Quote:
Originally Posted by Izatnice
KK 23%
QQ 43%
JJ 59%
TT 71%
99 81%
88 88%
77 93%
66 97%
55 99%
44 99.7%
33 99.9%
This is from page 99 of Mike Petriv's Holdem Odds Book.
Thanks findingneema at first I thought I was going crazy as I could not get the numbers, and I didn't want to say they were wrong.
We can also get the answer by building it up
There are 50 choose 3 combos to choose 3 cards from 50 or (50*49*48)/(3*2*1). IE the flop has 19,600 possible flop combinations. This is the denominator or total outcomes. Now we want to find success divided by total outcomes
Then we have 4 aces in the deck so 46 not ace cards (it's 46 as you hold 2 cards in your hand presumably not aces). The odds that one ace shows up on the flop is
A _ _ This is the flop we want. So we have one ace on the flop and 2 not aces [(46*45)/(2*1)]. So there is 46 not aces * 45 not aces. So you get a number 1035 and this would be the number if there was only one ace in the deck but there are 4. So multipled by 4 aces in the deck is 4,140 combinations or 21% chance.
Now there is also the possibility of A A _ coming out So there are 46 combos for that third card. There are also 6 different ways to have AA come up on flop. As there is 4 aces choose 2 ways to pick it.
So 46 *6 which is 276
Then there is 4 choose 3 ways to pick 3 aces or 4 total ways to get an AAA flop.
All together it's (4140+276+4) /19600 or 22.55%
Having said that, the odds are lower if you think your oppnent has an Ace.
That would lower the combinations to 3105+138+1 or 16.5%. So the true odds are 16.5%. Since the odds you're losing when you have KK to an ace is only 16.5%.
Last edited by Samboyle; 08-30-2017 at 04:02 PM.