Widening 4-bet ranges with AQ and mid pocket pairs

Assume 100BB stacks, 3betsize is to 10BB and we do not count the dead money we put in for initial raise.

Let x be optimal 3bet% for 4betting wider

Opponent will stack off with JJ+/AK (top 3%)

1) 55-TT (33% equity against JJ+/AK)
In a 200BB pot, 67BB belongs to us.
On average, we lose 33BB [100-67=33]
(100-3/x)*10BB – (3/x)*33BB = 0
x=12.9%

2) AQs or 44 (32% equity against JJ+/AK)
In a 200BB pot, 64BB belongs to us.
On average, we lose 36BB [100-64=36]
(100-3/x)*10BB – (3/x)*36BB = 0
x=13.8%

3) AQo (28% equity against JJ+/AK)
In a 200BB pot, 56BB belongs to us.
On average, we lose 44BB [100-56=44]
(100-3/x)*10BB – (3/x)*44BB = 0
x=15.2%

Opponent will stack off with QQ+/AK (top 2.5%)

1) 55-TT (36% equity against QQ+/AK)
In a 200BB pot, 72BB belongs to us.
On average, we lose 28BB [100-72=28]
(100-3/x)*10BB – (3/x)*28 = 0
x=11.4%

2) AQs (28.5% equity against QQ+/AK)
In a 200BB pot, 57BB belongs to us.
On average, we lose 43BB [100-57=43]
(100-3/x)*10BB – (3/x)*43 = 0
x=15.9%

3) AQo (24.5% equity against QQ+/AK)
In a 200BB pot, 49BB belongs to us.
On average, we lose 51BB [100-49=51]
(100-3/x)*10BB – (3/x)*51 = 0
x=18.1%

Seems that I have been widening my 4bet range too unnecessarily in NL200 against regs with <10% 3bet%. I should cut down on this and stop spewing off my chips.

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