Blockers what is the real effect of blockers? I'm watching wsop and the commentators are constantly talking about blockers. One example is ... the run out shows 3 clubs and they are saying well fred has a club in his hand so he is blocking chances at a flush etc etc etc ... Does one card really make that much difference? here is another ... Jim has got K9s so he is blocking Dave on having AK etc etc

It is possible to calculate how much change there is in either of these cases. It's in your interest to understand how these calculations works.

Without doing the calc, I doubt you having one of the 3 card suit on the board changes the chances significantly of villain having a flush. Now to do the calc. assuming a 5 card board:

Without a blocker in hero’s hand,

Pr(villain has 2 clubs = flush| you don’t have a club) = C(10, 2)/C(45,2) =4.54%

With a blocker in hero’s hand,

Pr(villain has 2 clubs| you have 1 club) = C(9,2)/C(45,2) = 3.64%

In absolute terms, less than a 1% difference; since the probabilities are small, the difference will also be small. So, although the relative difference is 20%, it is not too significant in terms of how one would play the hand.

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Thank-you Sir! As someone who is blessed with a form of dyslexia you are a god send. I sorta felt what you said, wasn't sure, but did know that someone here would,

There is another way of looking at the problem. My initial post was in response to OP’s assumption that the board was run out with 3 clubs, so I calculated the chance villain had the 2 clubs necessary for a flush.

Now let's assume after the turn there are two clubs on board and villain is suspected of having 2 clubs. The question then becomes – what are the chances of villain hitting his flush on the river if hero has or doesn’t have a club blocker?

Hero does not have a club:

Pr (Vill. Hits his flush on river | 2 board clubs and Vill. has 2 clubs) = C(9,1)/C(44,1) = 20.5%

Hero has a club:

Pr (Vill. Hits his flush on river | same) = C(8,1)/C(44,1) = 18.2%

Again, the absolute difference is small (2.3%) but somewhat more significant than for the other situation. With so many other uncertainties as in most poker situations (does villain actually have 2 clubs?), a 2% difference probably is not going to alter one’s strategy.

Blockers can definitely be a factor in how to play a hand. This is clearly the case in PLO to a significant degree and in NLHE to a lesser degree.

In NLHE blocking flush cards is probably the least important type of blocking and, as shown above, doesn't move the probability needle all that much.

From a probability perspective, blocking ranks is far more significant (e.g., having a King blocks AK, having JT blocks straight possibilities on some boards, having QQ blocks KQ, etc.).

Also, many poker decisions are close decisions between multiple options (raise, call, fold). The best players some times use blockers (or the absence of blockers) as the deciding factor in their choice.

Thanks! so the thinking is, with hands like K9 it makes it less likely villain has AK etc in numbers more significant than 2% - 3%

King Blocker. Here you would think the blocker effect is more significant than for the flush example since there are only 4 kings whereas in the flush example, there are 13 flush cards. Here is the analysis:

King Blocker Example: Villain is suspected of having AX. You are interested in the chance that X is a king. Hero has a K9 or Y9 where Y is not a king. How significant is the king blocker?

Hero does not have a king blocker:

Pr(Vill. has AK | Vill. has an ace and hero does not have a king) = C(4,1)/C(48,1) = 8.33%

Hero has a king blocker:

Pr(Vill. has AK | Vill. has an ace and hero has a king) = C(3,1)/C(48,1) = 6.25%

The blocker results in a 2.1% reduction in villain having AK , again a relatively small effect. So even though the reduction in king outs is significant, going from 4 to 3, the fact that the success probability is also relatively small, makes the blocker effect less important than one may suppose.

Whosenext comment about blockers certainly has merit especially for expert players. Poker with its incomplete information has many uncertainties so any edge that blockers give can be important for those who know the edge and can take advantage of it. For most of us, a 2% difference may not play a major role, but, as suggested, can be a decider.

When considering the ranked order of playable hands that are organized into a range by a poker player, the higher the rank the more often the card appears in the players hands.

Thus, for strategy purposes, the higher the rank of the blocker, the more combos it blocks in an opponents range.

Lower ranks can block draws or made hands on low boards, but this is muted by the absence of most low cards in players ranges, depending on the player of course.

But even the most unorthodox player will have more hands containing A, K, and Q, than 5, 6, or 7.

For flush draws, the higher the rank of your flush blocker, the more combos it blocks in your opponents range. But this is a little different, since flush blockers below a ‘7’ actually work better as “outs” and you want your opponent to be drawing to a flush with 5 percent less equity, so long as your made hand is currently the best hand.

A rough estimate, taking all of the above into account, is about 5 percent when considering the ranges of poker players for an ideal blocker situation.

Apologies for using rough estimates in the probability forum.

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