MATH: 45 extra chips to start 800-chip tourney adds >5% to ROI

[curtains]

Apathy this all threads from another thread where I suggest to raise on the button with 88 and 15-30 blinds. A few counterarguments were that the 45 chips in blinds don't actually mean anything, and so I said that I disagree because of this.

[Apathy]

[ QUOTE ]

Apathy this all threads from another thread where I suggest to raise on the button with 88 and 15-30 blinds. A few counterarguments were that the 45 chips in blinds don't actually mean anything, and so I said that I disagree because of this.

[/ QUOTE ]

Gotcha I'll check that one out.

My point still stands that it is faulty logic to justify a play that you wouldnt usually do by saying what it will add to your CURRENT roi because your CURRENT roi is not the same since you are changing the way you would usually play in certain situations, so you can't just add roi points for the balance of the increase in chips from your new play.

[curtains]

Dude I dunno what you're talking about, at least that's nothing I've ever argued!

[microbet]

My part in the discussion was purely based on just starting with different chip stacks. Academic. I'm not talking about crazy allins on the first hand.

[Apathy]

[ QUOTE ]

Dude I dunno what you're talking about, at least that's nothing I've ever argued!

[/ QUOTE ]

Meh never mind is was in the original post and the replies on the first few pages, you never said it.

[Apathy]

[ QUOTE ]
My part in the discussion was purely based on just starting with different chip stacks. Academic. I'm not talking about crazy allins on the first hand.

[/ QUOTE ]

It was pretty much the NicolasP posts at the start of this thread discussing some sort of all in early to double up strategy. I just came into this discussion at a weird time so nevermind.


Basically someone makes that post about taking flips early once every few weeks and I have some strong views about it and I thought that was what this discussion was based around after skimming through it.

[Insty]

Here is some mathematical proof that the original post was erroneous:


[ QUOTE ]
take a 15% ROI player in 10/1 tournaments
1.15*11=12.65/tournament (-11 buyin = 1.65 profit)


[/ QUOTE ]
Ok.

Some defintitions:
ROI(1) = 15%
$ENTRY(1) = 11
$WON(1) = ROI(1) * $ENTRY(1)
$WON(1) = 1.15 * 11
$WON(1) = 12.65

[ QUOTE ]

ICM says they should only bring in 10/tournament if even skilled
12.65/10=26.5% advantage due to player skill


[/ QUOTE ]

Ok, you have made up a new measurement called skill advantage.
Which you have defined as $WON/$EV

SA(1) = $WON(1) / $EV(1)
SA(1) = 12.65 / 10
SA(1) = 1.265

[ QUOTE ]

If you start with 845 chips and everyone else has 795 chips, then ICM says you should bring in 10.51/tournament


[/ QUOTE ]

ok.. It does. (This is also approximately -4.4% ROI)
$EV(2) = 10.51

[ QUOTE ]

10.51*1.265=13.29515 = what you expect to bring in due to skill advantage


[/ QUOTE ]

This is where things go wrong.
I dont think you can use skill advantage like this. But the multistep way makes it hard to see why.
This is what you have done so far.
$WON(2) = $EV(2) * SA(1)
$WON(2) = 10.51 * 1.265
$WON(2) = 13.295


[ QUOTE ]

13.29515/11=1.20865=20.865% ROI
that's 5.865 points higher than his usual 15%!!!


[/ QUOTE ]

This is just getting wronger.

What you have done.
ROI(2) = $WON(2) / $ENTRY(2)

Lets expand $WON(2):
$WON(2) = $EV(2) * SA(1)
ROI(2) = ($EV(2) * SA(1)) / $ENTRY(2)

Now lests expand SA(1):
SA(1) = $WON(1) / $EV(1)
ROI(2) = ($EV(2) * ($WON(1) / $EV(1)) ) / $ENTRY(2)

Lets expand WON(1):
$WON(1) = ROI(1) * $ENTRY(1)
ROI(2) = ($EV(2) * ((ROI(1) * $ENTRY(1)) / $EV(1)) ) / $ENTRY(2)


Since
ENTRY(1) = ENTRY(2) = 11

We can cancel them.
ROI(2) = ($EV(2) * ((ROI(1) / $EV(1)) )


Which gives us ROI(2) in terms of EV's and ROI(1) that is bad.
Which of these are you claiming is your real ROI?

You can transpose the above to:

ROI(2) / ROI(1) = EV(2) / EV(1)

Which just gives you some unsurprising ratios.



What you CAN do is recalculate skill advantage SA(2):

If you start with 845 chips:
SA(2) = $WON(1) / $EV(2)
SA(2) = 12.65 / 10.51
SA(2) = 20.4%

So if you always start with a 45 chip advantage you have a smaller skill advantage than before.

[ QUOTE ]

45 chips early on DOES make a difference


[/ QUOTE ]

Yes, you have a smaller skill advantage.

[Nicholasp27]

i'm not a proponent of doing the double-up first hand thing...i was simply doing an exercise to see what this argument would say about doubling-up first hand

if u got to my post with results, it showed you can push 99+,ato,ajs,kqs only from the sb if bb calls with top 15% of hands and everybody else folded first

it doesn't say to push any2 from any position with any number of limpers...it is a very small % of the time that you can do it...but it's based on the theory that 45 chips give you 4 roi points

[Nicholasp27]

yeah, that's why we later abandoned the whole skill advantage issue and just looked at icm only, so an average player...icm DOES discount the value of added chips as your stack gets bigger...


it says you go from 10 to 10.51 if you get 45 chips to start tourney (5 from each player)...that's 4.4 roi points

now, someone tell us why that is wrong for an average skilled player...

[Nicholasp27]

yeah, that's why we later abandoned the whole skill advantage issue and just looked at icm only, so an average player...icm DOES discount the value of added chips as your stack gets bigger...


it says you go from 10 to 10.51 if you get 45 chips to start tourney (5 from each player)...that's 4.4 roi points

now, someone tell us why that is wrong for an average skilled player...