[RayGarlington]

Here is greenage's hand along with sims and some comments. Assume you see everyone's cards as they are played, and we have the benefit of the sims listed below.

We have a 2 gap six low VS a 2 gap wheel VS a high pair (2 flush) battling for the ante's. Who should fold, when should they fold, and why?

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dead 4s tc 3d 7c

Seat 1: [5s 6c 2s Kh 7d Ad Qs] (HI: high card Ace; LO: 7,6,5,2,A)
Seat 5: [As 5d 4c Jh Js 2h 3s] (HI: a straight, Ace to Five; LO: 5,4,3,2,A)
greenage: [Qc Qd 6d Ac 2d 5h 9h] (HI: a pair of Queens)

3rd (.88 SB) +++++++++++++++++++++++
pokenum -mc 500000 -7s8 5s 6c 2s - as 5d 4c - qc qd 6d / 4s tc 3d 7c
7-card Stud Hi/Low 8-or-better: 500000 sampled outcomes
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
5s 2s 6c 60791 94624 405242 134 168156 54040 939 0.290
As 4c 5d 81992 118156 381714 130 178470 43200 896 0.335 <<< seat 5
Qc Qd 6d 82764 287076 212900 24 7378 6283 97 0.375

Seat 1
prebet equity: (.290 * .88 SB) = .255 sb
after all bet 1: (.290 * 3.88 SB) = 1.125 sb (seat 1's equity increase is .87 sb for this bet)
after all bet 2: (.290 * 6.88 SB) = 1.995 sb (seat 1's equity increase is .865 sb for this bet)

Here seat 1 (with the 2-gap six low) has the worst of it. At the start of the hand he has a .255SB equity, but with each bet he puts in, he loses ~.13SB to his opponents. Note that on his 2nd bet of the round the equity he was protecting has been lost and he is back to even.

4th (6.88 SB) ++++++++++++++++++++++++
pokenum -mc 500000 -7s8 5s 6c 2s kh - as 5d 4c jh - qc qd 6d ac / 4s tc 3d 7c
7-card Stud Hi/Low 8-or-better: 500000 sampled outcomes
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
5s 2s 6c Kh 62460 96961 403004 35 114499 28919 349 0.255
As 4c 5d Jh 62944 87027 412923 50 140830 20638 334 0.268 <<< seat 5
Ac Qc Qd 6d 147237 315959 184020 21 21620 8995 147 0.477

Seat 1
pre-bet equity: (.255 * 6.88) = 1.75
after 1 bet: (.255 * 9.88) = 2.52 (.77SB equity increment)
after 2 bets: (.255 * 12.88) = 3.28 (.76SB equity increment)

Here both low hands catch a brick, and seat one continues to have the worst of it. Now he loses .23SB with each bet. The other hands are in better shape, with the queens ahead by far.


5th (4.94BB) ++++++++++++++++++++++++++
pokenum -mc 500000 -7s8 5s 6c 2s kh 7d - as 5d 4c jh js - qc qd 6d ac 2d / 4s tc 3d 7c
7-card Stud Hi/Low 8-or-better: 500000 sampled outcomes
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
5s 2s 6c 7d Kh 46343 63736 436264 0 242792 37611 441 0.326
As Js 4c 5d Jh 57414 149505 350495 0 45334 17190 56 0.247 <<< seat 5
Ac Qc Qd 6d 2d 109086 286759 213241 0 46405 15831 449 0.426

Seat 5
pre-bet equity: (.247 * 4.94) = 1.2
after 1 bet: (.247 * 7.94) = 1.9
after 2 bets: (.247 * 10.94) = 2.7

Now seat 5 picks up a pair of jacks, but his equity drops! Each bet costs him ~ .3BB to protect his 1.2BB starting equity.


6th (7.94BB) ++++++++++++++++++++++++++++
pokenum -7s8 5s 6c 2s kh 7d ad - as 5d 4c jh js 2h - qc qd 6d ac 2d 5h / 4s tc 3d 7c
7-card Stud Hi/Low 8-or-better: 24360 enumerated outcomes
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
5s 2s 6c Ad 7d Kh 878 1653 22707 0 14990 8000 1370 0.356
As Js 4c 5d Jh 2h 2436 7224 17136 0 4644 4092 196 0.246 <<< seat 5
Ac Qc Qd 6d 2d 5h 2055 15483 8877 0 3260 4302 1370 0.399

seat 5
pre-bet equity: (.246 * 7.94) = 1.95
after 1 bet: (.246 * 10.94) = 2.69
after 2 bets: (.246 * 13.94) = 3.42

On sixth seat 5 picks up another wheel card, but his equity doesn't go up. Now each bet costs him ~ .26BB to protect his 1.95BB starting equity.