I am having difficulty determining how I can calculate the probability of one poker hand winning against a 'range' of other hands.
If Player A has Ace King suited and Player B has five three suited, then every possible combination of community cards could be dealt to determine the percentage that Player A wins and Player B wins.
But my question is:
If I know that Players A has Ace King suited and Player B has either five three suited or five four suited and I know that the probabilities for these two contests is:
AKs vs 54s = 0.613382 vs. 0.386618 AKs vs 53s = 0.625959 vs. 0.374041
then how do I calculate Player A's probability of winning against Player B's 'range'?
Is it as simple as $(0.613382 + 0.625959) / 2$?
This seems to give the correct answer, but I'm not sure why. When adding up these probabilities (if this is the right way) then I would have to take into account the fact that there are more occurences of offsuited card combinations than suited cards combinations.
Thanks in advance
By suited, I mean that the Ace King will be one of four combinations:
Ace Diamonds, King Diamonds
Ace Spades, King Spades
Ace Hearts, King Hearts
Ace Clubs, King Clubs
An off-suited combination will be one of the 12 Ace King combinations (out of a possible 16) where both cards are from different suits e.g. Ace Spades, King Diamonds.