Thinking Mathematically
Let me ask you a question? If one player as pocket aces and another has 53, who is the favorite and by how much?
I hope everyone knows the AA is a big favorite but by how much?
Would it surprise you to know that the 53 will beat AA about 15% of the time? You don’t have to know the exact math but it does help if you have thought through the possibilities once or twice to understand what could happen. So let’s do that.
A 53o can crack those aces if two fives come or two threes or one three and one five. Also the 53o makes a straight with A24, 246 and 467. All of this assumes that there isn’t another ace hitting the board to beat the trip fives, trip threes or two pair. Oh and then there is the matter of the 53449 board; the 53o makes two pair but the aces and fours win. And let’s not forget that A24 board that makes the 53o into a straight but then pairs the 2 or the 4 and makes a aces full house.
And should that 53 be suited, then we have to consider the flush potential and even if it is 53o, if the suits don’t match the suits of the aces, we could still lose to a four card flush board hitting the 5 suit or the 3 suit.
The complete odds are:
AA 83.85% over 53 off-suited (in suits not shared with the aces) 16.15%
AA 85.3% over 53o (both in suits shared with the aces) 14.7%
AA 79.9% over 53 suited (in a suit not shared with either ace) 20.1%
AA 84.6% over 53o (with one suit shared with the aces) 15.4%
“About four to one” is good enough for decisions at the table but a full understanding of how we come up with those numbers will serve you well in evaluating much closer decisions that you will inevitably face at the poker table.
-This is Beginner’s Poker Blog Post #59
