Hi, I continue to do study 6 max Intermediate Course along with my play.
Here is my homework on the Introduction to Combinations topic.
1.Villain’s range is 66+, AJ+. How many combinations of pairs does he have? Write them out, like this: AA(number of combos), KK(number of combos),etc
AA(6), KK(6), QQ(6), JJ(6), TT(6), 99(6), 88(6), 77(6), 66 (6) The total is 54 combinations.
2.Villain’s range is any two cards ten and higher (TT+, JT+,QT+,KT+,AT+). How many combinations is that? Write them out.
Paired hands: AA (6), KK(6), QQ(6), JJ(6), TT(6) 30 combinations
Unpaired hands: AK(16), AQ(16), AJ(16), AT(16), KQ(16), KJ(16), KT(16), QJ(16), QT(16), JT(16) 160 combinations
The total is 30+160= 190.
3.How many suited Ax combinations are there? Write them out.
AKs(4), AQs(4), AJs(4), ATs(4), A9s(4), A8s(4), A7s(4), A6s(4), A5s(4), A4s(4), A3s(4), A2s(4) 48 combinations
4.The flop is AQ5. We have AK. How many combinations of sets are possible for villain (assuming he can have any hand)? Write them out.
AA(1), QQ(3), 55(3) 7 combinations
5.The flop is AsQd5h. We have 6s5s. How many combinations of AQs can villain have? Write them out.
AhQh, AcQc 2 combinations.
6.The flop is AQ7r. We have 77. How many combinations of gutshots can villain have? Write them out.
KT(16), JT(16) 32 combinations
7.The flop is AQ7r. How many TP+ combinations are there? Write them out.
TP+: AK (12), AQ(9), AJ(12), AT(12), A9(12), A8(12), A7(9), A6(12), A5(12), A4(12), A3(12), A2(12), Q7(9)
AA(3), QQ(3), 77 (3). The total is 156 combinations.
8.How many combinations from question 7 do we beat with AT? Write them out.
A9(12), A8(12), A6(12), A5(12), A4(12), A3(12), A2(12) 84 combinations we beat.
9.Villain from question 2 (TT+, JT+,QT+,KT+,AT+) goes to the flop. The flop is As8s9c. Does he have more combinations of made hands (and 1P+), or draws (any FD, OESD, GS)?
As8s9c
Made hands:
2P+:AA (3) – 3
1P+:AK (12), AQ(12), AJ(12), AT(12), KK(6), QQ(6), JJ(6), TT(6) – 72
Total – 75
Draws:
FD: AsKs (1), AsQs (1), AsJs(1), AsTs(1), KsQk(1), KsJs(1), KsTs(1), QsJs(1), QsTs(1), JsTs(1) – 10
OESD: JT(15) – 15
GS: QJ(15), QT(15) – 30
Total – 55
The answer is: Villain has more combinations of made hands.
10.Villain from question 9 goes all-in on the flop with all of his made hands and draws. The flop is $10, and he has $15. Can we profitably call him with TdTc?
According to Flopzilla the equity of this range is 67% (We excluded KQo, KJo, KTo) and the equity of a hand is 33%. We need to call 15 into 25 pot so the required equity = price of calling/(pot size + price of calling)15/25+15 *100= 15/40*100=37.5% equity we need to break even. The equity of our hand is 33%. So this call is unprofitable.