Simple O8 question?

[rkiray]

Approximately how often does a low make it in O8? Although now that I think about it, maybe it's not so simple. Perhaps it depends on alot of things. But is there a rule of thumb? I'm asking because I sometimes have trouble knowing when to play four good high cards. Knowing the answer to this could impact that decision.

[Carl_William]

60 percent is a good estimate for there being sufficient board cards for one or more players to have a low. If you have four low cards in your hand the chance of a low goes down a little. Actual occurrences of low for one or more players in a nine handed game is probably in the range of 53% to 55% (just a swag). I have made numerous simulation runs with Wilson's Turbo OM8 program. If you really want to get into this -- then buy Turbo OM8 and make some simulations. Wilsom will sell you the program for $69.95 if you call him and ask for the discount....

Carl

[Buzz]

Rick - Probability of Low Before the Flop in Omaha-8 -

The probability of low before the flop is about 0.548 (54.8%) when you have four different low cards. (By low cards, I mean aces, deuces, treys, fours, fives, sixes, sevens, and eights).

The probability of low before the flop is about 0.583 (58.3%) when you have three different low cards.

The probability of low before the flop is about 0.649 (64.9%) when you have two different low cards.

The probability of low before the flop is about 0.656 (65.6%) when you have one different low card.

The probability of low before the flop is about 0.686 (68.6%) when you have no low cards.

If you're standing behind the rail and can't see any cards, then before the flop, the probability of low is about 1,561,728/2,598,960 = 0.6009 (60.09%).

These are calculated (not simulated) values, and I'm reasonably certain of them.

If Wilson's software had worked on my Power Macintosh G3, (but even with Virtual PC, I can't get it to work) I probably would never have bothered to learn how to make the probability calculations leading to the foregoing results.

The implication for playing hands such as KhQdJdTh or KhQhKdQd, is that the board will end up with a low almost 70% of the time when you have such (both playable from any position, IMHO) hands. However, usually you can get off the hand after the flop if you have missed, and in that event how often the pot is split probably has little significance to you. Perhaps of more significance to you would be the percentage of flops that have a fit with KhQdJdTh or KhQhKdQd, assuming a full, loose or semi-loose table. (It was to me). What do you think?

Buzz

[Aragorn]

>>The implication for playing hands such as KhQdJdTh or KhQhKdQd, is that the board will end up with a low almost 70% of the time when you have such (both playable from any position, IMHO) hands.

In two respects, KhQdJdTh is not as good as KhQhKdQd. With the first hand you are hoping for an ace and a picture or a ten. Almost 70% of the time the third card wlll give people a low draw. With an ace on the board, it is less likely anyone is in drawing to the nuts, so you might scoop. Also, there is a decent chance you will be worrying about flush draws and the board pairing. Both the low draws and flush draws will contribute when you scoop, but you are playing for the whole pot a bit less often and a straight, even the nut straight, isn't the strongest hand in Omaha.

With KKQQ double-suited, you are really hoping for a king or queen to flop and for the board to eventually pair. You will see a low less often when that happens.

[rkiray]

I think that is a very impressive post. I also think I would play all the hands you name in any position. I'm probably playing a little too loose though.

[Phat Mack]

Perhaps of more significance to you would be the percentage of flops that have a fit with KhQdJdTh or KhQhKdQd, assuming a full, loose or semi-loose table.

Buzz,

I'm interested in calculating this percentage in an attempt to assign a "cost" to playing KhQdJdTh or KhQhKdQd in limit O8. There would be flops that would make the nuts, and there would be flops that would enable draws to the nuts. But here would also be flops that provide draws to second nut hands. Which flops do you think would fit these hands? For example, when holding KhQdJdTh, a flop of JhTd9h would be nice, but a flop of three low cards -two of them hearts - might not be that great.

[Carl_William]

Pat:

Very good OM8 problem you posted -- I would also like to know a little more about that.... Remembering some of my most pleasant memories playing OM8 has been scooping big family pots with a pair of Kings or Queens while in excellent position. As you know: Sometimes this happens….

