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Playing a pat boat in POFC
You're only dealt a pat boat once every 3744 hands, so it's not a catastrophic hole in your game if you don't get max equity when you get it, but I think splitting it up--trips on the bottom, pair in mid or on top, depending on whether it is an FL pair--is the best play. If the trips are JJJ or smaller and the pair is an FL pair, the difference is bigger, but I think splitting the boat is still best if the cards are small.
In general, if you hold out til the bitter end, you'll catch quads on the bottom on one of the draws about a quarter of the time. Even if you don't, you'll end up making a boat on the bottom eventually by either drawing a pair or backdooring one fairly often. But even if you don't make a boat or quads on the bottom, breaking up the pair makes it much easier to get to FL.
In another post MMM shows that the odds of drawing a pair on 1 of the 4 draws is about 39%, but often if you make this play, the first pair you draw will go in the mid to make 2 pair (or the start of 2-pair if the initial pair was an FL pair played to the top or vice versa if the first pair drawn is an FL pair.)
Let's look at a couple scenarios.
Discards: 6d, Qh, Ah, Tc
I broke up the boat to set QQ on top to try for FL. The first draw brought 986, three live cards, and I set 98 in the mid. The next draw was Q82. The 8 paired the mid and the 2 was live, so 82 went in the mid. The third draw brought 77A, so I put the 77 in the bottom to complete the boat. I had 6 live outs for the last draw (opp had an 8 and a 9), which came K9T, making FL.
If I had set the boat, I would have ended up playing 98 mid, then 82 mid, then 77 top, then 9 mid K top to end up with:
Discards: 6d, Qh, Ah, Tc
There was never a route to FL once the QQ went on the bottom, so the hand makes 5 points less in royalties and doesn't make FL.
Here's one with small cards.
Discards: 5h, 8d, 2d, 8c
In this hand, 66 went in the mid, with the goal of making trips or 2-pair. The first draw came KQ5, and the two FL cards went to the top, so that a 6 or a pair in the mid and a K or a Q on top would make FL, and there were 3 draws to get there. The second draw came JJ8, with JJ going to the mid and the hand was now a virtually foulproof 6-out freeroll for FL. Draw 3 came 923, no K or Q, but quads on bottom. The last draw came AT8, and although the FL draw never got there, I got all the value I could have out of the cards I saw.
If I had set the boat, the hand would have played out like this:
Discards: 5h, 8d, 9s, 8c
Both the bottom and the mid end up weaker.
Sure, there will be times when you make this play when you won't get to FL and you end up with just trips on the bottom, losing 6 in royalties, but I'd argue that breaking up the boat--especially if the pair is an FL pair--gives you more chances to make monsters by getting to FL.
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