Wanna buy a duck? (flop-probability for Ah 3h 6s Kd)

[franknagaijr]

Does the following information look reasonable? Does it hold any meaning? Am I too strict on classifying a 'favorable flop', or too loose because the drawing flops should be tweaked downward?

All suggestions much appreciated. Not just on the stats, but also on what constitutes a favorable flop for this hand in a full ring PLO8 game.

Enumerating Favorable O8 Flops for A [img]/images/graemlins/heart.gif[/img] 3 [img]/images/graemlins/heart.gif[/img] 6 [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/spade.gif[/img]

If we have the hand A3K6, with a suited ace and two offsuit cards, and there are 48 unknown cards, what percentage of flops would be favorable in a multi-way situation?

There are 17, 296 combinations of the four unknown cards.

The favorable high side flop combinations are 2267, or 13% of the flops.

The favorable low side combinations are 3040, of which 438 overlap with the high side favorable flops.

There are 4857 combined favorable flops, or 28% of the time the flop will be favorable.

Favorable flops as follows.
Flush or flush draw with no paired board
1870 Comb

45x rainbow with no pair on board
230 combos

Flopping a QJT straight that is not 3 of 1 suit (not double counting flush draw boards)
51 combos

Flopping Trip Aces or Queens (not double counting flush draw boards) or Any Quads
116 combos

For flopping low, I considered any 2-low-x flop without a counterfeit Ace or Trey to be favorable. That's 3040 combinations, of which 450 cross-match with the high favorable flops, so 2590 favorable combinations not yet counted.

Total count = 4857 = 28.08%

[bbartlog]

Flush or flush draw with no paired board
45x rainbow with no pair on board

Some of these are not favorable for you and are more like flops to go broke on. 456r, A58 with two hearts, AQ4 with two hearts and many others are flops that look sort of nice and may win you the pot on the flop if you bet, but if you actually get into it with someone you'll mostly be getting crushed.
I would start with flops containing a 2 and no A or 3 and narrow it down from there. There are a few more of course like flopped FH, flushes and broadway straights but you are unlikely to get much action on those.

[mxyzptlk]

[ QUOTE ]
Flush or flush draw with no paired board
45x rainbow with no pair on board

Some of these are not favorable for you and are more like flops to go broke on. 456r, A58 with two hearts, AQ4 with two hearts and many others are flops that look sort of nice and may win you the pot on the flop if you bet, but if you actually get into it with someone you'll mostly be getting crushed.
I would start with flops containing a 2 and no A or 3 and narrow it down from there. There are a few more of course like flopped FH, flushes and broadway straights but you are unlikely to get much action on those.

[/ QUOTE ]

Start with this if you're new or have no idea how your opponents play. Otherwise, bbart is giving you too tight a recipe to extract the most out of this game.

First of all, in 45x, a 6 is not generally considered an "x", like a J would. Next, in all these situations, you're opponent is gonna need a four card hand to have you in serious trouble, and against your average player who overvalues top two OOP on the AQ4 board, your hand is the favorite. Conclusion: all the situations bbartlog criticized are on average highly playable. Play them in position and don't give action to ultra tight players who will only play back with monsters.

[franknagaijr]

The standard I'm looking for is, with this hand, if a rational player looks at the flop, it's not a clear muck, and reasonably playable, if we have no information on the table at the time. Assume four players saw the flop, and we don't know yet how many will continue post-flop.

I see your point about 456 and 345, as we are crushed by two reasonably likely holdings, A2xx and 23xx.

While we might not bet out on an AQ4 flop with a flush draw, are you saying this is a clear muck multi-way and/or heads up here, or that it might be reasonable to peel the turn card? I can't quite see the logic without an explanation. We could be facing 23xx or 235x, or QQxx, but in a multi-way, are we never getting the drawing odds we need to continue?

