Omaha 8 article -- The Flaws

[MeetUrTwin]

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So why are we arguing?

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Considering only a single hand, you are correct, scooping is more than 2x as profitable as splitting. However, this is useless information in isolation, and by constructing a case where the EV of the scoop vs. the split are equal, Buzz has inadvertantly created an idea that is very easily misinterpreted (by himself even). The mistake he uses is that he will run the split case twice, allowing the player to win the same revenue while risking two bets, yet he only runs the scoop scenario ONCE. Apples to oranges.

Let me draw up another example. Suppose you have a 50% chance of splitting. However, instead of a 25% chance of scooping, let's say you have a 10% chance of scooping only. Now, the scoop is still "more than doubly profitable" than the split; however, we would never be so stupid as to believe that this is justification for thinking it is better to draw to this scoop than to the split. Even if we run the split case twice, we arrive at EXACTLY the same conclusion Buzz arrives at in his article. From Buzz:

"It’s true that if you scoop once and lose once, you end up with the same amount as when you win half the pot twice (assuming pot sizes are the same). However, you will end up with more chips if you only put your chips at risk once and if you scoop that one time, than if you put your chips at risk twice and win half the pot both times."

BUT THIS IGNORES THE FACT THAT THE SCOOP ONLY COMES 10% OF THE TIME! You must take 10 trials here; 1 in 10 where the scoop wins, 5 in 10 where the split comes. ONLY then can you see how ridiculous it is to claim that the scoop is more valuable than the split.

Now, you might claim that everybody understands these concepts perfectly well (still, I'm not completely convinced that's the case). However, the spirit of Buzz's article and his usage of this confusing concept is entirely misleading to O8 players, and that is the real reason I'm arguing about it. Buzz is clearly trying to use this scenario study to promote the old adage in O8 that we should aim to scoop rather than split is correct in many senses. Unfortunately, his argument offers absolutely no justification for that adage, because in his scenario, a scoop is exactly identical to a split, in any intelligent interpretation of the scenario (which requires several trials to allow the true odds to be revealed). The "try to scoop not split" adage primarily is concerned with starting hands--it is the reason why we might prefer to play a hand like A234ds rather than A29Qr in a full ring game, since the A234ds will make many more nut high hands than the A29Qr against a field, DESPITE the fact that A29Q is statistically better head to head if both hands are always played to showdown:

Omaha Hi/Low 8-or-better: 500000 sampled boards
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
4c 3c Ad 2d 122764 215220 263769 21011 129827 0 143051 0.485
2s Ac Qd 9h 167107 263769 215220 21011 0 39534 143051 0.515

However, to say that scoop outs are "worth more" than split outs, using exactly the case that Buzz uses, where the EV of the two scenarios is identical, is complete nonsense. When it comes to scenarios where you split 50% of the time vs. scenarios where you scoop 25% of the time, the two ARE IDENTICAL.

edit: holy sht. I just realized that in the example he is using, hero has exactly the same % chance of making a winning hand in both cases. Then obviously the scoop draw is better. Jesus, I thought this article was analogous to that old thread, which was actually interesting. Instead, it's just an obvious spot of playing to half the pot for the same odds as playing to the full pot. Duh, Buzz.

btw, the thread I'm referring to is here:

http://forumserver.twoplustwo.com/showfl...rt=all&vc=1

[Brocktoon]

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Considering only a single hand, you are correct, scooping is more than 2x as profitable as splitting.

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I agree. Honestly I believe this is all that Buzz was trying to say the whole time. If you agree with the above then again, I don't see why we're arguing.

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Instead, it's just an obvious spot of playing to half the pot for the same odds as playing to the full pot. Duh, Buzz.


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He's saying that its more than twice as good to play for the whole pot than to play for half the pot with the same odds. Intuition would tell you that it is exactly double the profit of splitting.



FWIW, I found this from the original Super System:


David Sklansky wrote:

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Your primary goal at High-Low is to win the WHOLE pot.



