O/8 low board stats

The following low board stats are from a 100K hand no fold O/8 full ring game simulation. Low means a card 8 or less and unpaired on the board.


flop:


0 low =05% *


1 low =32%


2 low =47%


3 low =16%


turn:


0-1 low =19% *


2 low =42%


3 low =32%


4 low =07%


river:


0-1-2 low =40% *


3 low =40%


4 low =18%


5 low =02%


* no low possible


nut low =37%

2nd low =14%

3rd low =06%

other low =02%

total low =60%

nut low =37%


2nd low =14%


3rd low =06%


other low =02%


total low =60%


I'm not sure what this means. A wheel on the board 37% of the time? Can't mean that... A nut low made by one or more players?

Nut low = 37% means a nut low will was made 37000

out of the 100,000 hands played. Though this is

not a low board stat, it is a breakdown of the

made lows. Since these are no fold stats, 37% is

probably the highest % of nut lows possible.

Very interesting. When low was possible, nut was there 62% of the time. I would have suspected it would have been higher. I guess this is a result of the no-fold nature of the sim.


Is there any way to determine the nature of the board when a nut low made? I would suspect that in game conditions the absence of an A and a 2 on the board would make nut low more probable, but in a no fold sim, the occurance is random.


BTW, thanks for posting this. Was this canned software or did you write it?

Phat Mack is correct.


The five card OM8 board on average has a possible low 62% of the time. I calculated "exactly" this probablility, and it was a small percentage different than exactly 62 percent ( a hair over if I recall). I stored these calculations somewhere om an MS Excel spreadsheet. I calulated it using probability counting techniques "i.e. enumeration," it can be done with a little sweat.


An interesting point....


If you divide 32 by 52: you get .61538461538461538461538461538462 or approximately 61.54%. This is very interesting because: there are 32 low cards "8 or under," and 52 total cards in the standard deck. This is a very interesting coincidence -- maybe -- probably not a coincidence "who knows."


Pat or anybody out there: what do you think?


Also: After running millions of iterations "deals," Wilson's Turbo OM8 charts show 62% for possible low boards.

I want to make a point.


OM8 board stats: show that 62% of the time that a low is possible. Whether one or more of the players qualifies for a low depends upon each starting player's four card private hand, and how many players go to the showdown. There can be five unpaired low cards on board, two or more active players on the showdown, and still none of the players qualify for low. Almost anything can occur occasionally in OM8.

As you know -- low OM8 boards "sets" consist of:


(1) three unpaired low cards and two high cards.

(2) four unpaired low and one high.

(3) five unpaired low.

(4) five low with one pair.

(5) four low with one high.

(6) five low with two pairs.

(7) five low cards including a set of low trips.


Using probability counting techniques, the number of possible low boards for each of the seven situations listed above can be exactly calculated. Summing the number of elements in each of the seven sets list above and dividing by 2598960 equals .62 something (or 62%).


I think the list of seven exhausted the possible low board situations. If I'm wrong -- please respond.

Carl - You wrote, “OM8 board stats: show that 62% of the time that a low is possible.”


I think your 62% is in error. (More about this below).


You wrote, “Whether one or more of the players qualifies for a low depends upon each starting player's four card private hand, and how many players go to the showdown. There can be five unpaired low cards on board, two or more active players on the showdown, and still none of the players qualify for low.”


It often happens that no one can make a low, even though there are at least three different ranks of low cards on the board. Accordingly, I thought in a very loose game the percentage of low made would be in the neighborhood of 50-55%.


You wrote, “low OM8 boards "sets" consist of:

(1) three unpaired low cards and two high cards.

(2) four unpaired low and one high.

(3) five unpaired low.

(4) five low with one pair.

(5) four low with one high.

(6) five low with two pairs.

(7) five low cards including a set of low trips.”


For #(5) you must mean four low with one pair and one high. Otherwise, my thinking exactly.


You wrote, “Using probability counting techniques, the number of possible low boards for each of the seven situations listed above can be exactly calculated. Summing the number of elements in each of the seven sets list above and dividing by 2598960”


Still my thinking exactly.


“equals .62 something (or 62%).”


Here is where we disagree. My result is 0.60 something (or 60%).


You wrote, “I think the list of seven exhausted the possible low board situations. If I'm wrong -- please respond.”


Your choice of seven categories is the same as mine (with the slight discrepancy for wording in #4). Where we disagree is in the counting. You did not list your totals for each of your seven categories. Here are mine.


680,960 combinations (1) three unpaired low cards and two high cards.

358,400 combinations (2) four unpaired low and one high.

57,344 combinations (3) five unpaired low.

107,520 combinations (4) five low with one pair.

322,560 combinations (5) four low with one high.***(one low pair)***

24,192 combinations (6) five low with two pairs.

10,752 combinations (7) five low cards including a set of low trips.”


total of the seven cases = 1,561,728 combinations for low.


