I could set up this sort of calculation really easily if my computer had about twice as much memory . As is, it's easy to set up an approximation that might be kind of helpful.

This calculation is exact (to numerical accuracy) except that it doesn't include all the flops. In particular, I've chosen about 1300 flops such that any two cards show up on the flop with the right frequency. So, e.g., we get a 32X flop just as often as in the full game, no more and no less.

For comparison, if I solve this in the SB-opens-100% case, I find the total value of the game for the BB to be +0.1149 BB/hand, and in particular, I find that he folds preflop with 32o and some of the combos of 42o. (Obv the fact that all 42o aren't played the same is an artifact of the approximation.)

If I have SB open-fold 32o,42o+,52o+,62o+, then the BB's value drops to +0.0643 BB/hand on average, and he folds pre w/ 32o, 62o, 72o, and some combos of 42o.

I think it's interesting that a relatively small change in SB strategy (he's still opening ~91% of hands and jamming all flops) cut the BB's EV by nearly half.

I do find it interesting, and if my "gizmos" worked like they're supposed to this wouldn't take much work besides a relatively small amount of CPU time. Actually, it's a good thing that this helped me find new bugs; I need to fix them in either case, just don't know how long it will take. Maybe someone else can do the calculation quicker?

Meanwhile if that 91% goes down just a bit more the BB's EV goes back up pretty substantially I would think.

I think it'd have to go down quite a bit more before BB's EV started to go back up. SB's optimal opening range is almost certainly tighter than his optimal opening range in the shove-or-fold game -- he needs a stronger hand to play profitably to counteract the BB's advantage from his extra option to see a flop and then fold. And SB's optimal opening range in the 5bb shove-or-fold game is ~71.5%.

If we let BB choose his opening hands and keep the game otherwise the same, then BB's optimal opening range (still within the 1300 flop approximation) is

22+,A2s+,K2s+,Q2s+,J2s+,T3s+,93s+,84s+,74s+,64s+,5 3s+,A2o+,K2o+,Q3o+,J4o+,T6o+,96o+,86o+,76o,Tc2c,Qc 2d,Qc2s,Qd2c,Td2d,Qd2s,Qh2c,Qh2s,Qs2c,Ts2s

(70.6% of hands)

and BB only wins 0.006BB/hand (i.e. 0.6BB/100).

and also, in that case, SB sees a flop w/ everything except 32o-82o,83o

Preflop you've got 32.3% equity and you're calling 20 to win 60. This seems okay in itself and maybe looks like a call. However you have to look at it a little bit more and think about how it plays out post flop. On the flop you have to call 60 more to win 140. You can only continue with your hand, as you said, on 2xx 3xx 45x A4x A5x and 3 flush boards where you have the FD. You only get to continue about 35-40% of the time under these assumptions. Thus, you are immediately giving up the pot 60-65% of the time. When you do decide to continue you only have less than 55% equity in poker stove (55% with a pair on 3 card board, 58% with pair on paired board, 32% on monotone FD board, 27.5% on A4x A5x, 39% on 45x, crushing with better obviously but that is rare). Thus, when you see a flop, you're expecting to win the hand less than 20% of the time. This is a losing proposition if you compare it to the odds we needed when making the preflop call initially. I am not doing the exact numbers here as that would take too long. But this isn't even close IMO.

You should fold preflop. The only way calling becomes acceptable is if you think you can call and then shove the flop (any flop, really) and get folds a lot of the time.

Did you read the thread? The calculation has been done by at least three different posters and although your conclusion that 32o is a fold is correct, it actually is close. 62o and 72o are calls. 32o becomes a call if the starting stack is increased from 100 to 126 chips.

.

