## Hand Quiz 1

### 7 Card Stud, Hand Quizes

February 23, 2009

Here’s a little quiz.  I figure it might get some interesting discussion going.  I realize we haven’t done any stud on cardsharp, but think of it as a chance to broaden your horizons.

The game is stud high. You are the bringin with [8h 8c] 2d. The 3s, Jh, Qh, 6d fold. The Kh completes. The As and Ac fold. You call. Two notes:

1) the structure is such that your 3rd street call is correct (ie. sufficiently large bringin & ante relative to the completed bet).

Assume a (rather unfortunate) 2 unit ante, 5 unit bringin, 10 unit small bet, 20 unit big bet structure if you need concrete numbers.

2) Villain is tight enough that his hand is either a pair of kings or the case aces.

On 4th, you catch 2c and villain catches 7d. You bet, he calls.
On 5th, you catch 9s and villain catches Jc. You bet, he calls.
On 6th, you catch 9d (for 3 pair) and villain catches Js. You’re first to act with two pair showing on board.

Now, you’re clearly behind but can also clearly represent a hand that beats villain (namely 2s full). The question is how you proceed on 6th and 7th.

Question 1) What is the game-theoretic optimal rate to (semi-)bluff 6th and/or 7th? And is the optimum strategy to bluff one or both? This article provides some background.

Question 2) If you wouldn’t adopt the strategy from 1), what strategy would you adopt and why?

Question 3) There’s a point in the process of solving question 1) where you have the option of adopting or eschewing a Bayesian view about something. What was it, which way did you choose to view the problem, and why?

Question 4) If your computation from question 1/2 was too complicated to do at the table, how would you have gotten an acceptable answer more quickly?

Even if stud isn’t your game, give this a shot.  It’s a surprisingly deep problem that touches on a whole bunch of different areas of poker theory and practice.  Post responses and questions and I’ll try to keep up with moderating the comments so we can have an effective discussion.  I’ll post my answers and reasoning along with responses to reader comments next week.

### 6 Responses to “Hand Quiz 1”

1. jUzAm Says:

1) (little question : do we assume that he’ll just call on 6th & 7th ? and what would he do if we check ?)

If I have well calculated, the pot is 56 and we have to bet 20

Villain will have 76 to 20 odds to call, so we need to bluff 26,32% of the time
If we bluff more than that, he could exploit us by calling all the time
If we bluff less, he would fold all the time

For 7th street, if we have bet the 6th :
86% of the time we don’t improve
14% of the time we improve (for simplicity’s sake we assume that when we improve he doesn’t hit 1 of his 3 outs to make better full) (tried to compute it but it’s too difficult and my brain will explode, lol)

We’ll bet 20 in 96 so he’ll have 116:20 odds (5,8:1) on his call
So we need to bluff ~17% of the overall time we bet
We’ll value bet 100% of the 14% we improve, and 3,3% of the 86% we don’t improve

2) We have 6 outs and 42 unseen cards, so we have approximatively 14% equity
EV >= 0 FE * 56 + E(W) * 76 – E(L) * 20 >= 0
EV >= 0 FE * 56 + 0,14 * 76 – 0,86 * 20 >= 0
EV >= 0 FE * 56 – 6,56 >= 0
EV >= 0 FE >= 6,56 / 56
EV >= 0 FE >= 0,11

So we need that villain folds more than 11% of the time on 6th street to make a profit

If I have made a good profile of villain and think that he’ll fold more than 11% of the time in this spot, I would bluff the 6th street 100% of the time
I think I would come back to game-theoric strategy on the 7th if i’m called

If I think he’ll never fold the 6th street nor the 7th street, I’ll check 100% of the time and will only value bet on the 7th

3) I didn’t use it (I tried to use it when I tried to compute times he’ll improve when we improve, because he has 1 out when he has AA and 3 outs when he has Kx, and he has a lot more Kx than AA, but finally I erased all what I’ve written and made it simplier)

4) I almost never play stud hi so I don’t know how I’d have react at a real table
Because i’m a maniac i would have probably bet & bet (if villain is so tight that he just plays [AA]K & [Kx]K, I would think that he’ll fold often enough, seeing that I could have a full house), lol

2. Wayne Vinson Says:

One thing worth considering: I don’t believe bluffing only 6th or only 7th makes sense. If you only bluff 6th, villain gets much better odds becuase he still has a draw to beat 2s full. If you only bluff 7th, it’s not credible that you were already full on 6th, again laying villain better odds.

3. jUzAm Says:

I agree with you

But it’s limit, so villain has very good oods (near 6 to 1 on 7th if we have bet 6th) to catch our bluff

So we need to (logically) value bet all the time we hit one of our 6 outs, but to bluff only 3% of the time we don’t improve

If we were in PL or NL and bet pot, we could have bluffed half the time we wouldn’t improve, but in this case, only 3%

If we bluff 100% of the 7th street when we bluffed @ 6th, I think we lose money (if villain thinks he can call on 6th because he thinks he’s WA/WB, he’ll call the 7th very often aswell, particularly with better odds)

You think there would be cases where villain would call 6th & fold 7th ? (and the bayesian process would be from his pov, he would think that the fact we’re betting again on 7th street would significate that we more probably have a full house than on 6th ?)

Impatient to see what will your answer be !
I may be totally wrong but tried to do something !

4. jUzAm Says:

Hi,
When will you post the answers ?

5. Wayne Vinson Says:

It’s posted.

6. jUzAm Says:

Cool ! Thx