Using
Binomial Probability Equation:
Assuming the following:
- all-in pre-flop each time with AA
- exactly one caller with an underpair
- 80% to win the hand (4 out of 5 chance to win the hand)
- 20% to lose the hand (1 out of 5 chance to lose the hand) ... no split pots
2 times (out of 2 hands) in a row: 4% (1 in 25 chance)
3 times (out of 3 hands) in a row: .8% (1 in 125 chance)
4 times (out of 4 hands) in a row: .16% (1 in 625 chance)
5 times (out of 5 hands) in a row: .032% (1 in 3125 chance)
6 times (out of 6 hands) in a row: .0064% (1 in 15625 chance)
What I'm saying is if we tracked your next six situations where you were all-in pre-flop with AA versus an underpair, there is roughly a 1 out of 15625 chance of you losing all six hands. I only say roughly, because 80% is a very general estimate. Remember, suit combinations, how far gapped the pairs are, and the chances of chopped pot all slightly affect the actual probability.
Frendly Reminders:
- Multi-way pots can reduce the chances of AA winning.
- Our minds can play tricks on us. We sometimes exxagerate things in our mind, and overfocus on all the bad beats, and completely overlook the situations where AA won us an uncontested and/or small pot.
- There will be times when the cards completely misbehave. Manage your bankroll accordingly, so you can survive bad runs like these.
- There will be times whe the cards completely misbehave (part 2). Your job as a poker player is to try to minimize your losses whenever possible. Minimizing losses affect long-term profits as much as maximizing our winning hands.