I have Wilson’s Turbo OM8 and will try to run on some simulations that give some idea about your problem statement. Perhaps if you have Turbo OM8 you could do this…. As soon as I find time I will attempt to get some info for this problem. Your underlying assumptions were:

“Perhaps of more significance to you would be the percentage of flops that have a fit with KhQdJdTh or KhQhKdQd, assuming a full, loose or semi-loose table”

I will try to run off a few simulations and post it. But: It may be a while because I’m leaving for Ohio for my 50th high school reunion. But I will do it if nobody beats me to this interesting problem – I promise. Also….

As you know: computer simulations are just a tool to give us some inkling on a relative basis of what to expect – they are not the real world.

Stay well,

Carl

[Carl_William]

Run six simulations on Wilson's Turbo OM8: 100,000 iterations or trials,
Results for player # 10 (deal spins around)

Player OM8
Simulation Player#10 Profile Hand
1 Mrs Marple Tight Kh Qd Jd Th
2 Dirty Harry Average Kh Qd Jd Th
3 Capt. Marvel Average Kh Qd Jd Th
4 Mrs Marple Tight Kh Qh Kd Qd
5 Mrs Marple Tight Kh Qh Kd Qd
6 Charlie Chan Tight Kh Qh Kd Qd

Hands won (seat #10) with out of 100,000 (busts won excluded)
Ran #
Simulation Pair 2 pair trips straight flush Full House Quads SF Seed
1 161 3346 1628 9988 5447 3895 193 228 12
2 34 2065 1211 9273 5104 3985 214 286 267
3 1015 5782 2391 10867 6112 3792 149 246 519
4 194 2453 8317 2618 6738 10209 1739 193 67
5 190 1850 7828 2482 6363 10031 1654 217 34
6 236 4332 10703 2785 7425 10649 1605 198 781

Hands lost with (seat #10) with out of 100,000 (busts won excluded)
Ran #
Simulation Pair 2 pair trips straight flush Full House Seed
1 1542 5171 1401 2800 2851 343 12
2 1059 5151 1574 3167 3039 389 267
3 2712 5675 1194 2327 2587 295 519
4 1461 6704 7414 851 3488 1807 67
5 1419 6353 7602 848 3464 1865 34
6 3031 7858 6106 693 3229 1568 781

[Carl_William]

Sorry -- doing this in a hurry using: Wilson's Turbo OM8; (2) Excel & Microsoft Word and copying to twoplustwo. Can't get columns to line up.

I will try to re-edit & send later

[Aragorn]

It would ne nice if you could explain what it all means, too. Since I don't know the program the output isn't very clear.

[tiltboy]

Carl, if you want columns of data to line up, use the <font color="red"> Code</font> Instant UBB Code option when you reply. You'll get something like this:

<font class="small">Code:</font><hr /><pre>
http://twodimes.net/h/?z=51703
pokenum -mc 500000 -o8 as ac 2s 3c - 6h 7d 8s 9c
Omaha Hi/Low 8-or-better: 500000 sampled boards
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
As 2s Ac 3c 256807 301302 198698 0 213571 5754 86 0.670
8s 9c 7d 6h 86627 198698 301302 0 48784 159131 86 0.330
</pre><hr />

[Phat Mack]

Also, I don't know what "seed" means.

[Buzz]

“Which flops do you think would fit these hands?”

Hi Mack - I’m going to write this response in two parts. In the first part, Part A, I’m going to answer your question as directly as possible. Then in the second part of my response, Part B, I’m going to explain why I really can’t answer your question.