"Who didn't know that?" you might say. Well...a lot of people don't know it. Because if they did, they wouldn't be in the pot so often trying to escape with half of it. They don't know how much more profitable it is to win the whole pot. A simple example will show you what I mean. Let's say you're in a three-handed pot and each player has $600 in the pot when it's over. If all you do is split the pot, you wind up with a $300 profit (half of the $600 that one of the players lost). That's really not much when compared to the $1,200 you'd win if you won the whole pot. As you can see, its not twice as good... its four times as good. And when the action is only heads up, a split means mearly that you get your money back (with the exception of the very small profit you get from splitting the antes). But when you win the whole pot heads up, its the difference between winning practically nothing and winning everything.

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*all bold and italics are Sklansky's, not mine.

[MeetUrTwin]

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He's saying that its more than twice as good to play for the whole pot than to play for half the pot with the same odds. Intuition would tell you that it is exactly double the profit of splitting.

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yes, my point of confusion is that Buzz has (in the past) claimed that scooping is more than equally profitable to splitting and winning half, when the chances of achieving the split are exactly twice the chances of scooping. That is, 50% chance to split in the split scenario, 25% chance to scoop in the scoop scenario. It is that claim that I thought he was repeating, and it is that claim which is incorrect.

The difference is subtle, because in his current analysis, you only have to run the outcome once since the odds are the same.

[Phat Mack]

I've noticed that one source of confusion is that there is no established algebra of outs. If you can say that having a hand with 10 scoop outs is more that twice as valuable as having a hand with 10 split outs, you can't derive from this statement a futher statement that having a hand with 10 scoop outs is greater in value to a hand with 20 split outs. The math won't support it.

OP starts with two quotes. The first quote talks about (hands) that win 1 scoop pot vs. hands that win 2 split pots. It is not clear to me that Buzz is discussing a split draw with twice as many outs as the scoop draw, but that is what OP assumes.

OP then projects this concept of twice as many outs on the second quote. But the second quote is about the same hand with the same number of outs drawing a scoop and then drawing for a split. It does not compare a hand with 10 scoop outs with a hand having 20 split outs.

While it is possible to say that 10 scoop outs equals 20 split outs, it is not possible--unless, as Brocktoon notes, the existing pot goes to infinity--to state that 10 scoop outs has exactly twice the value as 10 split outs.

The introduction to Buzz's article starts out by saying that a scoop out is more valuable than a split out, which is true when comparing hands with equivalent outs. It then goes on to say that 1 scoop out = ~2.5 split outs, which is fine if is discussing earning potential, but is confusing if it leads readers to believe that a hand with 10 scoop outs = a hand with ~25 split outs.

JMO

Mack

[jai]

The main point of Buzz's article—that a scoop out is better than 2 times a split out in terms of net winnings is irrefutable. But that is patently obvious to anyone who has spent more than 2 minutes thinking about split pot games and, to be frank, not very useful information. Furthermore, trying to quantify the relative value of a split out to a scoop out is absurd—it will be too heavily dependent on final pot size relative to bet size (as an aside, as pot size approaches infinity, the net winnings on scooping once approaches exactly twice the net winnings on splitting once). What *is* useful is being able to figure out EV knowing whether you have split outs or scoop outs. And when you think about outs in this way, then split outs are exactly equal to 1/2 of scoop outs.

To illustrate, let's look at the example that PhatMack provided where you have top set and are either drawing to scoop or split.

In case 1, we have 10 outs to split. What is our EV? Let's count our split outs as 1/2 outs, so we have 5 "outs" in this case. We are calling 100 into a pot that will be 1000 and our equity is 5/40, or 12.5%. 12.5% of 1000 is 125, so our EV=125-100, or 25.

In case 2, we have 10 outs to the whole shebang, so let's call that 10 outs. Equity is 25% into a pot size of 1000, which is 250. EV=250-100=150.

So split out equity is exactly 1/2 of scoop out equity. And in terms of actual dollar amounts, the split pot EV gets closer and clozer to 1/2 the scoop EV the larger the pot gets (to see this, increase pot size by 1000 increments and calculate EV).

