We are playing no limit Holdem.
scenario 1:
Hero is sitting in UTG+1 position with AQ of heart. The table is ten handed.
Our hero here is strictly following a set of strategies: (from Harrington on Holdem)
In UTG+1 he will raise with AQ suited but fold AQ offsuit
Now we have UTG player fold his hand and flip it face up
If the dead cards contain one heart (say 2) or two heart (27)
Will these dead card affect hero’s action ? should he now fold his AQ?

if he showed you an A or Q I think that would be more important than him showing 1 or 2 hearts.

While this forum obviously deals with questions and issues pertaining to poker strategy, the forum is not a poker strategy forum per se.

It sounds to me that you are asking a poker strategy question so if you are really looking for a discussion of this issue, I'd recommend posting it in one of the many 2+2 strategy forums.

The Probability forum is better suited to answering questions like:

- (1) what is the probability that AhQh will make a flush at a ten-handed table?

- (2) what is the probability that AhQh will make a flush at a ten-handed table given that one heart (2h) is dead?

- (3) what is the probability that AhQh will make a flush at a ten-handed table given that two hearts (7h,2h) are dead?

Many members of the Probability forum can provide accurate answers to these questions. And that is not to say that members of this forum cannot or will not provide thoughts on poker strategy, but that is not the raison d'etre of this forum.

In keeping with whosnext’s comment, I will not consider detailed strategy but will address some probability issues.

Given a suited hand, the probability of

..A flush draw on the flop = C(11,2)*39/C(50,3) =10.94%

..Flopping a flush =C(11,3)/C(50,3) =0.84%

Given a suited hand and a folded player exposes his cards with one of your suit, the probability of

..A flush draw on the flop = C(10,2)*38/C(48,3) =9.89%

..Flopping a flush =C(10,3)/C(48,3) =0.69%

Given a suited hand and a folded player exposes his cards with both of your suit, the probability of

..A flush draw on the flop = C(9,2)*39/C(48,3) = 8.12%

..Flopping a flush =C(9,3)/C(48,3) =0.49 %
.
So, from a strictly math basis, the question becomes: Given you have a suited hand, if a folded player has one or two of your suits and you know it, do the math results justify a change in strategy?

Now that I re-read my post above, I see that I was probably too "strident" in my views. I was merely giving my own personal opinion.

This forum, like all the various forums on 2+2, is largely whatever its members want it to be. If members of the Probability forum want to engage in poker strategy discussions (however general or specific and/or however much "probability focused"), then I am all in favor of that.

I did not intend to stifle any discussion and if that was the upshot of my post, then I apologize.

I ran some simulations last night to help better understand the impact of these dead cards. I am not saying that these simulations are the best way to look into this issue, but they may shed some light on it.

I programmed a 10-handed table. Hero (UTG+1) is dealt AhQh. Every other player at table enters pot if and only if they have a top 15% hand using the Poker Stove hand rankings. Every player that enters the pot pre-flop goes to showdown. Each simulation consisted of 1,000,000 valid deals (showdowns plus raise-and-take-its).

In simulation 1, UTG folds (I ignore any hands in which UTG has a top 15% hand) and does not show either of his cards. In this simulation, Hero wins 64.4% of deals.

In simulation 2, UTG folds and shows the 2h (of course this means that the 2h is not in any other player's hand and is not in the deck stub from which the board is dealt). In this simulation, Hero wins 63.0% of deals.

In simulation 3, UTG folds and shows the 7h & 2h (of course this means that the 7h & and the 2h are not in any other player's hand and are not in the deck stub from which the board is dealt). In this simulation, Hero wins 62.0% of deals.

can you do it for cases where UTG shows A or Q?

I'll do those cases later today, but the runs take several hours.

I’m surprised these programs take so much time, although admittedly it doesn’t seem easy to quickly find the best five card poker hand among several players.

Results from two additional simulations are in:

In simulation 4, UTG folds and shows the As (of course this means that the As is not in any other player's hand and is not in the deck stub from which the board is dealt). In this simulation, Hero wins 65.2% of deals.

In simulation 5, UTG folds and shows the Qs (of course this means that the Qs is not in any other player's hand and is not in the deck stub from which the board is dealt). In this simulation, Hero wins 63.9% of deals.

The first result indicating that a dead ace is actually good for Hero (AhQh) is probably due to the fact that with another ace dead there are more raise-and-take-its for Hero.

thanks, interesting results. although I still think that for real poker dead A or Q have more impact than dead 2 hearts since most of the playability of big unpaired hands is based on flopping a big pair with a good kicker.

What if you adjust for the card removal effect so that other players are still playing 15% of hands from their perspective?

Thanks for doing these calculations. Could you calculate the probability of completing the flush by the river in all three scenarios?

Flush by river with hero holding 2 suited cards with a folded player possibly revealing his hand:

No folded hand revealed: 6.4%
One of flush suit revealed out of 2 revealed cards 5.4%
Two of flush suit revealed out of 2 revealed cards 3.9%

Note: Several players could have a flush or better. Hero can have a straight flush but no full house or quads if he has a flush.

Since I have all the hands handy and I am interested in such esoterica, I performed one additional calculation factoring in UTG into the equation.

Under the scenario in which UTG opens if and only if she has a Top 15% starting hand, when UTG folds and does not reveal any of her cards the probability that Hero (Ah Qh) makes a flush by the river falls slightly from 6.40% (as shown above by statmanhal) to 6.37%.

What, if anything, are we learning from this?

well I'm not the fastest bunny in the forest, but I really thought it would have more impact than 1% or so. thanks for the info

Wow, thanks for those info

Card removal is playing an effect here. With low hearts dead people will get playable hands more often.

OK, as others have pointed out: chance of flush is reduced ever so slightly...but the chance of hitting a flush is very small anyhow and certainly not the reason why anone would play AQ.

On the plus side: if you still hit flush over flush then your opponent will almost certainly not make you for a flush and you can stack him more assuredly (even if he has a very weak flush).

How would these numbers change if you assume the player flopped a flush draw?
I was more looking for the percentage of completing the flush from the after the flop assuming the guy flopped two to a flush. This seems more relevant, since more hands will play out under this scenario.

Flush by river with hero flopping a flush draw with a folded player possibly revealing his hand:

No folded hand revealed: 35%

One of flush suit revealed out of 2 revealed cards 32.7%

Two of flush suit revealed out of 2 revealed cards 29%

Note: Same results apply if hero had only 1 flush card and had correct monotone floop. Several players could have a flush or better. Hero can have a straight flush but no full house or quads if he has a flush.