1,561,728/2,598,960 = 0.6009 = probability there is a possible low.


You report that your simulated results also equal 62%. I wonder what simulator you are using.


Buzz

"nut low =37%

2nd low =14%

3rd low =06%

other low =02%

total low =60%"


Plowseed - Your list totals 59%, not 60%. I wonder if you added yourself or if your computer added and rounded to the nearest percent. I don't know how often no one can make a low even when low is enabled (at least three different ranks of low cards on the board), but it surely isn't all the time. In actual play it is common, even in a very loose game, for nobody at the showdown to be able to make a low.


Did you run your simulator for 9 handed, as in Los Angeles, or 10 handed, as in Las Vegas? I would have guessed that a Monte Carlo type simulator would have shown roughly about 50-55% as the total of made lows for a full game. The difference between 50-55% and 60% would account for those times when nobody could make a low, even though it had been enabled. I suppose it's possible that the difference between 59% and 60% accounts for the times when nobody can make a low even though it has been enabled, but the 59% still seems high, IMHO. What simulator did you use?


I thought I had it all straight, but now you have posted something in disagreement with my understanding.


Anyway, thanks for sharing your results.


Buzz

Buzz


Buzz, thanks for the board correction.


322,560 combinations (5) four low with one high.***(one low pair)***


If I can find my calculations (Excel spreadsheet) for the possible OM8 low boards, I will review it. I made these calculations about 20 months ago, and I thought I remembered it was a little over 62%. It's no big deal. Thanks very much for the reply.


I will search my hard drive. If I find my calc. I will let you know.


If I can find the energy -- I will do the analysis again if I can't locate the spreadsheet.

I made the analysis because an OM8 player at the Hawaiian Gardens Casino in LA County, CA was curious and then I became curious.

Buzz


I just reviewed five 500,000 OM8 simulations and all five results were essentially 60.1 % for possible low OM8 boards. So you are right on, Buzz. I use Wilson's OM8 Turbo Version 3. My memory must have failed me from 20 months ago.

Carl - Thanks for responding. As you know, it doesn’t matter exactly how often low occurs when you have not yet looked at your cards. Far more important is knowing what your odds of making the nut low are (and also what the odds of an opponent making low are) after you have seen your hand - then again after seeing the flop, and then again after seeing the turn. (By the time you get to the river, you usually have a reasonable idea of what cards your opponent is holding).


I have not been playing poker in casinos for very long, just a couple of years, and mostly Omaha-8. The question of how often low occurs was what got me started on probability calculations. I did not realize at the time that the question was of little importance.


Back in 1957, in my junior year at UCR, I signed up for a math department upper division/graduate math elective titled “The Theory Of Numbers.” The class was only offered every two or three years and was taught by the math chair, professor Clark. I think that was his name. I was not a math major but thought, because of the catalog description, the class might touch upon the subject of probability.


Of course everyone else in the class was a math major. Most of those present were graduate students, several of whom were TAs, and everybody in the room was smarter than me. Sometimes Dr. Clark would come to class with notes evidently taken from one of the current math journals, which he copied on the chalk board. A lively discussion, which was way beyond my level of comprehension, would follow. Usually one of the graduate students would seem to know more about the particular topic under discussion than Dr. Clark. After a few weeks, the only probability of much interest to me was that of my surviving the class. (Somehow I did). It was not until decades later that I considered the possibility that Dr. Clark was choosing topics related to the research areas of his graduate math students.


The final exam had one problem, a Diophantine equation, which I, alas, did not solve until several months later when the answer and method of solution both suddenly popped into my head while I was digging a hole and thinking about something else. The depths of my subconscious brain must have been slowly cranking away at the problem all that time.


At any rate, although I had a mild interest in learning more about probability over forty years ago, after that humbling math class experience the interest did not resurface until I started wondering how often low is possible in Omaha-8. I wonder how my life might have been different if Dr. Clark or one of his graduate math students had shown an interest in probability. No matter. You play the cards that are dealt you in life as in Ohama-8, and I have no complaints about mine.


Thanks again for responding. I was fairly certain my calculation (60% for possible lows before you look at your cards) was correct. Still leaves me wondering about Plowseed’s 60% total for made lows. Seems like it should be lower.


You mentioned Hawaiian Gardens casino. I plan to be there for the low limit Omaha-8 tournament early Tuesday afternoon. I’ll ask Rusty if you are there. Rusty knows me as “Frank.” Be nice to meet you in person.


Regards,


Buzz

The other low is 3%. These results are from a 10

handed no fold turbo o/8 simulation. 10 hands

are playing for that low regardless of how weak.

The results are only acurate to 1%. Under these

game conditions a nut low wins more than twice

as often as 2nd low and 3rd low is very weak.

Similiar to very loose real game conditions.

"The other low is 3%."


Plowseed - Is "nobody can make a low" included in "other low"?


Buzz