Maths help!

[MC]

I'm trying to work out this problem:


A player has a 10% ROI in $15+1 tournament. He therefore earns $1.60 a game.

That game becomes a $10+0.85 tournament. How much does he earn per game? (assuming the player pool is of the same skill level)



It's not as simple as: he earns $1.09 per game because the rake ratio has increased.

If the rake ratio was the same as $15+1, the tournament would be $10+0.67 instead of $10+0.85

Does he therefore earn $1.09 - ($10.85-$10.67) = $0.91

[Bongo]

Can we express it a bit differently?

If we say he has a 17.333% ROI (he must win $2.6 to make $1.6 after rake) in the game and pays $1 for the privilege of playing then we can apply that to the other situation too.

He'll earn $1.7333 a game he plays and pay 0.85 to play and make $0.883 a game.

[MC]

Can we express it a bit differently?

If we say he has a 17.333% ROI (he must win $2.6 to make $1.6 after rake) in the game and pays $1 for the privilege of playing then we can apply that to the other situation too.

He'll earn $1.7333 a game he plays and pay 0.85 to play and make $0.883 a game.

Looks interesting, you might be onto something. ROI incorporates rake though, does that affect how you've worked things out?

[smashedagain]

just thinking out side the box james can both be compared acuratley. are the payout structures and %ages the same are the field sizes the same (thinking you must be playing the 180 sng)

[Bongo]

I've calculated the ROI without rake, and then transferred that to the other game. Logically rake shouldn't affect ability (given the stipulation that the field is the same skill level), so that ROI should hold whatever - much like it would if the rake on the 15+1 games was changed to 15+.75 or 15+1.5

[MC]

Yup yup, looks good, gonna go do some calcs, tytyty!

jason - yeah, you're right about accuracy being a problem because of other factors

[gatso]

bongo's spot on. another way to explain it that may be simpler to understand

let's assume 100 runners in both tournies, same payout. in the 15+1 the prizepool is $1500 and our average payout is $17.60 so we win 1.173333333333333% of the prizepool

in the new tourney we should win the exact same % on average if against the same playerpool, the prizepool is $1k so we on average win $1.1733333 which is a profit of $0.83333333

[smashedagain]

Yup yup, looks good, gonna go do some calcs, tytyty!

jason - yeah, you're right about accuracy being a problem because of other factors

few was sat here thinking someone was gonna post shut up you donk. lol

[Sheriff Fatman]

I'm trying to work out this problem:


A player has a 10% ROI in $15+1 tournament. He therefore earns $1.60 a game.

That game becomes a $10+0.85 tournament. How much does he earn per game? (assuming the player pool is of the same skill level)



It's not as simple as: he earns $1.09 per game because the rake ratio has increased.

If the rake ratio was the same as $15+1, the tournament would be $10+0.67 instead of $10+0.85

Does he therefore earn $1.09 - ($10.85-$10.67) = $0.91

My gut feel on first reading your post was that the drop off in earn you'd calculated 'felt' too big to me for the change in rake applied.

My take on it is this:

If we assume that he's making $1.60 a tournament (i.e 10% ROI) at present, then he's achieving a distribution of results to overcome the rake applied at that level.

If we call this distribution of results 'Z' then

10% = 0.1 = Z x 15/16

Therefore Z = 0.10667

Assuming that the distribution of finishes doesn't change at the new structure and that the payout %'s are unchanged for each position, we can use the above constant to calculate his new ROI for the revised structure, as follows:

New ROI = 0.10667 x 10/10.85

New ROI = 9.83%  (i.e. the change in proportion of rake has dropped his ROI by 0.17%)

Applying this to a buy-in of $10.85, he therefore now expects to earn $10.85 * 9.83% = $1.066 per tournament.

So in effect, he loses $0.51 per game from the reduced buy-in, and a further $0.024 per game because of the change in rake.

Hope this makes sense - I await the first shots to be fired at my logic!