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Maths: Why do we get in part of our range which loses vs their Range?

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Posted by posted in Mid Stakes

Maths: Why do we get in part of our range which loses vs their Range?

Maths: Why do we get in part of our range which
loses vs their Range?

To make a simple scenario:

Blinds are $0.5/1.  We are assuming
blinds will fold.  Stacks are $37.5.  Co raises to $3.5
with 35% of hands.  Button makes it $12 with a 10% range.  When
CO 4bets BN calls it off.

For CO to profitably 4 bet:  they are
risking $34 to win $76.5, so they need 44.444% equity in the hand to 4bet get
it in. 

My question is why do we want our range to have
this equity, as opposed to narrowing our range and having a play which makes us
more money?  
- is it just to make CO less exploitable in a game
theory sense? as BN could adjust and just ramp up their 3 betting range when
they figured out CO's range is too tight?  

Below are my numbers to show how a tighter range is
more +ev.

By using Pro poker tools to find out what range of
all hands have 44.444% equity, it is roughly the top 23% of hands.  So
CO is shoving 23/35 = 65.71% of the time.  The average equity for CO=
44.88%. BN equity = 55.12%. using this info we can create an Ev table:

Now, if we are to have the same scenario but with
CO only 4 betting the top 8% of his range we see that CO is shoving 8/35 = 23%
of the time, but this time has an average equity of 51.92%.  If we
extrapolate the rest of the numbers needed it creates the table:

So in a vaccum, with these ranges (which happen to
be the propoker tools hand equity ranges) it is clearly more +ev after being 3
bet to 4bet the top 8%.

So intuitively, the top of the range is
compensating for the bottom of the range as shown by how well the 8-23% of the
range does.   So with a similar table to the above we see the CO
4bets 15/35 = 42.85% of the time.  When shoving  Co has an
average of  41.731% equity.  From this we can create the
table:

So this portion of our range clearly loses us
money.  Why do we want to keep it in having reached the scenario of
being 3bet?


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