So after all this discussion I finally got a chance to ICMize this hand. From the action provided by OP and the size of the pot, blinds must be 6.000/3.000 with a 600 ante. Its worth nothing, that this is a very flat payout structure, where 2/3 of the money is distributed on the bubble. Once its down to 4 players, $40 has already been allocated, and there is only $20 more left to play for. For comparison in a normal MTT, its only around 30% of the money, that is distributed on the bubble. So this is a format, where you really want to cash before playing for the win.
I turned on FGS (Future Game Simulation), which take into account future
hands, and this actually narrowed SBs jamming range a bit. FGS3 was the maximum number possible meaning next 3 hands, and when this narrow our range, we probably want to not jam the most marginal hands, since taking even more hands into account would likely decrease the EV of jamming further. I am guessing, that the main reason for this is the two short stacks, that have a decent chance of busting, when they get hit by the blinds next.
Anyways the results. At the Nash Equilibrium SB should be jamming 82% of hands (likely a bit less as discussed above), and BB should call with 22% of hands. J8s is a clear jam winning us 0,53% of the price pool. The hand perform well, because its suited and connected and very "live" against the calling range. For comparison K2o only win 0,2% of the price pool, and we need to go all the way to K9o to find a hand, that perform better than J8s winning 0,54% of the price pool.
So if BB defend correctly, it would be a massive blunder to walk him with a hand as strong as J8s. However we also want to check, if the 22% calling range is realistic, and in my opinion it is. BB is supposed to call with 55+, A5o+, KTo+, QJo, A3s+, K8s+, QTs+. If anything I would actually argue, that many players might not find all those calls.
BB is the second largest stack, but if he call and lose here, he is left with 1BB and essentially out of the tournament. So is he really finding a call here with 55, A5o or QTs? Maybe. But I would not be super worried about getting called to wide, so I would just go with the Nash range here and maybe pass on the very marginal hands like Q2o, J3o or 32s, that are only winning 0,02-0,04% of the price pool.
However if BB actually is calling to wide like 30% of hands, then jamming J8s becomes unprofitable losing us 0,26% of the price pool. But this means, he is now calling with any ace, K8o, K5s and Q8s. And I just dont see many players doing that, when they can so easily fold here and still be in a good situation to cash. But if we have a reason to think, this guy dont care about cashing and just will not fold that kind of hands, then the best play is to walk him.
I would not limp and assume, that he is unwilling to fold hands like K8o or K5s preflop but at the same time wont fight back at us, if we limp. He does have position, and he does have us covered although only by a tiny amount. So if we go postflop with him, he basically has all the cards. And a scenario like, what happened in this hand, will be very common in my opinion. Or he jam on us preflop, and then we obviously need to fold.
