Overpair vs Possible Set Game Theory Question

[ZeeJustin]

Situation 1:
$5/$10 NL

Player in EP limps. EP has a pair other than aces. Each pair is equally likely. It folds to MP who makes it $44 with AA (face up). Only EP calls.

Flop: Q72 rainbow - $100 in pot ($3 rake was taken out)

EP checks. MP bets $100.

Action is on EP. EP has 2 options, all-in or fold (both players started hand w/ $1,000 stacks). After that, MP obviously has 2 options, call or fold.

Observations:
EP must bluff here for optimal strategy. The question is how often?
To make the math easier let's assume when EP has a set, he's a 10-1 favorite. When he misses, he's a 10-1 dog.

Questions:
1) What % of the time should EP move all-in to give MP a break even strategy? I.e call and fold have equal equity.
2) is this optimal strategy for EP? If not, what is, and then what is MP's optimal strategy?

Situation 2:
Same situation as before, but now EP has 2 different options. He can either fold, or raise to $300. After that, MP has 2 options, fold or all-in. And finally, EP can call or fold.

What would be the optimal strategy for each player in situation 2?

[ZeeJustin]

Wow, does no one find this question interesting?!

[1800GAMBLER]

Question 1 is just math, MP will be getting 1200:900 or 4:3 so he needs to win, in this case catch a bluff 3/7 to break even. EP needs to bluff 3/7. 9 combos of sets for legit, 6.75 combos of bluffs.

Question 2.

EPs best strategy is to bluff if he will think MP will fold, or bet legit if he think he will call, and not use correct bluffing frequnecy. ... unless he thought he was the dumber player.

MPs strategy is to fold if he thinks EP thinks he will call; and call if he thinks EP thinks he will fold.

And so on, for each level of psychology.

Situation two is the same with new math.

Playing paper scissors stone on your 20th birthday maybe you think of this post eh?

[anduril]

[ QUOTE ]
Same situation as before, but now EP has 2 different options. He can either fold, or raise to $300

[/ QUOTE ]

I don't like this situation because I wouldn't do either.

[dfan]

How is EP getting 1200/900? There is now 200 in the pot, EP has 956 left after his 44 call, and MP has 856 left after his 44+100 bets. If EP pushes, he is putting in his remaining 956 to win the pot + opp remaining stack = 200 + 856 = 1056. So 956 to win 1056, or 1.10 to 1.

Or am I missing something here?

[1800GAMBLER]

[ QUOTE ]
How is EP getting 1200/900? There is now 200 in the pot, EP has 956 left after his 44 call, and MP has 856 left after his 44+100 bets. If EP pushes, he is putting in his remaining 956 to win the pot + opp remaining stack = 200 + 856 = 1056. So 956 to win 1056, or 1.10 to 1.

Or am I missing something here?

[/ QUOTE ]

My math was rough, yours is correct.