5CD Valuebet with two Player StandPat / PreDraw CAP-Pot

You can use example 17.4 from the Mathematics of Poker ( by Chen and Ankenman ) to get to the optimal solution because essentially the ranges of the two players can be considered identical. The pot has 4.54 bets after the rake, so I eventually get ( from three equations I use ) y1 ~ 0.537322308, the second player's legitimate betting frequency; this essentially means ( multiplying by 19092 pat combinations ) that AKQJT+ can be value bet and KQJT9 with 2-1-1-1 suit distribution can be value bet and possibly some pat KQJT9 combinations with 2-2-1 suit distribution can be value bet. This is assuming that the ranges in question are all legitimate pat hands; however, this may not be the case for at least two reasons: 1) you and/or your opponent may have a bluffing range ( not a wheel, which is "legitimate" ); and 2) you really ought to break some pat hands that are also a one-card draw to a straight flush which are low pat straights ( 87654 or lower ) and you really ought to break any wheel for which you can draw to a cathop ( but don't break anything better than a wheel to draw to a cathop ). Also, I have not considered card removal effects.

In practice, quite often one or both players don't really have much of a pat bluffing range, so I think the borderline value betting hand for the second player is a KQJT9 pat straight with precisely 2-2-1 suit distribution. Of course, some players can never lay down a legitimate pat hand, so if you know that, you can value bet the hand in question, even though it has 3-1-1 suit distribution.

You can also apply the above result to the situation when both players draw two ( presumably to trips ) and then the second player's marginal betting hand will be 888; he can bet ~29% of those unimproved trip eights ( presumably, some of those 888 hands for which at least two higher ranked cards have been seen ); this also assumes that the two players have essentially identical distributions and never have anything other than trips and always draw two to trips ( likely too many assumptions ).

@bigpooc, thanks...sorry I was very busy in recent times
I dont know the book and the example 17.4 --> I this book only for 5CD ? Must to have ?

Step by step

from three equations I use ) y1 ~ 0.537322308

I dont understand this... if i have the book , i understand this better ?

Okay, it's not trivial for me to communicate this to you in a significantly better way and the book is a MUST if you want to get close to optimal play; however, it's not important if you play anything less than ~$10-20. The book is really about some elementary poker theory and can be applied in a number of scenarios, including common situations in 2-7 TDL. You may not understand this signficantly better even if you get the book, but even if you don't you should look at this specific example from the book because it sheds light on how wide betting frequencies are on the river.

Originally posted by Rettungs1zeichen
Unknown Player shows weakness (post draw).
It could be weak flushes or straights.

First off all the A-high straights are out there.
Next, unknown player could be trapping.

Nothing wrong with checking to get the information, even though you may be mathematically ahead of his range.
Some worse might call, but you're more-or-less forced to fold to a check/raise unless you know for sure he can bluff here, and he's unknown.
So nothing wrong with checking ... Hmmm I'm in a logic loop here

VS

Originally posted by Rettungs1zeichen

b) Straight Combinations : 10200 (without Cardremoval)
= c(10,1) * c(4,1) * c(4,1) * c(4,1) * c(4,1) * c(4,1) - [c(10,1) * c(4,1)]

Beat Me: Straight : = 102 Combinations (without cardremoval)
Question/Help: Combinations with cardremoval ? Formula ?

Split : ? 102 Cpmbinations (without cardremoval)
see above

I beat : 10200 - 204= 9996 Combinations (without cardremoval)
see above

I am not sure it's so important (I really think that opp had bluff range, may be not real bluff, but sort of "blocking value bet" bluff, and to estimate this range correctly is much more important. Not card removal) but you are incorrect:

Without card removal there are for sure 1020, not 102 Broadways =4**5. With card removal I think there are 324 broadways = 4*(3**4). And 243 splits.

Actually 242 splits; but I also made an error since the number of bets <4.5.

There is some chance the opener will checkraise too: hands that I think that are definitely worth considering to do this with are: any low straight flush ( not a wheel sf ) and a hand like 55588 not having every suit represented.

You can also go through an exercise similar to that found in Malmuth's book Winning Concepts in Draw and Lowball starting on p. 169 which will likely lead to answers pretty close to the correct betting frequencies for both players.