88 Strategy Question

[JoeU]

I know this post probably belongs in a probability thread, but I think it applies in small stakes due to the situation posted. I am especially interested in the math involved here. This started as an argument between me and my brother, so here it goes:

You are on the button with 8 /images/graemlins/spade.gif8 /images/graemlins/diamond.gif. It is a very loose/passive 3-6 game. ALL players call to you on the button. You call here (is this correct or is a raise or a fold correct). The SB completes, and the BB checks. 10 players to the flop for 1sb each:

Flop:
A /images/graemlins/heart.gifK /images/graemlins/club.gifQ /images/graemlins/spade.gif.

You have a very fancy underpair /images/graemlins/grin.gif. The SB bets, and ALL players call to you. Here is the crux of the argument: do you raise, call, or fold here? Say the turn is a blank and the SB bets out again and ALL players call the turn bet. What do you do on the turn. The river in this case becomes a very obvious decision at this point, but what would you do on the flop and turn in this situation, and mathematically, why?

Joe

[Ed Miller]

Preflop, folding is madness. I think raising is best, as you will win this pot more often than 1 in 10, so your raise is for value... and raising on the button with a pocket pair has other benefits like tying people onto the pot and potentially allowing yourself to see the turn card for free if the flop comes unfavorably.

As for the flop, you have a clear fold. You are getting 19-1 on your call which might be fine if the flop were ragged to take one off to spike a set, but since the flop is coordinated, you will often spike your set on the turn and then lose on the river either to a T or J completing someone's gutshot or to a completed backdoor flush.

[JTG51]

I'd call before the flop most of the time, and raise occasionally. Others would probably recommend raising more often. Folding would be really, really bad. Tragically bad.

Your flop play depends in part on your preflop play. If you had raised before the flop and the SB still bet into you on the flop, your pot odds would be approaching 19000-1, which would make folding a disaster. In that case, calling is definitely the best choice. Raising when you are drawing to 2 outs and are closing the action can never be a good thing.

If you just limped before the flop, you'd be getting 19-1 odds to call (I'm assuming this is a 10 player game), while the odds of hitting your set on the turn are 22.5-1. Normally it would be an easy call with any pocket pair since you'll make up the extra 2 or 3 bets if you hit on the turn.

With that flop though, you'll hit your set and lose a lot more often than normal. I'd guess that you'll only win 70 or 75% of the time when you hit an 8 on the turn. When you do win though, you should get lots of action. I think that makes it a pretty close decision but I'd lean towards folding. I doubt it's too much of a mistake either way.

It would very rarely be correct to call again on the turn if you missed.

[Ed Miller]

If you spike an 8, and everybody is going to call the turn, then you should call on the flop. You'll have too much of an overlay on those turn bets to pass up the chance. But, frankly, that's ridiculous, there is no game like that. You should generally be folding when you flop 3 overcards in an unraised pot, which is really the point.

[JTG51]

I also assumed that you wouldn't necessarily have everyone calling on the turn again. If you somehow knew you'd get 10 callers all the way then folding on the flop would be a disaster.

[JoeU]

Thanks for the responses guys. I guess I have two more questions:

1) What are the calculated odds on hitting your 8 on the turn or river?

2) Is there a way to calculate that your set would hold up on the river if someone has to hit some type of draw here?

JTG, you asked if this was a 10 handed game. It is, and to expand on that answer, all 10 players are in for 1 bet on the flop and you would close the action post flop with a call. (19-1 to you).

Thanks again,

Joe

[trillig]

I had this happpen twice today with 88 and I folded both with a bad flop and bets.

I don't bother raising with this hand, I want people in if I hit and books I read said 88 in LP is not good enough for a raise unless I am first bettor.

I had equally bad luck with 77 as well, but nailed a nice TT pot.

Middle pairs suck...

-t

[MrDannimal]

I'd raise it if I were sure that 7 or more would call AND that I wouldn't be 3-bet. I mean, it's 7.5-1 to flop the set, right? You can be farily sure that there's no bigger pair out there if the set comes, and if 7 people call you're getting 8-1 plus implied odds (which may be less since you raised, but there's got to be *some*) if you hit.

FWIW, Both Jones and Sklansky seem to favor raising with 88 on the button. Jones explicitly (Summary of pre-flop late position play), and Sklansky in HeP p. 43.

Calling isn't terrible, though. Folding pre-flop, as has been said, is crazy.

On the flop, I muck this without really thinking about it. I mean, it's about 1 in 6 there's an Ace out there, making me a big dog and that doesn't even consider any K, Q, or draw out there.

It's been said before, but one more time: There will be another hand in a few seconds.

[CMangano]

You can figure out the odds for any hand as long as you know the number of outs needed. So, to make 3 8's you have 2 outs. There are 47 cards you haven't seen and 2 of them make your hand. This leaves you with 45 bad cards and 2 good ones. Now you divide these numbers (45/2) to get 22.5. So the odds are 22.5:1 against an 8 coming on the turn. On the river it is 44/2 for 21:1 against the 8 coming on the river.

[Mike Haven]

if the turn is the 8h and someone has two hearts in hand, they have 7 good hearts left in the remaining 44 cards - their odds are 37 to 7, or 5.3 to 1 to beat your set on the river

(however, from their point of view they don't know you have three 8's so they are calculating odds of 37 to 9, or 4.1 to 1 for them to flush)

if they happen to have KhQh they have 9 hearts to help them plus two Kings plus two Queens - their odds are 31 to 13, or 2.4 to 1 to beat your set

same thing if the turn is the 8c etc etc

if they have Jx or Tx they need 1 of 4 cards for their straight out of the 44 we don't know - their odds are 40 to 4, or 10 to 1

[Mike Haven]

i just realised i answered your question arse about face

so, to turn it round to the way you wanted it, taking the two hearts in hand odds for him to flush of 5.3 to 1, for example, to find the percentage of time he will hit and win you have to do the following, (don't ask me why!):

use the odds divided down to "something to 1", (16 to 3 is how you might choose to say the odds, but for the purposes of the following calculations you need to start off with it as 5.3 to 1)

add 1 to the 5.3 = 6.3

divide 100 by the 6.3 = 15.9

this gives you the answer that 15.9% of the time he will flush

therefore 100 - 15.9 = 84.1% of the time he will not flush

(if you wish to check that we have not made a mistake in our final calculations there is a simple test where you simply divide the 84.1 by 15.9 and it should equal the 5.3 we started with)

try the same technique with the 2.4 to 1 odds

you will get:

.
.
.
.
.
.
.
.
.
.

add 1 to the 2.4 = 3.4

divide 100 by the 3.4 = 29.4

this gives you the answer that 29.4% of the time he will flush or full house

therefore 100 - 29.4 = 70.6% of the time he will not flush or full house

(if you wish to check that we have not made a mistake in our final calculations there is a simple test where you divide the 70.6 by 29.4 and it should equal the 2.4 we started with)

so, in respect of your question "Is there a way to calculate that your set would hold up on the river if someone has to hit some type of draw here?" the answer is yes, (say), 84.1% of the times that he has a flush draw your set will hold up

i hope this helps you and anyone else who, like me, wants to work these problems out from first principles, when i find that their worth seems to sink in better

for instance, during this post i have realised that although his odds of flushing in one situation, at 5.3 to 1, and his odds of flushing or full housing in another situation, at 2.4 to 1, sound enormously different to my ear, in fact, as we have seen, mean the difference in our winning 84.1% or 70.6% of the time - which does not sound, to me, to be nearly such a great difference - this has helped me by bringing odds and percentages into perspective in this respect