Part A -

After you’ve seen your cards (assuming no peeking or exposed cards) there are 17296 possible flops. Which of these seventeen thousand possible flops would you play if you held KhQhKdQd? The following are the flops I’d probably play under most circumstances:

1. Any flop with at least one queen or king.
2. Any flop including the ace of hearts plus at least one more heart or the ace of diamonds plus at least one more diamond.
3. Any flop with a pair of jacks, tens, or nines or a flop with a low pair plus a jack, ten, or nine.
4. Any flop with JTX, unless the cards are all black suits.
5. Any flop with three hearts or three diamonds.

Further explanation and discussion of each of these groups is shown below.

1. There are 4052 flops included in this group, 57.6% of the flops I’ll play when holding KhQhKdQd. 812 of the flops in this group are paired, so that I’ll either have flopped quads or a full house. On the other 3240 flops of this group, where the flop is not paired, I will have flopped trips. the flopped trips might win, but I really want the board to pair on the turn or river so as to end up with quads or a full house.

2. There are 690 flops included in this group, 9.8% of the flops I’ll play when holding KhQhKdQd. These are flops where I’ll either have the nut flush or a nut flush draw - mostly the nut flush draw. If the board pairs on the turn, or if the turn is a king or a queen, then I’ll have a four-out draw to a full house or better - but the nut flush draw will be dubious.

3. There are 1206 flops included in this group, 17.1% of the flops I’ll play when holding KhQhKdQd. These are flops where I have two overpairs and am mostly looking for one of four outs (a king or a queen) to appear on the turn or river. It’s possible, depending on the action and the odds, that I would not play hands in this group after the flop. It’s also possible, depending on the action, that I would have odds to play after the flop but not have odds to continue after the turn.

4. There are 812 flops included in this group, 11.5% of the flops I’ll play when holding KhQhKdQd. These are flops where I either have flopped the nut straight or am primarily drawing for a nut straight after the flop - but where I also could end up with something else. These are flops where you see one more card and then decide what to do.

5. There are 280 flops included in this group, 4.0% of the flops I’ll play when holding KhQhKdQd. These are the flopped 2nd nut flush boards. In theory, with an unpaired board at a full, loose table, the 2nd nut flush should win something like three hands out of five and lose to the nut flush something like two hands out of five. That three to two winning to losing ratio makes the flopped 2nd nut flush difficult to play sometimes. I usually bet it (or raise with it if an opponent has already bet) - and then decide what to do next based on the reaction I get. But if there’s also a low or a low draw, it’s difficult to tell where you are in the hand with the flopped 2nd nut flush - and you probably have to back away - or even fold the hand.

Hope this helps. Part B to follow immediately.

Buzz

[Buzz]

Part B -

“Which flops do you think would fit these hands?”

Hi Mack - Wow. That’s hard to do without knowing the specifics of the situation.

For example, suppose you hold KhQhKdQd in second betting position, five of you see the flop of JcJs9d for one bet, the player in first position bets, and all of your other opponents fold.

You’re getting implied pot odds to call the single bet.

If you don’t see it, make four separate piles of chips, one pile for each betting round. Put five red chips in the first pile to represent the bets from the first betting round. Then put a sixth red chip in the second pile. Next put a blue chip in the second pile.

You should immediately see you’re getting 6 to 1 pot odds.

To figure your implied pot odds, you have to assume that if you catch a queen or a king on the next card (the turn) you’ll be able to get two big bets from your one opponent (on the next two betting rounds).

To see your implied pot odds more clearly, next put two red chips in the third pile and finally put two red chips in the fourth pile. If I’ve written my directions clearly, you should have ten red chips and one blue chip in the combined chip piles. That’s ten to one implied pot odds. (You don’t put more blue chips into the third and fourth piles because you assume you have a winning hand if you catch a queen or a king on the turn). Meanwhile the odds against your catching a queen or a king on the turn (also called your hand odds) are 41 to 4 or 10.25 to 1 against you.

The balance point is when the implied pot odds are the same as the odds against making your hand. You’re not quite there - but it’s very close, 10 to 1 compared to 10.25 to 1. And there are some other considerations.

Notice that low is no longer a consideration after a flop of JJ9. This is as simple as it gets.

