Trips vs. 4-flush on 4th Street--relative odds?

In heads up action on 4th street (assume the other 6 players folded on 3rd or 4th) between a live 4-flush and trips, what are the odds of each hand winning if both go to the river? Does the 4-flush win 20 hands out of 100? 25 hands? Does anyone know the relative strength of these hands?


A related question: what if the matchup is three deuces vs. a live 3-flush/live pair of Aces on 4th street?


(these questions arise from the 10-20 hand at Foxwoods posted below)


Thanks in advance for any insight.

In the first case it's about 70% for the trips.

The trips do even better in the second case. Over 80%.

the flush is a 2-1 dog (approx). the size of the trips doesnt matter.


pat

Pat, what if the matchup is trips vs. a live overpair/live 3-flush (such as 3 deuces vs. a live pair of aces/live 3-flush) on 4th street?

i am kind of guesstimating, but it is around 85% for the trips. But one issue is that it is probably not that important to know the answer to this question exactly. there are very few situations where this is important since the pair and a three flush is not strong enough to play unless the pot is huge. whether it is 5-1 or 6-1 you rarely have enough pot odds to play. The first example is one that will come up fairly often,for example when you play vs a paired door card. Even then it is more important to assess the probability of trips based on how the opponent plays than to know that vs. trips you are a 2-1 dog. in any game below 15-30 (and even at 15-30) in that situation the pot will usually be big enough to keep playing.


Pat

Hi,


The 4-flush should always fold in this case. It is not just an odds-question, but also a question of raising possibilities. If the trips fill up it can always raise and reraise, while it is very difficult for a flush to raise, because of the risk of being reraised, if the trips fill up.


JN

to complete the flush,U are NOT a 2 to 1 dog to WIN.

Why??

Sitting Bull

you are mistaken. the chances of making a flush are a lot better than 2-1. you are about 2-1 dog to win. But, the chances of completing a four flush if totally live is over 50%. the trips can redraw and will make a full house or better about 40%. These numbers are approximate since it depends on the number of cards out and the number of dead cards.


So, the chances of winning are .5 times .6 (chance of not filling) or 0.3, which is 7-3.


Pat

2c 2d 2h 9d-$1.35

As 4s 8s Qs-$0.65


2c 2d 2h 9d-$1.63

As 4s 8s Ac-$0.37


These return on the dollar results are from Turbo

7cs, 100K hands no fold profile and are rounded

to the nearst penny.

Thanks for the info. Are those stats based on the spades and aces being live, or are they just based on a random distribution of cards to that point (outside the 2 hands in question)?

The results are from two handed no fold play.

If you want specific cards "dead", let me know

what they are and I'll rerun the simulation.

I'm curious what the odds are if (a) in the 4-flush example, the spades are 100% live, and (b) in the 3-flush/aces example, the spades and Aces are both 100% live.


Thanks.

With Kc Jd Th 7c 6d 5h dead,


2c 2d 2h 9d-$1.30

As 4s 8s Qs-$0.70


2c 2d 2h 9d-$1.56

As 4s 8s Ac-$0.44

If you have a four flush, the probability of making a flush is 0.472. If you have 3 of kind and an odd card, the probability of making a full house is 0.389. Thus in a heads up situation you have the advantage and should play to the river.

If you have a four flush, the probability of making a flush is 0.472


I don't know where you got this figure but it is definitely wrong. If the four-flush is compltely live, you will make a flush by the river 53.46% of the time.


So, you are GUARANTEED to lose 46.54% of these hands. (Note that you would lose more often using your figure)


When you do make your flush, you will not always win the hand.


32.08% of the time your flush will hold up.


21.38% of the time your flush will lose to a full-house.


Therefore you will lose approximately 68% (21.38 + 46.54) of the time. If your flush draw is not 100% live, you will lose much more often.

for a detailed analysis on 7 card stud hands and their winning probability Please read 7card stud poker by Konstantin Othmer- Strategy One Publishing


wombat6

I have no problem folding my 4-flush against my opponents' trips; but, how do I know he has trips? When he pairs his door card, what are his chances of trips? If we assume he stayed this far with any pair and only with a pair, it was 2/3 that this hypothetical pair includes his door card. Now that he has paired it, we should revise downward our estimate that his original pair included his door card.


In the (low stakes) games I play, people call the bring-in with all kinds of junk and there is not a lot of raising on 3rd street. In these games, these opponents' chances of trips (when showing a paired door card) are way less than 50%. Nonetheless, I have learned to fold almost always against a paired doorcard (largely from comments in this forum) and it has improved my results. Basically, it is just too tactically difficult to play these hands: if I will fold later, I should just fold now and save a bet (or 2 or 3), If I will obstinately stay to the river, I will often lose a lot when drawing dead (or nearly so).


Still, I don't believe that calling with a 4 flush against a paired door card is nearly as bad as the calculations in this discussion suggest. If the opponent has 2 pair or a 3 straight and a pair, you are better off. Sometimes he started with trash and has only a pair. And while the 3 flush plus pair A's does much worse in the calculation, it does very much better against these alternate starting hands. Additionaly, you should consider how much action you might get from losing hands if you actually do make the flush; I suspect that in my low stakes, loose-passive games, it is a great deal more than I deserve.


I have enormous respect for the poker experience of some of the posters in this forum. I am glad to have learned the error of this call. But I don't believe the calculations at all.

Assuming an opponet has a pair and only a pair on

3rd street and then pairs his door card on 4th,

his probability of having trips is 57%.


a) 2 2 3*

b) 2 3 2*

c) 3 2 2*

* is door card


a) has 3 outs to pair door card

b) has 2

c) has 2


(b+c)/(a+b+c)=4/7=57%