And here's why.......
First a little background. There are two types of conditional probabilities that are relevant in poker. One conditional probability is hand combinations, and it's purely mathematically. For example, I know that there 16 ways to make AK but given the condition of an A on the flop I know there will only 12 ways to make AK. Hand combinations are one VERY important variable to consider. But not the only one. The second type of more qualitative conditional probability is game situation. It is important to take into consideration how the hand is played. Is the play of the hand consistent with the particular hand in question ? If not the probability must be adjusted.
So let's look at the hand in question. In order to simplify the discussion Let's assume that there are only two types of hand that our opp may have, sets and flush draws. Let's start with a hand combination analysis.
1. Nut flush: ace-x suited in hearts (AK, AJ, AT, A9, A7, A6, A5, A4, A3, A2), 10 combinations.
2. Sets: QQ = 2 combos, 88 = 3 combos, 77 = 3 combos...total = 8 combos.
Notice that I haven't even considered non-nut flush draws, specifically pair plus flush draws --- and I already have flush draws as more heavily weighted (more likely) than sets. If I include other flush draws the hand combo will increase. So if anything I'm understating the excess weighting error for flush draws. As we'll see more clearly below.
Next let us consider our second conditional probability, game situations. Let us say that based on extensive HH analysis I know I will more frequently be shown sets than flushes because my opps play flush draws more passively than sets. More specifically, I might be able to determine that based on HH in game situations like this --- opps with a nut flush draw only go all in 1/4 or maybe 1/5 of the time while sets go all in nearly all the time. This is game situation conditional probablity knowledge. And it is important.
Based on this knowledge it is clear that using only a hand combination approach will be *wrong*. Instead I must re-weight the likelihoods in favor of sets. If you never give any thought to game situations and only consider hand combos you are making a mistake.
In this case you'll make the mistake of underestimating sets.



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