I think the most likely two possibilities for your one opponent, in general, are (1) a hand with one jack (making trip jacks with a redraw to quads or a full house) or (2) a bluff. The next two most likely possibilities are (3) a pair of aces and (4) a flopped full house. Choice number (5), flopped quads, is a more remote possibility.

If your opponent has flopped (1) trip jacks, then any ten, four more outs, would make you a straight, increasing your chances of winning if your opponent doesn’t a better hand than a straight make on the turn or river - and thus creating a dilemma for you if you do make a straight on the turn. There also is a back-door diamond flush consideration (and a 1/990 runner-runner straight flush draw, not worth serious consideration, but which along with the 1/990 runner-runner quad queens draw and the 1/990 runner-runner quad kings draw makes 1/330 for a runner-runner dream hand).

If your opponent (2) is bluffing on the flop, then your two flopped two pair, kings over jacks, is the best hand.

If your opponent (3) has a pair of aces, then you have eight outs (tens queens and kings) on the turn. It’s really more like 7.5 outs because your opponent could catch an ace on the river to beat all eight of your outs and could catch a jack on the river to beat four of your outs (the tens). Note that your opponent could hold a pair of aces and not tip you off about them by avoiding raising with them before the flop. At any rate, if your opponent has a pair of aces, the hand odds against you after the turn are only 37.5 to 7.5, or 5 to 1, rather than 10.25 to 1.

If you opponent (4) has a flopped full house, then you have four outs on the turn and the odds against you are 10.25 to 1, or possibly a bit worse, since you could make a higher full house on the turn and then your opponent could make quads on the river.

If you opponent (5) has flopped quad jacks, then you’re obviously in terrible shape. However, note that most Omaha-8 players would probably usually slow play flopped quad jacks after a JJ9 flop. The odds of an opponent being dealt and seeing the flop with a pair of jacks is a long-shot - and then the odds of an opponent betting the flopped quad jacks and risking running everyone else out of the pot is an even longer long-shot. I’d put it in the same long-shot group as catching runner-runner-perfect to make a straight flush or quads for the KhQhKdQd hand.

Thus after these various considerations, giving more weight to the more likely possibilities, my thinking is you have implied pot odds to play KhQhKdQd after a flop of JcJs9d - and after five of you saw the flop for one bet and then three opponents folded to a bet by the fourth.

O.K. Now let’s take the same hand, KhQhKdQd after the same flop of JcJs9d, with the same betting on the first round (five small bets in the pot) - but now let’s have one opponent bet and another raise with the two others folding on the second betting round. Now you don’t have implied pot odds to call the double bet. Now you perhaps have implied pot odds of 8.5 to 1 but the hand odds against you are 10.25 to 1.

What I mean... In other words, for a specific hand like KhQhKdQd, some flops can be playable under some circumstances but not playable under other circumstances. And sometimes the circumstances are only slightly different.

And that fact makes it very difficult to list playable flops for any hand in limit Omaha-8.

Just my opinion.

Buzz

[Buzz]

Carl - Thanks.

"I will try to re-edit &amp; send later"

You don’t have to bother aligning and reposting. I copied your data to a word file and then replaced the spaces with tabs. It’s all lined up just fine on my screen. Thanks again.

The data itself is very interesting. Looks like full houses were responsible for more wins than flushes or straights. The ratio of wins/losses with a full house with this particular hand is roughly six to one. Most of those losses must be to aces full. Quads and straight flushes simply don't occur that often.

Trips are in second place in terms of wins - but trips lose almost as much as they win.

The 2nd nut flush is in third place in terms of wins - and the 2nd nut flush wins about twice as much as it loses. I would have expected the 2nd nut flush to win about one and a half times as much as it loses. Wonder why there is a discrepancy. Maybe the tight simulation players are somehow sensing when to fold the 2nd nut flush and when to play it. Wonder how that works. More likely simulation players are folding suited aces with little else to go with the hands. (Just a guess). Another factor is that when an ace in the flush suit appears on the board, then your 2nd nut flush hand is elevated to nut-flush status. At any rate, your simulation data offers proof that 2nd nut flushes are indeed profitable to play.

