btw I'd probably defend wider.

EDIT: I would defend wider

Guys, I'm soooooo sorry. The ante is $1. So so so sorry, I dont sleep much, work too many jobs, play too much pokers, quickly posted this.

so i'm assuming the bring-in isn't 5$?

No, it is, confirmed, was playing earlier, and watching a game now.

ProPokerTools Stud Hi/Lo Simulation

600,000 trials (Randomized)

Hand	Pot equity	Scoops	Wins Hi	Ties Hi	Wins Lo	Ties Lo
49	9T	36.88%	204,867	237,463	266	0
9*, 78, T8, JT, A*, *s*s, 22-88	9sAs	63.12%	362,271	362,271	266	55,447

^u forgot low cards in ur sim and the actual structure i think is $1 antes/$2 bring-ins if this is carbon/merge.

how wide do u guys open based on the ante/bring-in structures?? this is something i've had really hard issues coming up with a solution with. I mean at game speed, I just play based on the function of my villain's range rather than focusing on how much value i lose if i don't open at least xx% in an xyz ante structure.

let's say we play 10-20

imagine if the antes were pennies and the villain brings in for pennies.
the correct strategy for hero is to open only aaa (not hands where equity > 50% or 48.whatever% b/c of dead money) since villain is only defending aaa.

now imagine if the antes were in the millions and the villain brings in for millions. the correct strategy is to play every hand (not necessarily raise every hand).

1) if $3 antes and $5 bring-in, joe opens, villain gets gets 4.2:1 (5 for 26) closing the action.
2) if $1 antes and $2 bring-in, joe opens, villain gets gets 1.75:1 (8 for 22) closing the action.

How wide is Joe suppose to open in either 1) or 2)? 20%? 50%? 80%? Should Joe construct a limping range in order to play a wider range? How wide is villain suppose to defend? When does pot odds become a more significant factor than poor equities? (eg. joe opens and villain defends a hand with <35% equity b/c of huge antes)

I mean if I were in either spot, I just use fpdb or some kinda hud and play based on vpips and pfrs rather than focus on the structure. I don't even have the slightest clue what the optimal opening/defending ranges are or should be. I can see the antes becoming a huge factor to determining the answer here.

I mean I haven't gotten to the point where I even think those questions really matter since I only play fishes. but it's always something I've thought about for a long time.

Seems like you should do some work on what the optimal defending and opening ranges then.

clumsiness mixed with my poor logic

Theory wise you should have a limping range, however if villain isn't defending enough exploitively we should be raising all of our hands.

I think the fold is fine vs the villain described.

+1. And categorizing all your opponents as fish, whether or not it's true, is no excuse for not knowing your fundamentals. The goal when you play should be to maximize your overall EV, not just get some +EV and pat yourself on the back for beating inferior players.

For the structure in this game ($1 ante, $5 bring), Villain has to defend > 40% of hands to deny Hero a +EV strategy of completing 100% of the time. Since the EV of folding is always 0, this is the frequency Hero should adopt, even if it means giving up 100% of the time if he gets resistance. At the other extreme, if Villain were to defend 100%, what should Joe's opening % be? Well there isn't much dead money in that case ($2) which probably pays the average rake, so an equally skilled Hero should basically open 50%. Since Joe is certainly an above average player (and for sure isn't playing HUHU without a significant edge), let's bump that up to 60%.

So as a reasonable approximation, Hero should open according to this table:

Vil defends	Hero opens
0%	100%
20%	100%
40%	100%
55%	90%
70%	80%
85%	70%
100%	60%

is it possible to know, which rank hands like k23, 358 etc have?

Drew over at pokerstove used to have a listing based on showdown value. I'll post a link if I can find it. If you have propokertools, you can generate custom rankings based on specific opponent ranges with the spreadsheet tool.

That link has been taken down, however I did capture it here: http://forumserver.twoplustwo.com/sh...77&postcount=2

It is a 8 handed Monte Carlo sim, not short/HU however.

Ante is low, so defense should be honest, but by the time we fold there's enough money in the pot that it's a bad fold.

In situations like this, I think mostly about what would a decent villain do with actions up to that point. Hard for him to beat Nines if he doesn't raise our completion on Third. He's unlikely to have a fd because he should be raising Third. His most likely hands then are connected cards that have picked up backdoor low equity (68)9A for example, bigger rundowns (QJ)9A for example, or an underpair. Any of these hands could have picked up a 3-flush, but you still shouldn't fold.

I played around with a bunch of sims and couldn't make one where you aren't better than flipping.

