SossMan

[gunbuster]

You're right. If you have a satellite where the winner takes all, it does not appear to be a diminishing effect as you add in more chips.

I worked out the example again, this time assuming that 30% gets paid to 2nd place, and 70% goes to first. Assuming again that every play is all-in (I know, a gross over simplification), the player who bought in for 11K (while others bought 1K), will get the following distribution:

45% - 2nd place - 6000
55% - 1st place - 14000

So if they expect to win 6k 45% of the time and 14K 55% of the time, that only totals to (2700 + 7700 = ) 10400. This of course assumes that the player with 11K chips can't finish lower than second -- which though unlikely, is still possible. In this theoretical example, there is -EV for buying so many damn chips.

So it seems that the value of the chips do diminish as you continue to buy more and more chips. I wonder at what point does it stop making sense to rebuy? I wonder if we could simulate different % finishes...