The straight is in third place in terms of wins. Not surprising. There are only two straights that can be made with the king-queen combination, the only straight combination - not enough to give the hand a greater number of straight wins. But look at the quality of the straights! When Wilson’s tight simulation players played a straight, using KQ, - it was a winner more than three times as much as it was a loser.

Of course straight flushes and quads do well. I usually group quads with full houses. When you have trips and ten outs (for the board to pair) on the turn, quads are one tenth of those outs. Thus the ratio of full houses to quads should be nine to one. If we add the numbers for full houses, losing and winning, and compare with the total number of full houses in your tables, 36129/4998 = about seven to one, rather than nine to one. I wonder why. Might have something to do with the particular flops played.

Finally, one can see that the simulation players take a bath playing one pair or two pair in this game, losing much more than they win with these hands - but we already knew that.

There must be some implications, in terms of types of flops to play with KhQhKdQd. Based on your data, maybe for starters I should draw to the second nut flush more than I have been doing. Hmm. Deserves more thought.

Thanks again for the data. Have a nice time at your reunion.

Buzz

[Phat Mack]

This is some really good thinking, Buzz. When I read about flopping an under pair in part A, I thought it might be a misprint. Clearly +EV in the right circs.

[Phat Mack]

Another thought before retiring...Something else to consider when playing this hand is the "overhead." You listed 7040 "favorable" flops for this hand out of 17,296 total, or roughly 40%. If you are playing in a game where you can see a flop for 1 bet, it will actually cost 2.25 to see a favorable flop: an additional cost of 1.25 that will have to be recovered. I realize this "overhead" is a sunk cost, and shouldn't influence the play on any given street, but if you have a 10.25:1 draw, you really want 11.5:1 implied odds, or you will eventually go broke playing this particular hand. It's calculating this "overhead" that gives me fits in limit 08.

[Buzz]

Flops to play with KhQdJdTh: 5394/17296 = 31.2%

The bulk of playable flops for KhQdJdTh (about 89% of them) come from groups #2, #3, and #4 below.

Flops with three cards of the same red suit are included in group #6 and are omitted from the sub totals of groups #1 through #5.

1. Any three of the following: king, queen, jack, ten, but not all of the same black suit...
204/5394 = 3.8% of the playable flops for KhQdJdTh

2. Any two of the following: king, queen, jack, ten plus any other card, but not all of the same black suit...
2160/5394 = 40.0% of the playable flops for KhQdJdTh

3. One ace plus one of the following: king, queen, jack, ten plus any other card (except another ace), but not all of the same black suit...
1408/5394 = 26.1% of the playable flops for KhQdJdTh

4. One nine plus one of the following: king, queen, jack, ten plus any other card, (except another nine or an ace), but not all of the same black suit...
1232/5394 = 22.8% of the playable flops for KhQdJdTh

5. Nine-eight-seven, not all of the same black suit...
60/5394 = 1.1% of the playable flops for KhQdJdTh

6. Three flopped hearts or three flopped diamonds...
330/5394 = 6.1% of the playable flops for KhQdJdTh

Playable flops are difficult to list for a particular hand because unless you flop a sensational hand (a straight flush or quads), there simply is no way around playing your opponents in addition to playing your hand/flop fit. Just because I’ve listed a particular flop as playable with KhQdJdTh doesn’t mean I think it’s always playable - and just because I haven’t listed a particular flop doesn’t mean I think it’s never playable.

You might want to back away from some of the flops listed as playable for KhQdJdTh, depending on the action and your read of the situation.

For example, AKK, AQQ, AJJ, and ATT (from category #2) all seem particularly vulnerable, as do some non-nut flush making flops (from category #6).