[franknagaijr]

Afterthought - Maybe I need to classify the flops as

1) Not worth a bet or a call mathematically. (we can only win with a bluff)
2) Occasionally worth a check-call multi-way.
3) Generally worth a call even HU
4) Worth taking the lead on the betting

[mxyzptlk]

[ QUOTE ]
Afterthought - Maybe I need to classify the flops as

1) Not worth a bet or a call mathematically. (we can only win with a bluff)
2) Occasionally worth a check-call multi-way.
3) Generally worth a call even HU
4) Worth taking the lead on the betting

[/ QUOTE ]

Concepts are more important than classifications, because you can apply them dynamically. Here are some concepts for HU play, and how you can apply them to the AQ4 flop when you have A36K with the nut flush draw:

1) Don't build big pots OOP with moderate hands. Don't lead this hand OOP on the flop when the pot is relatively small, but it's generally worth a check-call. You got a pair, a low draw, and a flush draw. You got scooping potential. Try to keep the pot small for now.

2) However, if the pot size on the flop is big and a CR can get ~75% of your stack in there, do it against all but the tightest rocks. You're ahead of lots of hands, and those that are you behind require all 4 four cards to be working together, which is less likely. Plus a CR allows you a chance to win the pot right there.

3) In position, you want to punish the OOP players. If there is a bet, raise it. If it checks to you, bet. If some scare card, like a 5, falls on the turn, most players with 23 will check, and you can check behind, and you still have draws to 3/4 or 1/2.

If it's multiway, you have to play more carefully. It may be the case you are against two hands of 23xx, but it's more likely you are against AQ or a set, and 23xx. You are a favorite against either hand individually, but against both you are dog, and don't have very good equity.

WRT to HU play, if you aren't prepared to play for stacks when you are a 55-45 to 60-40 favorite, your progress in this game will be limited.

[Buzz]

[ QUOTE ]
There are 17, 296 combinations of the four unknown cards.

[/ QUOTE ]Hi Frank - No. The 17296 is the number of ways three cards (for the flop) may be chosen from the 48 cards remaining in the deck.

C(48,3) = 17296.

[ QUOTE ]
The favorable high side flop combinations are 2267, or 13% of the flops.

[/ QUOTE ]Wow. You have to think about all the favorable high flops, list them all, and total. Very tedious, demanding work. Then you double and triple check your chart, looking for an error. There are lots and lots of places to go wrong. Let’s see...
[ QUOTE ]
Flush or flush draw with no paired board
1870 Comb

[/ QUOTE ]
3 hearts on flop have 11*10*9/6 = 165 combos.
2 hearts on flop with no pair:
11*10/2 = 55 combos for two hearts.
one of them is Kh6h
• 1*33
another bunch is KhXh and 6hXh. must be 9 of each
• 18*32
the rest (36) must have two hearts of different ranks than Hero’s hand.
• 36*31
thus 33+576+1116 = 1725, and then
165+1725 = <font color="red">1890</font> are total three card combos with either 3 hearts or two hearts and no pair.

Close. I was hoping we’d get the same number. One of us is evidently in error. But close. I don’t feel like doing any more of this for high, at least at this time. Well... maybe one more.

[ QUOTE ]
45x rainbow with no pair on board
230 combos

[/ QUOTE ]I don’t know why “rainbow.” Why not simply “no three cards of another suit.”

No matter. There are 240 45X unpaired rainbows. Here they all are:<ul type="square">4s5hXd.....10
4s5dXh.....9
4s5hXc.....11
4s5cXh.....9
4s5dXc.....11
4s5cXd.....10
4h5dXc.....11
4h5cXd.....10
4h5sXc.....11
4h5cXs.....10
4h5dXs.....10
4h5sXd.....10
4d5sXh.....9
4d5hXs.....10
4d5sXc.....11
4d5cXs.....10
4d5hXc.....11
4d5cXh.....9
4c5sXh.....9
4c5hXs.....10
4c5sXd.....10
4c5dXs.....10
4c5hXd.....10
4c5dXh.....9[/list]4*60 = 240
I’m wondering how you got 230. Doesn’t matter. Enough for the highs .

Hmm. You got 3040 for the favorable low flops.
<ul type="square">I get
flopped nut low 576
flopped 2nd nut low 544
flopped nut low draw 1520
flopped 2nd nut low draw 2856.[/list]There is not any reasonable way I can put these numbers together to get 3040. One of us is in error. Could be me.

