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

[Nicholasp27]

take a 15% ROI player in 10/1 tournaments
1.15*11=12.65/tournament (-11 buyin = 1.65 profit)
ICM says they should only bring in 10/tournament if even skilled
12.65/10=26.5% advantage due to player skill
If you start with 845 chips and everyone else has 795 chips, then ICM says you should bring in 10.51/tournament
10.51*1.265=13.29515 = what you expect to bring in due to skill advantage

13.29515/11=1.20865=20.865% ROI

that's 5.865 points higher than his usual 15%!!!


45 chips early on DOES make a difference

[Nicholasp27]

Now, someone tell me where the flaw is in the following double-up first hand strategy....


1600 stack vs 8 800 stacks...

.1844 is your new ev


18.44*1.265=23.3266
23.3266/11=2.1206 or 212% roi!!

now the games you don't double up first hand, you have -100% roi...

and the games where they all fold to your first-hand push, you will be at 20%, so still better than 15% you started out with if you fold hand one...

and if u wield a big stick for more than 26.5% skill advantage, your roi increases even more...not to mention $/hour implications and the increase in RB...

[schwza]

50/50 bust vs double up: 50% = 0. 50% = .184 or so by icm. on average, you get .092. not good.

[Nicholasp27]

yeah, that was the flaw...u aren't 0% roi if u bust

[Nicholasp27]

so you need to win 54.34% of the time if u do the double-up or bust strategy first hand to average out to .1 (.184/.1) that you have if you just fold

UNLESS

you have more than a 26.5% skill advantage when you are big stack...

if you are 50/50 first hand doubling up:

12.65/9.20=1.375

so if your skill advantage grows to over 37.5% roi and you can double up 50% of the time first hand, then it's worth it to you, as a 15% roi player normally, to go for it

however, u aren't gonna be 50% doubling up because you will face a better-than-average hand when called, so your random hand will be a dog

[microbet]

[ QUOTE ]
take a 15% ROI player in 10/1 tournaments
1.15*11=12.65/tournament (-11 buyin = 1.65 profit)
ICM says they should only bring in 10/tournament if even skilled
12.65/10=26.5% advantage due to player skill
If you start with 845 chips and everyone else has 795 chips, then ICM says you should bring in 10.51/tournament
10.51*1.265=13.29515 = what you expect to bring in due to skill advantage

13.29515/11=1.20865=20.865% ROI

that's 5.865 points higher than his usual 15%!!!


45 chips early on DOES make a difference

[/ QUOTE ]

Seems like a wierd way to calculate it. I did this in the other thread for a 1000 chip game, but I would put your max at:

$1.65 (you normally make) + $.51 (you are given) = $2.16 (what you now get)

$2.16/$11 = 19.6% for an increase of 4.6%.

[Nicholasp27]

why do you only get 51 cents?

that's what ICM says the AVERAGE player gains...you are 26.5% better than the average player, so you should get more than 51 cents...

what's the error in that logic?

[Nicholasp27]

let's try to get some criteria for when you should go for the doubling up first hand...

we know if everyone folds to your push, you gain in roi

if u just steal the blinds to be 825, then ICM says 10.28

10.28*1.265=13.0042/11=18.22% roi



so X% of the time, you steal blinds for 18.22% roi
Y% of the time, someone calls you and you win those hands Z% of the time for a 212 roi
the other times you get called and lose for ev=0


X(13.0042)+YZ(23.3266)>12.65, then you should do it



let's see what % of time your hand has to hold up for different calling %s Y:


10=12.65-11.70378=.94622/23.3266=.04056/.1=40.56%
50=12.65-6.5021=6.1479/23.3266=.263557/.5=52.7%


ok, so let's say that the average player will call with top 15% hands

if you are sb, Y=.15
if you are button, Y=.2775
if you are button-1, Y=.385875


so sb, you need to win 45.6% against top 15% of hands...which hands do that?
so button, you need to win 50% against top 15% of hands...which hands do that?
so button-1, you need to win 51.8% against top 15% of hands...which hands to that?

and so on...

[microbet]

Well, in the end the 8000 chips are worth the same to a winner as a loser, so each chip is certainly not worth some static non-zero percentage more for a good player than for a bad player.

I really think determining exactly what a chip is worth to various players based on their skill is just impossible. One could probably learn some stuff about this with massive computer simulations, but they would indeed have to be truly massive.

It does not seem obvious to me that giving a certain number of chips would give more money per tourney to a good player than a bad one (or vice versa), so I just assume it is the same.

I generally think of good players as building equity by making winning decisions, not as having more equity per chip.

[raptor517]

[ QUOTE ]
take a 15% ROI player in 10/1 tournaments
1.15*11=12.65/tournament (-11 buyin = 1.65 profit)
ICM says they should only bring in 10/tournament if even skilled
12.65/10=26.5% advantage due to player skill
If you start with 845 chips and everyone else has 795 chips, then ICM says you should bring in 10.51/tournament
10.51*1.265=13.29515 = what you expect to bring in due to skill advantage

13.29515/11=1.20865=20.865% ROI

that's 5.865 points higher than his usual 15%!!!


45 chips early on DOES make a difference

[/ QUOTE ]

i dont really care what any of these things say.. if you give me 45 extra chips my roi wont go up 5%. thats all there is to it. holla