Here are the answers to the poker situations posed here. The odds were determined using a calculator available from Cardplayer.com here.
Situation 1 Answer: d. pocket 10s
The odds of each hand winning are as follows:
pocket 10s at 87%
9h10 = 70%
Ac, Jh = 67%
3d, 4s = 42%
Theophile’s hand was set to an arbitrary hand of 2 7 off suite in order to determine the above odds.
Situation 2 Answer: d. pocket 10s
The odds of each hand winning are as follows:
pocket 10s at 2% vs. 10h,10d and 80-81% winning vs. pair 2s to pair 9s
9h10h = 16-52% win vs. pair 10s to pair 2s
Ac, Jh = 42-47% win vs. pair 10s to pair 2s
3d, 4s = 17-44% win vs. pair 10s to pair 2s
This is quite obvious to want to hold a better pocket pair.
Situation 3 Answers:
Answer 1: Theophile most likely has AK, maybe AQ. He would probably re-raise with AA or KK unless he feels like trapping you, but at this point, he most likely prefer the most money in the pot before the flop comes. There’s a slight chance he’d call with a lower pocket pair 9’s or 8’s if he put you on AK, but again- not likely.
Answer 2: This is tough mainly because the lack of chips left to play with. If you try to make a play, you are dedicated to the pot. Queens are pretty much dead after the Ace comes but the only (plausible) way to win is to take a shot hoping that Theophile had KK or the lower pocket pair and thinks you hit the Ace.
Now the question is, how much do you bet when half of your chips are in the pot and the other half are in front of you? Only an all in bet would push Theophile away (if he doesn’t have anything at all) because betting anything less is a sign of weakness and he can simply raise and win. Unless you would make a weak bet, and then call the raise, which is an even weaker play. Checking on the flop at least gives you a chance to see a free card.
Answer 3: Theophile has been showing strong hands all day long. If he has A2, you have the greatest chance of winning at 10%, AQ gives you a 4% chance of winning. Unless you’ve gone to church, or done all your mitzvahs, I don’t think there is much chance of hitting your queen or K J for the straight possibility. It is best to fold and have your money in the pot when the odds are in your favor.
HOWEVER, if the remainder of your chips would force you to go all in within at least the next 4 hands, I would call. You have an opportunity to win the entire tournament rather than being forced to wait for a solid all-in hand which most likely won’t come within 4 hands. This is truly a situation that has 100s of variables and you must go with your gut in the end.