I didn’t count any A-6 or 3-6 combinations for low. In other words, I didn’t count any flops as favorable where the ace or trey was counterfeited, but I don’t think you did either. And I also didn’t count any back-door low draws, but I don’t think you did either.

It’s very tedious and time consuming to do these. In particular, high is a real bitch to figure and tabulate. I’ve done it, and I recommend you do it too. But there are lots of places to go wrong.

How about we run a simulation for As3s6K instead?

I can run the simulation using various Wilson characters, a mix or all tight aggressive (maybe all C. Chan). Whatever group of characters I use gives different results. The character chosen to represent Hero has different results depending on the character chosen for Hero and the characters chosen for opponents.

I prefer to use the Wilson showdown character, Painless Potter, in all seats. Painless Potter always calls and never bets or raises. The dollar amount is immaterial in this type of simulation, and of course your real opponents often fold hands that would have ended up as winners, as do you. However, you can see how a particular hand fares relative to random hands dealt to opponents. And then if you compare how that particular hand against other particular hands for the same type of simulation, you come to have a feeling for the relative value of hands. (Or you can just take my word for it).

How about if we plan a series of 100,000 deals where we seat Painless Potter in seat #10 with Ah3h6dKs. And we’ll leave the other seats blank and the board blank, so that on each successive deal, fresh random hands will be dealt to all opponents and to the board. And how about if we have eight opponents (like we have at a full table in Los Angeles) and have the computer deal random cards to the eight opponents and also random cards to the board 100,000 times.

And then after about a few minutes there will be screens and screens of data from this particular simulation. It’s running on a different computer as I type this....

You need to have done this a number of times in order to have a good perspective. You are able to come up with an assessment or feeling of relative value when you know how various other hands fare relatively.

simulation results:
These particular cards simulate as a strong starting hand.
If nobody folded a hand that would otherwise end up a winner, Hero would:
• win about 6.22% of the total pots by scooping.
• win about 3.25% of the average pot size as a part of a split pot by winning or tying for high, and
• win about 8.49% of the average pot size as a part of a split pot by winning or tying for low.

That’s a grand total of 17.96% of the total pots for this hand. The average in a nine player game is 11.11%. Thus relative to random hands, Ah3h6dKs wins more often. Of course if you happen to be in a deal where your opponents are dealt cards such that your outs are mostly used up, then the hand will not fare well. Or if you’re up against A234 for low, the hand also won’t fare well. It always depends on what cards your opponents were dealt and what cards they’re playing - but A36Ks is a relatively nice starting hand. If you’re not seeing the flop with it, in my humble opinion you are playing too tightly.

It should be apparent Ah3h6dKs is more of a low hand than a high hand, but that it also has a decent scoop component. I don’t know about you, but I need to scoop to do well in this game. If I don’t scoop enough, I have a losing session. This hand, as simulated against random hands, has a good enough chance to scoop (and win overall) for me to want to play it as a starting hand.

By way of contrast, 2h3h6d8s sucks as a scooping hand. In a similar simulation, 2h3h6d8s:
• wins about 2.43% of the total pots by scooping.
• wins about 2.34% of the average pot size as a part of a split pot by winning or tying for high, and
• wins about 7.01% of the average pot size as a part of a split pot by winning or tying for low.
2h3h6d8s, with total wins of 11.78% in a nine handed game, wins slightly more than average (11.11%), but has a very low scoop percentage.

And 2c3h6d8s, the rainbow counterpart, does even more horribly in the scoop category:
• wins about 1.91% of the total pots by scooping.
• wins about 2.16% of the average pot size as a part of a split pot by winning or tying for high, and
• wins about 7.07% of the average pot size as a part of a split pot by winning or tying for low.
2c3h6d8s, with total wins of 11.14% in a nine handed game, wins slightly more than average (11.11%), but has an extremely low scoop percentage, as simulated.

Lot of stuff here to digest - too much really. I started out hoping we’d get the same calculated results, but we didn’t. Oh well... the more I think about these various hands, the more I understand how to play better. But I still occasionally get out-played.

