A
AnAnarchist
Rising Star
Bronze Level
I've been working on creating my own set of mathematical ranges as both an improvement exercise and to see why certain standard ranges online differ so much. (I know range charts are just a leap off point for playing blind, I still believe there should be an optimal blind set of ranges.)
To work out the ranges the Hero should play from each position I first worked out the range that when dealt our hero will on average be ahead of all the remaining players left to act.
UTG >10%
MP >12.5%
CO >16.66%
BTN >25%
SB >50%
I then considered the impact of position on these opening ranges. This unfortunately to the best of my knowledge hasn't been mathematically worked out so the best I could do was estimate.
Looking at HU most pros advocate round about a 90% opening range on button. Given that hand strength indicates a 50% opening range we can say that position gives a 1.8 multiplier to opening range %.
So if our BTN opening range is about 25% based on hand strength we can then apply the 1.8 multiplier and come up with a 45% opening range on BTN. Seems pretty reasonable.
In 6 max while opening,
CO - has position on 2/3 opponents
MP - has position on 2/4 opponents
UTG - has position on 2/5 opponents
Adjusting and then applying the multiplier to other positions,
If our CO opening range is 16.66% * 1.533 = 25.56%
If our MP opening range is 12.5% * 1.4 = 17.5%
If our UTG opening range is 10% * 1.32 = 13.2%
You'll notice I left out SB here as you will always be OOP when opening from SB. I believe a typical SB range should probably look like a defending range for HU play, though some 6max charts advocate a much looser approach. It's something I'm still looking into.
So our opening ranges (ignoring SB) are,
UTG (13.2%)
MP (17.5%)
CO (25.56%)
BTN (45%)
All very well and good! Pretty standard ranges!
However
Lets consider UTG. We've effectively opened up our UTG range to compensate for position when we are in fact OOP the majority of the time!! How can this make sense? Surely when adjusting for position we should in fact tighten our UTG range due to being OOP more often than not?
I'm thinking that my adjustments of the 1.8x multiplier are basically incorrect when it comes to any position with >50% chance of being OOP.
So here I am scratching my head. I'm no mathematical genius, not by any stretch; this is just my attempt to better understand the fundamental maths behind why we're opening what we're opening. If someone smarter than me can explain the UTG problem, critique my overall approach or just tell me where I'm going wrong or right I'd appreciate any and all help. Thanks!
To work out the ranges the Hero should play from each position I first worked out the range that when dealt our hero will on average be ahead of all the remaining players left to act.
UTG >10%
MP >12.5%
CO >16.66%
BTN >25%
SB >50%
I then considered the impact of position on these opening ranges. This unfortunately to the best of my knowledge hasn't been mathematically worked out so the best I could do was estimate.
Looking at HU most pros advocate round about a 90% opening range on button. Given that hand strength indicates a 50% opening range we can say that position gives a 1.8 multiplier to opening range %.
So if our BTN opening range is about 25% based on hand strength we can then apply the 1.8 multiplier and come up with a 45% opening range on BTN. Seems pretty reasonable.
In 6 max while opening,
CO - has position on 2/3 opponents
MP - has position on 2/4 opponents
UTG - has position on 2/5 opponents
Adjusting and then applying the multiplier to other positions,
If our CO opening range is 16.66% * 1.533 = 25.56%
If our MP opening range is 12.5% * 1.4 = 17.5%
If our UTG opening range is 10% * 1.32 = 13.2%
You'll notice I left out SB here as you will always be OOP when opening from SB. I believe a typical SB range should probably look like a defending range for HU play, though some 6max charts advocate a much looser approach. It's something I'm still looking into.
So our opening ranges (ignoring SB) are,
UTG (13.2%)
MP (17.5%)
CO (25.56%)
BTN (45%)
All very well and good! Pretty standard ranges!
However
Lets consider UTG. We've effectively opened up our UTG range to compensate for position when we are in fact OOP the majority of the time!! How can this make sense? Surely when adjusting for position we should in fact tighten our UTG range due to being OOP more often than not?
I'm thinking that my adjustments of the 1.8x multiplier are basically incorrect when it comes to any position with >50% chance of being OOP.
So here I am scratching my head. I'm no mathematical genius, not by any stretch; this is just my attempt to better understand the fundamental maths behind why we're opening what we're opening. If someone smarter than me can explain the UTG problem, critique my overall approach or just tell me where I'm going wrong or right I'd appreciate any and all help. Thanks!