Case 3: Tournament Play (Solutions)

Massachusetts Institute of Technology 15.S50 – Poker Theory and Analytics IAP 2015 Case 3 Issued: Friday, January 23, 2015 Due: Friday, January 30, 2015 Notes: This case contains twelve (12) questions and are labeled as (1.1) through (2.5). Please answer all questions concisely and show all work. State any assumptions you are making. This case is graded pass/fail where a passing grade is 7/12 points. Partial credit will be awarded for incorrect answers with appropriate work shown. Using approximations is acceptable. These questions rely on PokerTracker’s ICM Calculator, or an equivalent ICM calculator. Scenario: It is Thursday, July 3, 2014 and you are playing in a $550 Mega Satellite to the WSOP Event #68: $10,000 NLHE Main Event. The structure of this tournament is that 1 in 20 players wins a $10,000 ticket to the main tournament. There were 140 entries and the top 7 players will win tickets. There are 60 players remaining in the tournament. The table is 9-handed as follows. Blinds are 1000/2000 with 300 ante. Seat 1 2 3 4 5 6 7 8 9 Name Hero UTG UTG+1 MP1 MP2 LP CO BTN SB Chip Count 40,000 160,000 140,000 114,000 154,000 76,000 168,000 182,000 160,000 1 Question 1: Prior to this hand, you have developed an image of being very tight, and as a result you are facing a raise every time you are in the BB. As a short stack, losing this BB every round is painful are you are looking to defend your blind. Assume each steal attempt is a raise of 3BB and the Villains are stealing with any two cards. What is your M? (1.1) 40,000 / (1,000 + 2,000 + 300*9) = 7.1 If you decide to re-raise to 6BB, what odds does the Villain have to call if he is the BTN? (1.2) Villain is facing a call of 6,000 (3BB) into a pot of (1,000 + 2,000 + 300*9 + 6,000*3 – 2,000) = 21,700. So he would need his equity to be 6,000/27,700 ≈ 22% to call. Given that he has a range of ATC, what would your range have to be to make this a bad call for him? (1.3) Exact: Threshold at top 2% (QQ+, AKs+) vs ATC is 80%/20% Model: Threshold at 22% = 50% + 0.085*ln(C%) – 0.085*ln(1) at C% ≈ 3.7% If the Villain re-raises all-in, what odds would you have to call? (1.4) Effective stacks are 40,000. After this raise, stack would be 40,000 – 12,300 = 27,700. The pot would be 15,700 + 12,000 = 27,700 before the raise. So you would be facing a bet of 27,700 to win a pot of 3*27,700 for 33% equity If you raise the maximum instead of 3BB, what odds does the Villain have to call? (1.5) Effective stack is 40,000 – 6,300 = 33,700. We would raise this amount into a pot of 21,700, giving the Villain 33,700 / (21,700 + 33,700*2) ≈ 38% to call 2 If you have QTo and re-raise all-in, do you prefer a call or a fold? Assume Villain will call with any two cards. (1.6) QTo is 57% vs ATC. If the Villain folds, our EV is 100% * 15,700 = 15,700. If the Villain calls, our EV is 57% * (15,700 + 33,700) - 43% * 33,700 = 13,667, so we prefer a fold Question 2: You reached the final table of the satellite and there are 8 players remaining to win seven $10,000 tickets. Everyone values the tickets at $10,000 (they are indifferent to playing the Main Event if they win the satellite). You view yourself as an approximately average player compared to the remainder of the table. The chip stacks are as follows: Blinds are 8000/16000 with 2000 ante. Seat 1 2 3 4 5 6 7 8 Name Hero UTG UTG+1 MP1 MP2 LP BTN SB Chip Count 66,000 13,000 80,000 30,000 31,000 73,000 49,000 78,000 Per PokerTracker, what is our $EV in this tournament? If a chop (prize split) is offered and each player will get $9,000, should you take it? (2.1) Our ICM equity is $9,668. We shouldn’t take a deal for $9,000 unless we are very risk averse You have A♥ A♣ and SB open pushes all-in with ATC. What is your chip EV from calling? (2.2) 3 AA vs ATC is 85%. So our cEV is (48,000+8,000*2+16,000+2,000*8 )* .85 – 48,000 * .15 = 74,400 What is your $EV from calling? Should you call? (2.3) If we call and lose, we have 0 $EV. If we call and win, then the stacks are as follows Seat 1 2 3 4 5 6 7 8 Name Hero UTG UTG+1 MP1 MP2 LP BTN SB Chip Count 144,000 11,000 78,000 28,000 29,000 71,000 47,000 12,000 giving us a $EV of $9990. Our $EV from the call is then .85 * $9990 + .15* 0 = $8492. If we fold, our stack is 48,000, giving us a $EV of $9445, which is higher than $8,492. So fold. What is the $EV loss from doing the wrong action? (2.4) Difference between calling $EV and folding $EV is $9445 - $8,492 = $953 loss The following hand, it is folded to you in the SB and the BB (seat 2) is forced allin. What range should you call? Assume you folded the previous hand. (2.5) BB’s range is ATC. If we fold, we have 38,000 chips, giving us a $EV of $8,452. If we call and lose, our stack is 37,000, giving us a $EV of $8,384. If we call and win our $EV is $10,000. So we can profitably call if our chance to win is x, where x solves $10,000*x + $8,384*(1-x) > $8,452, or x > 4%. So call with ATC. What is the $EV of calling optimally? (2.5) We should call any time our equity is more than 4% (i.e. always). This gives us an equity of 50% vs ATC, meaning our $EV from calling is 50% * $10,000 + 50% * $8,384 = $9,192 4