Here’s the scoop on A36K. Play it. See the flop with it. Raise or not, but if someone else raises, don’t be overly afraid of A2XY.

• Obviously play flopped quads and full houses.
• Play the heart flush flops
• Play the non-paired heart flush draw flops.
• Play all flopped trips
• If you flop two pairs, and they’re aces and kings, tend to see the turn and then make your decision, depending.
• Any two pairs other than aces and kings requires discretion. If the flop is something like Kc6s5h, now you have kings and sixes, plus a 2nd nut low draw, plus a back-door heart draw. The trouble here is you’ll probably get stuck on the river for a fourth round bet too. You could make a good case for folding A36K after a flop of K65, but I’d probably see another card and hope my antennae do their job properly. Sometimes you’ll get fooled.
• If you flop a Broadway without the board being a 3-flush, play it.
• If you flop a low straight, play it.
• Play all the deuce-low-low flops, even paired (with no ace or trey).
• Play all the deuce-low-high flops (with no ace or trey).
• Play all the 2nd nut flopped lows.
• Avoid playing 2nd nut low draws, unless there is some other stuff also going for the hand. You just have to use some good judgement here. The second nut low is going to win about half the time. You want to be playing it when it wins but avoiding it when it loses. This is one of the places where card playing skill matters. Card playing skill in any card game, bridge, pinochle, gin rummy, poker, you name it - mostly depends on correctly putting your opponents on cards and acting accordingly. This being poker, a game of deception, sometimes you’ll get fooled.
• If the flop is something like 2sKc9h, bet. Maybe you can steal the pot. And if you don’t, and you’re in late position, maybe you can see the river for free. (You do have some back-door possibilities).

Did I include all the playable flops for Ah3h6dKs? I hope so, but maybe I inadvertently left out something. If you don’t have one of the above hands, I think you generally fold.

Buzz

[franknagaijr]

Buzz - Thanks as always for the reply.

Yes, that was a typo/brain fart for the 'four card combinations', I did mean 3 on the flop.

I arrived at the 1870 for flushes as follows:
48 unknown cards -11 hearts - 37 non-hearts
3 flush cards on flop =165 combos
2 flush cards on flop C(11,2)=55 times the non-flush cards that do not make a pair...

Oh, I see what you mean. I didn't discount the times that Kh or 6h is on the board. D'oh.

My 240 number was built in the same way as yours. It stands to reason that I missed a combination. I discounted the two-flush 45x flops since that would make two of the outs dirty for other flushes, and the heart flush 45 boards had already been counted.

For the 3040 number, I did not include the second nut low draws, but only included the nut lows and nut low draws, which is four twos times 19 cards to make a low, times 40 cards that are not Ace or trey. Yes, it's conservative to discount second nut low draw, but I'm trying to come up with a reasonable number.

The point of the exercise is not about winning at showdown, but more about calculating the quantity of favorable and playable flops for any given hand. This number would suggest how many players I would like to see in any given hand to justify a call, and exactly how bad of a hand is worth playing the small blind when there are X players seeing the flop. For example, if there are four limpers at 100, I can complete for 50 with reasonable certainty that BB will not raise, I can call with any hand where I will find Y percent of flops favorable. I'm sure that I'm playing too tight in many PLO8 MTT situations in the early stages, but I have no way to measure it.

I like your suggested enumeration of playable flops above, and may go back to the spreadsheet for another round of this.

Thanks
FNJ

[bbartlog]

what constitutes a favorable flop for this hand in a full ring PLO8 game.

So are we talking LO8 or PLO8? Because the advice from Buzz seems good for a limit game but I would have to disagree with some of it in a PL scenario...

[franknagaijr]

Correct, looking for favorable and playable PLO8 hands. Ideally, over time I'd like to build similar numbers for a wide range of hands, to see what kind of express odds or implied odds I'd need to justify playing any given hand.

I know that this particular hand is an easy limp, especially for half a bet, but once I refine the technique, I'd like to have statistical evidence as to whether a given trashy combination is playable in a PLO8 MTT situation.