here are some examples of preflop odds:
so AA is in a very dominant position---winning ~4 out of 5 hands---when the opponent is isolated. multi-way pots are much more of a gamble. AA in a family pot preflop won't even win a majority of the time so it's important to raise preflop. a lot of people slow play AA preflop and then end up in bad positions postflop.
Ok, let's see using not some sites, but math and theory of probability (I don't tell that information on sites is wrong or something like that, but maybe want to improve my skill in probability and maybe it will be interesting for you. Also, i want to check is my calculations will match with site information).
AA against ANY another pair:
In this example i will take situation where you have AA on your hands and going ALL in in preflop.
What outcomes can be:
There any the same card for you or your opponent - you win
There another A for you - you win with set
There another card for your opponent and no card for you - opponent wins with set
There card for you opponent and A for you - you win with higher set.
So, as we see, AA is really strong hand (opponent will win only in 1 against 3 outcomes). But what about language of numbers?
It's obvious, that full outcome consists of two probabilities: you win or opponent win. Together they create a
full space of outcomes (100 % outcome). (For honest, i don't know how it correct calls in english, in russian it will be -
пoлнaя гpyппa coбытий)
To make our goal easier, it will be better to count a chance for opponent's hand to win (otherwise we need to calculate 1, 2, and 4 probabilities and to add them).
This chance consists of
two parts:
a chance to get another card which connect with his hand AND
a chance that you do not get another A (this chance, with chance to get A also creates full space of outcome, so if chance to get A is 15 %, this will be 85 )
Less words, more numbers!
1. A chance to get AT LEAST one card: 2/48 (full deck 52, and we don't count his cards and your hand) + 2/47 + 2/46 + 2/45 + 2/44 = 0.041 + 0.042 + 0.043 + 0.044 + 0.045 =
21,5 % . But this will be a little wrong calculation, let me tell you why:
For example, we have two snipers, and question
"What a probability that at least (OR) one sniper will hit his target? Chance of the first sniper is - 0.8 and the second one - 0.5" As you can see, we can't just add them, because this will be 130 %, and this is idiotic. We should add them, besides one outcome, when they hit target both (yeah, this is the most complicated part, many can't understand why so). The probability this outcome will be multiplication of the chances this two snipers. 0.8 * 0.5 = 0.4 (or 40 %), so, the right answer will be = 0.8 + 0.5 - 0.4 = 0.9 ). yep, the correct formula depends from how full
events interconnected one with the other in space of outcomes (sometimes it's correct just to add).
But our case is the same with two snipers. So we should to subtract the case when we have two card on the table (Four of the kind):
2/48 * (1/47 + 1/46 + 1/45 + 1/44) = 0.3 % (yep, that's less than 1 %)
21.5 - 0.3 =
21.2 %And the chance for you
to not get another A card: 100 % - chance to get (
) because i count it before (21.2 %) it will be much faster = 100 - 21.2 = 88.8 %
And now, we need to multiplicate them (because we need TWO of this event to happen, meaning AND):
21.2 * 88.8 =
18.82 %You were right -
a chance for any another pair to win against AA is just 18.82 % AND BECAUSE OF THIS MY ASSHOLE BURNS MUCH MORE WHEN I HAVE AA CALLING ALL IN AND A GUY WITH 33 WINS BECAUSE HE GET THIRD 3 ON RIVER
P.S:
And yeah, mu calculations is enough close to what shows in this site, i'm satisfied
And yeah, i found why they have 19.251 and I 18.82 . They do not substract the probability that you get Four of a kind. This is a little wrong mathematically, but logically this is correct (it is obvious that you win for sure with 3333)
P.P.S: But i don't agree that a chance for the opponent to win will depend on what pair he have on his hands. 33 or 99 or KK it doesn't matter (if i understood right, T9s means two nines