Here are a couple of examples to check in case I'm still getting the syntax wrong

ProPokerTools Stud Hi/Lo Simulation

600,000 trials (Randomized)

Hand	Pot equity	Scoops	Wins Hi	Ties Hi	Wins Lo	Ties Lo
4c 9c 9s Td	57.51%	314,053	375,921	204	0	0
22-88, KQ, QJ, JT, T8, 87, 86, 85, 84, 83, 82, 8A / 9h	42.49%	223,875	223,875	204	78,859	0

ProPokerTools Stud Hi/Lo Simulation

600,000 trials (Randomized)

Hand	Pot equity	Scoops	Wins Hi	Ties Hi	Wins Lo	Ties Lo
4c 9c 9s Td	59.43%	316,383	396,672	159	0	0
22-88, KQ, QJ, JT, T8, 8$L, 7$L, 6$L, / 9h	40.57%	203,169	203,169	159	103,990	0

He will have a few slow-played monsters like rolled Nines or Aces, three-flushes with weak cards etc, so we should err on the conservative side, but I can't make this anything near a fold no matter what I do.

Poop, left off his Ah in those sims. Here they are:
http://propokertools.com/simulations...h+Ah&s=generic

http://propokertools.com/simulations...9hAh&s=generic

Posted links because table format not working with 2+2 formatting. (tl/dr: Still at least flipping)

Giving a mostly tight-passive player too much trust here. He does not raise/reraise most 3-flush hands.

Here is his range as I see it having hours of hand w/him:

ProPokerTools Stud Hi/Lo Simulation

600,000 trials (Randomized)

Hand	Pot equity	Scoops	Wins Hi	Ties Hi	Wins Lo	Ties Lo
49	9T	36.88%	204,867	237,463	266	0
9*, 78, T8, JT, A*, *s*s, 22-88	9sAs	63.12%	362,271	362,271	266	55,447

i'm very curious at how you came up with this chart. I'm trying to work out an approximation on 3rd street and I really have no idea whether or not i'm on the right track.

do you include villain reraising his bring in?

if the villain never or rarely has a flush draw in his narrow range, then I agree that calling on 4th is correct.

what I have in mind to solving this is first I'd group a bunch of different hands into categories. For example I'd group the 1225 combos (50*49/2) into 10 categories (good pairs, bad pairs, flush draws, overcards, straight draws, $L$L, good trash, bad trash, etc). I'd then construct hero's and villain's ranges based on those 10 categories. So hero's range can be good pairs or good pairs && bad pairs or good pairs && bad pairs && flush draws, etc. There would be a total combination of 100 different equities after I run my 10 ranges against villain's 10 ranges.

with those equities, i can now draw some sort of ev tree. if villain opens this && villain flats this then the hot/cold equity is this. There's 20 possible opening strategies for hero (assuming we don't limp): Bet or Fold. When we fold, the game ends and the EV of that strategy is 0. When we bet, we are met by 10 possible ranges and each of those ranges has the option to call or raise as a strategy. If villain has good pairs then villain can choose to raise or call. If villain has good pairs && bad pairs then villain can choose to raise good pairs && raise bad pairs or raise good pairs && call bad pairs or all good pairs && call bad pairs. An illogical/dominated strategy would be to call good pairs && raise bad pairs, so we can take that out of the tree. Villain has a total of 65 possible strategies against each of our 10 ranges. When villain calls, I'm just going to end the tree and base the EV based on h/c equity of the pot. Also since this is starting to look tedious, I'm going to assume hero doesn't reraise or fold. The game tree ends with 660 possible EVs.

Next I just compare the EVs of all responses and the response where both EV's are the closest is the optimal solution.

am I at the right ballpark? if so, is there an easier way?

edit: our folding range is also based on villain's strategy. so it seems like there's actually 650 + 650 EVs to be drawn out. my logic here is pretty clumsy, so hopefully someone understands where i'm getting at and can correct me.

edit 2: it's just 650 possible. I forgot I had to add the ev of folding to the ev of raising. that makes up 1 of 10 possibilities for hero. villain will then be able to respond in 65 different ways to each of those 10 responses.

I tried to spell it out pretty completely in my post, but all I did was calculate Hero's frequency at the limits of Villain's range of frequencies and then "draw" a straight line between the two points to fill in the table. (Hero should open 100% when Villain calls from 0-40%, and open 60% when Villain calls 100%). It doesn't take into account future actions, like what to do if Villain raises your open, which requires other skills in determining if it's worth continuing. It also doesn't include a limping range, which could be more or less correct in some spots.

If that's his range for continuing on Third and he's not raising any of those hands then never mind, he's too tight and passive to beat you out of anything even if you fold too much.