Lesson
Risking 3 to Win 4.5: The Break-Even Math Behind UTG Opening Ranges
Preflop Architecture · advanced · 7 min
Tyler walks Eric through the break-even math behind under-the-gun open sizes: how much fold equity a 3x open needs, and how combined three-bet pressure from players behind changes which hands can be opened. The lesson connects that math to solver behavior, showing why earlier-position opens shrink and why full-ring under-the-gun ranges become tight with mixed-in hands for board coverage.
Key takeaways
- A 3x under-the-gun open risks 3 big blinds to win 4.5, so if the table folds about 66% of the time, opening any two cards would be immediately profitable.
- Think about the players behind as a combined three-bet frequency: if they three-bet often enough, hands that cannot continue versus a three-bet become losing opens.
- Smaller under-the-gun raise sizes are a response to sufficient three-bet pressure from the players behind.
- In full-ring under-the-gun spots, many suited broadways and weaker suited aces cannot profitably continue versus a tight three-bet range, so the profitable region is very narrow.
- Solvers add mixed hands to tight under-the-gun ranges for board coverage and to prevent opponents from three-betting too freely against only premium opens.