I've done some calculations with big draws vs set to figure out if perhaps calling on flop and hoping to hit is better than getting it in there.
In the first example
Player 1 has a 20 out wrap and Player 2 has a bare top set. The pot on flop is 10bb
After the flop, effective remaining stack is 40bb.
I analyzed 3 situations:1st situation: Players get it all in on flop
When Player 1 calls a pot bet on flop it breaks down into two more situations
I analyzed a few outcomes on turn:
-a) Board pairs up and player 1 is drawing dead therefore he folds.
-b) Turn bricks and Player 2 bets pot, both players are flipping.
-c) Player 1 hits and is the favorite to win, so he bets pot and Player 2 folds.
-d) Player 1 hits and is the favorite to win, so he bets pot and Player 2 calls.
so there's 2 more situations , 2nd situation = a+b+c and 3rd situation = a+b+d
Ofc there's more possible situations but those rely a lot on the players behavior so I just analyzed these.
Assuming both players are very straightforward no money gets in on the river since one player has 100% equity and will take down the pot.
EV -> the EV of the 1st situation.
EV1 -> the EV of the 2nd situation.
EV2 -> the EV of the 3rd situation.
The second example also includes a flush, So I added another situation if Player 2 folds only if the turn brings a flush.(EV3)
Conclusion:
In this specific example it's better to call a flop and get it in on the turn if the board doesn't pair even if your opponent folds once you finish your straight/flush. If your opponent still pays you of if you hit the turn, calling the flop becomes much more profitable. Such play is also less varianced since you don't risk your whole stack every time.
Using bigger stacks would change the results and it might be that against some opponents it would be better to get it in on the flop
(e.g. against the very aggressive ones against which you won't know what hand you're against)