[7n7]

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But that is patently obvious to anyone who has spent more than 2 minutes thinking about split pot games and

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Well, not exactly true... [img]/images/graemlins/blush.gif[/img]

[jai]

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No getting quartered, no duplicated hands, yet the 10 scoop outs are worth six times as much as the 10 split outs.

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If you are trying to compare the EV of scoop outs to split outs directly then you are not thinking about the problem in the right way.

[jai]

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Hand 1: You have AAKK, and your opponent has A2QJ, and the board is KT98. So your opponent has the straight and you have a set and need to hit your full-house on the river to win, and there is no low draw. 10 of 40 unseen cards make your boat, and 30 of 40 cards get you nothing. So your equity as calculated by twodimes is 25%. You have 10 scoop outs.

Hand 2: You have A23K, your opponent has KKJ8, and the board is 679K. So your opponent has top set (KKK) and thus will always win high. You are drawing for low, and have 20 outs to win the low half (any A,2,3,4,5,8 that are not already in someone's hand). So 20 of 40 cards win you the low half of the pot, and the other 20 of 40 cards give you nothing. So your equity in twodimes is 25%. You have 20 half-pot outs.

Here's the important part: Your equity in both cases is the same. Your profit in both cases is the same your bank account after running this situation millions of times will be identical. A half pot out is equal to exactly one-half of a scooping out in terms of the money you win or lose.

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You are only partially correct. In the case where your split outs are exactly twice your scoop outs they have identical equity, hence the EV will be the same. When the ratio is different, you can not derive a general rule for how much scoop outs are worth, EV-wise, compared to split outs. PhatMack illustrates in his post an example where scoop outs are worth 6x as much as split outs.

Rather, you can derive that equity of 1 scoop out is equal to equity of 2 split outs. From there you can calculate EV.

[Phat Mack]

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No getting quartered, no duplicated hands, yet the 10 scoop outs are worth six times as much as the 10 split outs.

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If you are trying to compare the EV of scoop outs to split outs directly then you are not thinking about the problem in the right way.

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Agreed, I only meant it as an illustrative example. (I was toying with the idea of trying to find an algebraic structure for outs, but doing so would be both trivial and futile, and, as you say, not the correct way to think about the game.)

It would be nice to nail down some terms, however: Equity; EV; profit; revenue; worth, etc. I think confusion about what people were talking about drove a lot of this thread.

The summation in your first post tied things together nicely, I thought. (I'm not sure equity and EV are the same thing, but don't let's even go there [img]/images/graemlins/smile.gif[/img] )

Congrats to Buzz for providing such an interesting and provocative article.

[jai]

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The summation in your first post tied things together nicely, I thought. (I'm not sure equity and EV are the same thing, but don't let's even go there [img]/images/graemlins/smile.gif[/img] )

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No equity and EV are not the same thing, but I think we should go there because it's important. The equity calculators like twodimes, as the name implies, tell you equity. Some people think that means they give you EV. That is not the case. Once you have figured your equity, you can use this number to calculate EV using the general formula: EV=pot equity*amount in pot after all bets are made-amount to call.


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In simulations, winning half the pot two times in ten and losing the other eight times is exactly the same as scooping the pot one time in ten and losing the other nine times. Thus it may seem as though two cards that win half the pot for Hero are equivalent to one card that would scoop the pot for Hero. However, that is not true.

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This is from Buzz's article. And the following point is even more important. Buzz is saying that winning a split pot twice nets you less than scooping the pot once. That's true. Any retard can see that winning 1/2 the dead money in the pot twice is not as good as winning all of the dead money in the pot plus what your opponent bet once. Buzz you're 100% right about that. But that is completely and utterly irrelevant to how you should play the hand. . Your net gain on average is exactly the same for both cases in the above example. It seems as though everyone on 2+2 has tried telling you this, but you still don't believe it. In the example you cited above, your EV is exactly the same with 2 split outs as 1 scoop out, so you should play them exactly the same way. All this nonsense about what fraction of a scoop out a low out is worth is just wrong, misleading, and bad advice.