Thought exercise: what is your EV?
Consider this thought exercise (have I posted this before?):
There are 100 players in a tournament. The distribution of skill level is typical of your local tournament. 10% of the field gets paid, heavily skewed to the top three. The buy-in is $1 (we will ignore the vig).
What is your Expected Value (EV)? In other words, in the long run what will you expect to make when you play a tournament. Note that this is not about hourly rate it is about "money won per tournament played."
To solve this question, you will need to assign each of the 100 players an EV. The total must equal $100. Obviously, some players will be negative EV players and others will be positive.
So, what is your EV?
There are 100 players in a tournament. The distribution of skill level is typical of your local tournament. 10% of the field gets paid, heavily skewed to the top three. The buy-in is $1 (we will ignore the vig).
What is your Expected Value (EV)? In other words, in the long run what will you expect to make when you play a tournament. Note that this is not about hourly rate it is about "money won per tournament played."
To solve this question, you will need to assign each of the 100 players an EV. The total must equal $100. Obviously, some players will be negative EV players and others will be positive.
So, what is your EV?
Comments
Okay... this is not a mathematical proof, just a back-of-the-envelope
ball-park calculation. Of course, we need a few more specific
assumptions. You're all free to disagree with these assumptions, of
course -- they might not apply to your tourneys, or you may see your
tourneys differently. Make up your own numbers -- build your own
ball-park!
Assumtion 1: the players are in five groups:
5 highly skilled
10 skilled
20 solid
45 weak
20 terrible
Assumtion 2: on average the total amount of prize money going to
all the entrants in each group is:
$40 highly skilled
$30 skilled
$20 solid
$9 weak
$1 terrible
Then the EV is the total prize for the group divided by the size
of the group (less $1 entry fee):
5 highly skilled: $40/5-1 = $7.
10 skilled $30/10-1 = $2.
20 solid $20/20-1 = $0.
45 weak $9/45-1 = $-0.80.
20 terrible $1/20-1 = $-0.95.
That doesn't look completely right to me, but it's "in the ballpark".
(I'm sure the assumptions can be
tweaked to make the conclusion more realistic.)
This is, however, exactly the method that I use to solve the problem. The solution is to jigger the numbers to reflect what a person actually sees happening.
With the same player types as the prof, how about something like:
$15 highly skilled
$20 skilled
$25 solid
$30 weak
$10 terrible
Individually, that's
+$2.00 highly skilled (still too generous?)
+$1.00 skilled
+$0.25 solid
-$0.33 weak
-$0.50 terrible
Jigger those, baybeeeeee!
(Oops, too much coffee this morning it seems.)
ScottyZ
I think Scotty's numbers are about right, and I think I'd be at around +$1.5 or so, from a purely objective, results-oriented standpoint.
Regards,
all_aces
'Skill is important in tournaments. If you're three times as good as other opponents, you might expect to win one tournament out of a hundred."
-Mike Caro
see what's happening, so I just made up some numbers for argument's sake. Glad I found a useful
method, though....
5 highly skilled
10 skilled
20 solid
45 weak
20 terrible
Now, I have the following questions (I add in probabilities and fancy P things to make it look like I know what I'm doing -- when I'm really only taking a stab at this!)
a) what is the probability of each category to money? Pm(category)
b) what is the probability of each category to place in the top 3? Pt3(category)
c) what is the probability of each category to win? Pw(category)
Because the money finishes have a heavy weighting for top 3, I think we need to split out the EV calculation into three categories -- top spot, top 2, and the other 7 spots.
EV = EV of a top 7 finish + EV of a top 2 + EV of a win
EV of a top 7 spot finish =
(prob. of a money finish - prob. of top 3 - prob. of win)* (money for top 7 spots / 7)
EV of a 2-3 spot finish = (prob. of top 3 - prob. of win)* (money for 2&3 spots) /2)
EV of a top finish = prob of win * money for top spot
Now the fun part. What are the probabilities for each category? I’ve created a matrix to work out the probabilities.
I take the probability of a each category winning the tournament and multiply it by the number of players in that category, and add it up for all categories. The number must come out to 1 as there can only be one winner.
Then for a top 3 finish, I do the same – with the total number coming out to three. And finally for a top ten finish the total number must come out to 10.
The probability of a money/out of the money for each category must add up to 100. As I think about the following matrix, it feels right.
Note, if you have more highly skilled players, the probability of a highly skilled player must go down, as there can only be one winner. This would reflect reality.
Now does this matrix reflect Dave’s observation of bad players winning more often than they should. I think it does, as you have a 71% chance that a particular highly skilled player will not win any money at the tournament. And, you have a 7% chance that weak/terrible players will be in the money – 7% of 65 players has 4.5 of these players in the money! Note few of them would be in the top three. That would feel about right.
It’s a numbers game – with more of terrible players, it’s more likely they will money collectively. However, individually they only have a very small chance.
Now for my EV calculation.
Hmm....I guess I put way too much pressure on myself to get into the top three as I think I'm in the solid category. Note that this category of players makes more money from a money finish than a top three. Then the next category makes more money from the spots 2-10. And, the best make the most money from their first place finishes. I think this is also in line with real tournament experience. I'm not sure if this model works for smaller size tournaments.
Even on holiday in the Dominican I can't get away from the forum. THis post looks to me to be brilliant. Once I return to Canada and dry out from the Cuba Libras I will give it my full consideration.
I propose that this forum be known as
Canada & The Dominican Republic's Poker Forum
until you get back. :cool:
ScottyZ