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Old Jun 21, 2011, 3:41pm   #7
killcrazy
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Quote:
Originally Posted by darryl View Post
Is this a good strategy in general for PLO?
not really, it's too simplistic, and the wrong kind of simplistic.

you can boil big bet poker down to two basic necessities. you must be able to figure out your equity, and you must be able to control or failing that at least evaluate the action.

in this case you should know that if you and one other player get all in, he's going to have either a set or a straight (very rarely a weaker combination draw where you're about 3/1 favourite or rag two pair when you're about 2/1 favourite), and your equity will be around about 50%. it could be as much as 55% or as little as 40%, and on average it's going to be fractionally under 50%.

you have nut outs, 9 nut flush outs (no spades make a possible boat, although 6s makes a possible straight flush) and 6 additional nut straight outs, excluding whatever blockers show up.

firstly, if someone else pushes you all in, you can play, because 250 into a total pot of 570 is 44%, and you do have 44% equity against any reasonable range. the question therefore is how do you get as much money as possible into this pot?

we've got two guys plus the bettor putting $40 into this already, if you jam and one of them calls you, you're going to be making $35-40 on the spot, since you both have around 50% equity, you basically chop the other two guys money, and he gets slightly more of it than you. alternatively if a third player joins you all in (which is unlikely even in a game like this), you'll actually have about 40% equity against them both, and will make about $60-65 here. so we do at least know that the jam line is profitable, the question is whether it is maximally profitable.

if we smooth call we can anticipate that on average one of the two remaining players will call. that puts $200 in the pot of which we contributed $40. lets also assume that if we make our straight someone else makes the same straight and we chop. ignoring additional action, we would make like $13.50 following this line...

however, we have $210 left in our stack, a pot that stands at $270, four targets and last action. 20% of the time we flush and 13.(3)% of the time we straight (why is flush such a natural verb and straight isn't? i guess because to flush is a verb but the verb for straight is to straighten...whatever).

well if we hit the straight we are getting all in with probably another straight, however we have 9 redraws, so we chop up the $200 from the flop 80% of the time and take his $210 20% of the time. i'll spare you the math because i've shown how to do it so many times, so suffice to say this contributes about $16.50 to our overall EV

then of course, 2/3 of the time we get a brick and more on this later, but for the moment lets just say we're going to lose our $40 here, and this contributes -$26.50 to our overall EV (and the running total is now -$10)

the 20% of the time the flush card comes, what happens? well, this is substantially trickier. worst case scenario is everyone checkfolds and you pick up the $160 they gave you on your draw, which would contribute $32 to our overall equity and put us up $22 on the line (and we're looking for about >$41 from this line to make it better than jamming the flop).

now, a set is going to have about 22.5% equity against you (and will think it's fractionally higher because he thinks he has 10 outs and we know he has 9), if you can be certain the bettor won't try a hero bluff with anything other than a boat if the board pairs, you can manipulate him by laying him correct implied odds which you won't actually follow through on. the total amount he can win is 480 so a bet of $125 would be laying him implied odds of about 3.85/1, which is slightly better than his true odds of hitting which are about 3.5/1...this contributes an additional $13.75 to our equity, and assumes he is disciplined enough to fold his set if he misses, just as we will fold our flush if he hits and leads out.

there is another possibility, which is that your $125 bet will trap a weaker flush into calling, or that it will donk into you. with this many callers, there probably are other flush draws in play, and if we were being good and i wasn't doing this without a calculator first thing in the morning i would have factored this into our outs from the start and done the whole wankbucket of possible variables, but fuck off. can KXs QXs fold here? eh...probably not to be honest. why did he draw? the spades make up a lot of the perceived value of his hand on the flop, almost nobody can draw on a flush then fold it. so lets say that 50% of the time another flush pays off, in which case he also has to pay off on an unpaired river. also this will guarantee the guy with the set comes along, and again i'll spare you the math, and just say that this makes the flush's total contribution to our EV a delicious $53

so we make $16.50 on the straight, we lose $26.50 on the bricks, and we win $53 on the flush, for a total EV of $43...what were we looking for, $41? well, yeah i'd hoped for a bigger number here.

but we've been inaccurate in that i should have done a bunch of different calculations for other flush/straight draw exists/doesn't exist and all that bollocks. the smooth call line has an additional advantage of keeping your variance low and letting you dodge when the boat comes on the turn, it also creates much more room for an opponent to make a mistake against you.

coming back to the bricks on the turn, depending on which brick it is exactly, we'd still be about 2/1 against the guy with the set, and an 8 gives us a boat draw of our own. some more math would be required if this comes about, but i've done enough math, and there is shit I need to get done today because I have a thoroughly enrapturing chess club meeting in a couple of hours. yeay, two hours of reports from a dozen different "officers" in a club of like 25 people. but at least they're giving me a big trophy at the end of it. go me.

i may have shat on the math somewhere in this, i don't think i have but i'm far from infalbilale and i didn't show my working. normally i proof these posts and doublecheck everything but today i won't, that way someone has the chance to aha! kc is finally wrong about something after all these years and thousands of posts. also note that all the calculations i did on the turn, i completely ignored the $70 that was in preflop because fold equity isn't a factor in this, we weren't working with pot odds (except when trying to price the set in when we hit) but with bet and implied odds.

Kc
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