The hand: https://youtu.be/xEre87X1URE

Saw this video and thought it would be interesting to generate some discussion on whether or not Sammartino should have called Phil's 2x river overbet shove with the nut straight. Here's my take on it. Obviously I've made a lot of assumptions and I don't play MTT's or high stakes at all so please correct me if my ranges/assumptions/math is off.

Phil shoves 135k into a pot of 70.3k (roughly 2x the pot) so this means he's allowed to have 66% value hands and 34% bluffs (135/205.3). Therefore Sammartino must defend with 34% of his range else he be exploited.

Sammartino's line:
Pre-flop: call
Flop: check/raise
Turn: bet
River: check

Sammartino's range:
Pre-flop is too wide to really go into detail but the main point is I think TT always 3-bets and 88 3-bets often (50%). Also T8 may not call the raise unless suited. Combination wise this gives: 33(6), 88(3), T8s(3) = 12 combos of full houses by the river.

By the river, he probably never checks with a full house since he loses too much EV when Phil checks back with a flush. Therefore his river checking range barely (if ever) includes a full house.

He doesn't have many strong flushes either. Hands like AKhh, AQhh, AJhh, KQhh, QJhh would all re-raise pre-flop since Phil is stealing from the button. This leaves only a few flush combos in his range: A2, A4, A5, A6, A7, A9, Q9, Q7, Q6, Q5, J9, J7, 96, 76, 65 = 15 combos (assuming he plays somewhat reasonable hands).

So if Sammartino needs to defend 34% of his range after he's checked, in order to not be exploited, he must expand his calling range into non-full house territory.

He has a few hands in his flop check-raising range that can reasonably give up on the river: any Ace or King of hearts hand with or without a pair: Ah3x-Ah9x, Kh3x-Kh9x = 38 combos. But let's say he wants to bluff with some portion of these to balance the times he bets with a full house. Since he has 12 full houses, at a 2:1 value:bluff ratio, this means he bluffs with 6 combos leaviing 32 combos of Ah/Kh hands to check fold with.

Other strong hands in his checking range are: 96 suited w/o hearts bottom straight (3 combos), and trip 7's that bluffed flop with a heart and now backed into showdown value (let's say 20 combos of Qh7x/Jh7x/97/76). He can check these hands and win vs. Phil's overpairs.

.: total combos that check on the river = 67
34% of 67 = 23 combos. Recall we only actually have 15 combos of flushes. So this proves we need to extend our calling range into non-flush hands.

As for which hands are best to call with, we want to use hands that don't block Phil's bluffing range. If we can expect Phil's most likely bluff by the river to be a busted flush draw, then we don't want any hearts in our hand to maximize the times he's bluffing. So J9ss seems to be a really good bluff catcher in that sense.