Button Raise First In

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Posted by posted in Mid Stakes

Button Raise First In

Thinking about RFI rules of thumb from the button.

Think the equation for opening our weakest hands looks like this:
-2.5(x) + 1.5(y) + ((pot size when called - average rake taken)(z) - cost of getting to the flop)(1-x-y)

where x is how often we get 3b (assuming we fold to all 3bets)
y is how often the steal works
z is the % of the pot we realize when called

Now with the bottom 15% of hands we have 40% equity vs top 65% hands minus a 10% 3b range.

If we assume that we realize that 40% (which seems reasonable because the factors of having a hand that does a poor job of realizing equity opposes the fact that we have position and the 'uncapped' preflop range) and that our opponent doesn't adjust to our strategy, we get the following break-even points:

(Cumulative 3b%/Steal-success rate)
12/39, 15/42, 18/45, 21/48, 24/50

Since the numbers seem to scale together we can come to the rule of thumb that:
If Steal Success Rate - Cumulative 3b% > 26 or 27, then opening any 4 cards assuming opponent is not adjusting is better than folding

Assumptions: 2.5x raise, only the bb calls (5.5bb pot), and .75bb average rake taken

Also interesting to think about is how the graph of % of hands we should open vs opponents overall defending % given a constant 3b% would look.
My guess is something like this (using 18% cumulative 3b (what it actually is in my hm database)):

https://gyazo.com/76289e0c2201b551d816cedc5bb55450

Any thoughts appreciated

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