With 200 stacks you still need to win the hand 25% of the time from preflop. Then on the flop:

You will be calling 160 to win 240. You now need 40% to make the call. You have to fold the open ended draw now as well. Now you are only going to continue with a pair or better, or about 32% of the time. About 80% of that range has 55% equity, about 20% of that range has about 85% equity (slightly more for trips but I didn't even bother to include flush draw boards in the other ones). I am just going to round this entire range, on the variety of different boards we continue on, to about 61%. So we're folding on the flop about 68% of the time and when we continue we're only a 61% favorite. Using this logic we're only going to win the hand about 19.5% of the time... and that is with a 200 stack. It is pretty clear to me that stacks would have to get reasonably deep before this is a call at all preflop.

i didnt check your numbers themselves, but your own numbers show that call is better than fold.

according to your numbers, if we call pre, we fold flop 0.68 of the time and end up with 160 chips and call flop 0.32 of the time and end up with 400*0.61 chips

so, total expected stack after we call pre is 0.68*160+0.32*400*0.61 which is approx 187.

187 is larger than the 180 we'd have if we folded pre.

perhaps you were comparing calling to sitting out before the beginning of the hand instead of comparing calling to folding.

anyway, as amy mentioned, these calcs have been done exactly several times now.

It´s -EV by 5-6usd in a 50-100 game without rake if your strategy is to call any flopped pair/oesd/fd or better, which is suspect is very close to correct.

42,52,62,72 are all really close, maybe slight +ev, cant be bothered to run sims all day.
Sometimes they come out at slight -ev, sometimes at +ev after running the spot 400.000 times.

It probably doesn´t matter much, just dont fold much at all and you aren´t bleeding money..

I don't understand what this means.

You're right that we need 40% equity to call on the flop. But you're slightly underestimating the number of flops where 32o have this equity against a random hand. The exact number is 6,513 out of 19,600, or 33.22%. Our average equity on these flops is 57.75%. So (ignoring split pots) 0.3322 * 0.5775 = 19.18% of the time we win the all-in and our stack when the hand is over will be 400 chips. 0.3322 * (1 - 0.5775) = 14.04% of the time we lose the all-in and end up with 0 chips. And (1 - 0.3322) = 66.78% of the time we fold on the flop and end up with 160 chips. Add this up and we get 183.59 chips on average. If we fold preflop we lose our big blind and end up with 180 chips. We lose chips by calling but lose even more if we fold.

Edit: I wrote this before reading yaqhs post above.

If you read the thread you'll see that a lot of the gutshots also have enough equity to call. It's still -EV to call preflop (with stacks as per the original problem), but only by $1.068.

In the 72o example it is a bit easier since I don't need to go through different board textures. It is a clear case of continuing on pairs or better (~32%) and flush draws (~2%) and folding everything else. In this spot you're folding 34% of the time and your equity when continuing is about 63% (quite a bit more for the pair of 7s without over cards but less because the flush draw is still bad equity). Here you only win the hand about 21.5% of the time when you still needed 25% from preflop.

Hrmmmm yeah interesting. I guess I've just got it so ingrained in my head about "early street mistakes" and that being the general way to think about them... when playing deep stack poker that is the assumption I am working off of. I see how it isn't true here (or basically during such shallow stack poker).

Looked at it again, and you get 7:3 post, which is 30% ?, so oesd is good and +ev, gutters only have 27% though, so those are folds ?
Which gutter do you think have more equity than that?

Most of the calls are on 55A and 44A flops; 32o has between 32.66 and 35.18% equity on these. Also some AA5 flops, e.g. 2s3h on Ah5hAd (30.55%). And a few with AK5, AQ5 and AJ5. On the other hand, the very worst gutshot only has 17.57% (2s3h on 4d6d7d).

I have now been able to run this calculation with my solver and I get almost the same solution. It's not 100% exact but I ran it for 10 billion iterations with my most detailed flop abstraction so it should be very close.

SB will open-fold: J4o-, T5o-, 92s, 95o-, 83s-, 85o-, 73s-, 75o-, 63s-, 62o+, 52s, 52o+, 42s+, 42o+, 32s, 32o (29.6% of hands)

BB will fold when SB raises: 82o, 72o, 62o, 52o, 42o, 32o (5.4% of hands)

EV to BB: 0.0056 BB/hand.