Thoughts on VP$IP as a function of M during a MTT

[Nougat]

Wow. That's quite an impressive achievement and certainly useful to a great many people including myself. Congrats.

[rama96ab]

This is very interessting for me - Excellent thanks!

I've ordered the book today to read more...

I discovered a few thing with the equilibriums with M=6 which you posted. Compare with the function 1/X, where X is active players left in the hand. First-in from BTN , where X=3 gives 33% pushing hands, CO X=4 gives 25% pushing range..etc.. this function is VERY equal to the Killer pushing ranges in all position with M=6!

With the M=6 this gives an 20% VP$IP (BB=9% range!) (If first-in in all positions). Compared to Harrington's pushing ranges Killer is much tighter! Going through lot's of his examples and "plotting" Harrington's hand ranges, his willing to puch with a lot more hands.. (Ex. any to cards first-in on BTN with M=5).

My origial ideas with M=6 was 10% (my share on a 10 person table) plus 1/M = 1/6 = 17%, which sums up to 27% VP$IP.

I've now tighted this in my Excel sheet to watch's Killers recommeded ranges - great! (Anyone interested to see let me know) - I got 2nd place trying in 1 SNG so this showed the correctness ;o)

My new challenge is plotting a few other point into the function F(M) = VP$IP to model the function when M differs from 6. Say M = 3 and M = 25.. or whatever - at least one point above and one point below with M = 6. You wrote Killer "only" put ranges for M<=8, so I guess I need to make some assumption with higher M's!

Let's do a thought about the high M. Playing with an M = 33 you're pretty functional poker player (using Harrington's term) so let's assume this is the point where you want to hit VP$IP = 10% which should be your share in a 10 man table. What I do is to take each possitions pushing ranges and normalized by 10% / 20% - So I'd play half the range with M=33 - dropping below I'd have convergence to 20% as M -> 6.

With a very high M (>33%) i'd then play less my share of 10% etc. which seem pretty intuative to me
and in much other literature - play tight early in tournemants.

Any thought on a good "break-even" M where you hit 10% VP$IP - M= 33 good? M=20 or 50?

What does Killer say with M=3 and M=8 - just to get an idea of the function F(M) = VP$IP? I have an intuition that the function is something like a*Ln(M)+b = VP$IP, especially to get f(33)=10% and a appropriate convergence to f(6)=20% !

Thank for the respnses so far..

Best regards
Rama96ab