Just my opinion.

Buzz

[Buzz]

"If you are playing in a game where you can see a flop for 1 bet, it will actually cost 2.25 to see a favorable flop: an additional cost of 1.25 that will have to be recovered. I realize this "overhead" is a sunk cost, and shouldn't influence the play on any given street, but if you have a 10.25:1 draw, you really want 11.5:1 implied odds, or you will eventually go broke playing this particular hand. It's calculating this "overhead" that gives me fits in limit 08."

Mack - I think you may be adding your "overhead" in the wrong place. Actually, if you're referring to a rake, I think you may want to subtract it from the size of the pot. I intentionally omitted the rake from consideration because sometimes the "collection" is made in some other fashion, but you are correct in noting that the rake needs to be considered in a game where the pot is raked. In a game where you're paying an hourly charge, you're paying the charge whether you play a hand or not and the hourly charge should not be included as a consideration when you are comparing hand odds to (implied) pot odds.

Just my opinion.

Buzz

[Phat Mack]

Actually, if you're referring to a rake...

Actually, I forgot about rake, but that has to be recovered, too. What I was referring to was that if a hand is played 100 times for a cost of one chip, and the hand may proceed past the flop 40% of the time, then it will surely be thrown away on the flop 60 times, for a loss of 60 chips. It is these 60 chips that must be recovered during the play of the hand for the hand to be profitable over the long run. I don't know if overhead is a suitable term.

[Buzz]

...."What I was referring to was that if a hand is played 100 times for a cost of one chip, and the hand may proceed past the flop 40% of the time, then it will surely be thrown away on the flop 60 times, for a loss of 60 chips. It is these 60 chips that must be recovered during the play of the hand for the hand to be profitable over the long run. I don't know if overhead is a suitable term."

Mack - I understand what you mean by “overhead.” You’re referring to chips you put in the pot on the first betting round.

Temporarily forget about split pot considerations. If you think of a starting hand as winning 20% of the time, and if the first betting round costs you 1 chip each time, and if you enter a pot with 4 opponents, then four times out of five you will lose your one chip, but one time out of five you will get your one chip back and also win four chips, one from each of your opponents.

Thus if you win the whole pot 20% of the time, and if you have four opponents each time you play, you’ll break even for your first bet.

However, if you have more than four opponents each time you play a hand, say five opponents who also see the flop, and if you still win the whole pot 20% of the time, then you’ll lose one chip four times out of five, but you’ll win five chips one time out of five. That amounts to averaging winning a fifth of a chip each time you play the hand.

So where do you account for the “overhead”?

<font color="red">On the very first betting round. </font>

When somebody else wins the particular pot into which you have placed your chip, you have simply lost your wager. If your hand has a 20% win expectancy, think of this particular hand as one of the four out of five times you’ll lose one chip. Another time will be the one out of five when you’ll get your chip back plus one chip from all your opponents who also see the flop.

I don’t want to make matters more complicated than they need be, but there is another important consideration. If you can recognize a flop as one of the four out of five where you will not end up with the winning hand and can get off the hand after you have seen the flop, then all you will lose is your one chip - and you will still win the one chip from each of your opponents on the one time out of five that you are destined to end up with the winning hand, whether your opponents recognize this one time out of five as your winning time or not. (Because their chips are already in the pot which is destined to be yours). In addition, you will win additional, extra chips from your opponents when they do not recognize that they have encountered the one time out of five that you are destined to win.

Thus when you have a hand that is expected to win 20% of the time at a full table - implied in wagering your one chip on the first betting round is that on the one time out of five you are destined to win, in addition to the chips put in the pot by your opponents on the first betting round you will also win chips your opponents will put into the pot on later betting rounds.

At any rate, you account for the one chip (or whatever it costs you to see the flop) on the first betting round only. After that, on each successive wager, that initial chip of yours is simply part of the pot, just like all the other chips in the pot, regardless of their origin.

Clear?

Buzz