Part IV: Scooping The Pot

It's been too long since I wrote the first three parts of my limit Omaha Hi/Lo (henceforth "LO8" to save me from Repetitive Strain Injury) guide. I look back on them and see a few things I could have added here and there, although as a beginner's guide, which it was intended to be, I feel it "does a good job", so to speak. This part is a little different, and more in-depth and specific. It contains a little bit of maths, but it's not overly complicated and you should not be daunted by it.

One thing I didn't mention in parts 1-3 which is absolutely crucial to LO8 is the importance of 'scooping'. Scooping is essentially taking the whole pot, as opposed to just half the pot with a high or a low hand. It is of course obvious that scooping is 'good', but what might not be quite so obvious is precisely how 'good' it is in many scenarios that occur especially in low limit LO8 games. Let's look at a quick example...

You are playing $1-$2 LO8 We are dealt 4 cards which don't matter. Your opponents stacks (aside from assuming everyone is deep enoug to cover all the bets that go in), cards, our reads and suchlike do not matter for the sake of this example.

A player from early position raises. Someone in middle position calls, you call from the button, the small blind folds, big blind calls. The pot is $8.50 before the flop. You have invested $2 so far.

Three cards which don't matter come on the flop. The preflop raiser bets, middle position and you call, the blinds fold. The pot is now $11.50 and you have invested $3 so far.

A turn card which also doesn't matter is dealt. Early position and middle position check, you bet, early position calls, middle position folds. The pot is now $15.50 and you have invested $5 so far.

You already guessed the river card doesn't matter. Early position checks, you bet, he calls. The pot is now $19.50 and you have invested a total of $7.

Why does this all actually matter then? Well, let's take a look at what we gain if (a) we split the pot, and (b) if we 'scoop' the pot.

(a) If we split, we win $9.75 from the pot (imagine the game is rake-free for the sake of simplicity). As we invested $7, our profit is $2.75.

(b) If we scoop, we win $19.50 from the pot. As we invested $7, our profit is $12.50.

See what's happened here? Scooping is worth twice as much in terms of the pot we're winning, but in terms of profit, because of the money we have invested, scooping in the example above is actually about 4.5 times 'better' than splitting the pot.

Working through it in terms of purely proportions of the pot may help a little in understanding this.

We have invested 7/19.5 = 0.359 of the chips that are in the pot by the close of action on the river.

If we split, we gain 0.5 of the pot. Our profit in terms of proportion of the pot is equal to the proportion of the pot we've won less the proportion of the pot we invested. In this case, we win half (0.5) of the pot, having invested 7/19.5 (~0.359) of the pot. So we've profited to the tune of 0.5 - 0.359 = 0.141 of the total pot.

If we scoop, we win the whole pot, so we just subtract our investment from the whole pot to get our profit. In this case, that would be 1 - 0.359 = 0.641 of the total pot.

The latter divided by the former gives us the same figure of roughly 4.5, of course.

Mathematically, we can express this as follows.

i = our investment in the pot
t = total pot
v = scooping value compared to splitting value

v = (1-[i/t])/(0.5-[i/t])

What does this all mean? Well it means we should play to scoop, obviously. Scoop outs (i.e. outs that can win you the whole pot) are far more valuable than outs to only half the pot - and in fact they are worth many outs to half the pot. In the example above on the turn, if we assume our opponent will call a river bet if we hit, any outs we have to scoop are worth 4.5 outs to split. It follows on from this that it is usually a bad idea to call down with no scoop and only split outs - in some cases even a couple of scoop outs can make the difference between an obvious fold and a very clear call.

The effect of scooping is magnified even further in heads up hands, considering that we have invested a larger proportion of the pot. In a blind vs. blind battle, assuming everyone else has folded to the small blind, scooping is literally [i]infinitely better[/i] than splitting, as if we split a pot we of course only get back our money we invested in the pot (again, assuming no rake), whereas if we win the whole pot we get back double our investment.

Mathematically, using v = (1-[i/t])/(0.5-[i/t])...

We have invested half the pot, so t = 2i, and i/t = 0.5.

v = (1-0.5)/(0.5-0.5)
v = 0.5/0

Anything divisible by zero is "undefined" in mathematical terms, but here, for the purposes of this example, the answer is infinity. Hence, scooping is indeed infinitely better than splitting.

The opposite applies somewhat to games with many players seeing flops and proceeding deep into the hand. The lower our proportion of money invested in the pot, the less of a difference there is between scooping and splitting. Obviously it is still far better to scoop - taking an extreme example of all nine players at a table going to the river, we will gain a net profit of 7/18ths of the pot if we split (essentially [1/2]-[1/9]), but we will gain the whole pot, and a net profit of 8/9ths of the pot if we scoop. Hence, scooping even in this extreme example is (8/9)/(7/18) = ~2.29 times better than splitting the pot, still more than the general 'twice as good' that you may have expected before reading this. In these very loose games filled with weak players who will go deep into a hand with very weak holdings, it can often be worthwhile to draw to half the pot without any 'scoop' outs - just be sure that you are drawing to the nuts as [i]getting scooped[/i] having gone all the way to the end of a hand is the single worst thing that can happen to you in LO8.

This all may seem quite daunting at first, especially given that in an online environment we only have about 30 seconds to make a decision but with practice, working out (or even accurately estimating) the actual value of your scoop and split outs becomes surprisingly simple, just as pure pot odds calculations should be to an experienced player. If you take one thing from reading this article though, make sure it's "Play to scoop, not to split".

Until next time, good luck at the tables - Article Written by Dorkus Malorkus.

Go back to Part III of the Omaha Poker Strategy Guide.