Quiz # 2

Quiz # 2


Here is another quiz that you can use very similar methods on, but it is slightly more in depth. Answering question #1 will help you answer question # 2 and question # 3


Assume you have As-Js, and the flop comes Qs-8h-2s. From the solutions to quiz # 1 we have determined our chance of completing the flush draw by the river was 35% or 1.86:1. However, sometimes making your flush draw will pair the board.


Question # 1: What would your chances of winning be if you were 100% certain that the player to your right (the cutoff) held the 8d and the 8c (a set)?


Question # 2: Assume there are 6 people in the pot for 1 small bet each including the SB and BB. You are the button and the cutoff has the 8d and the 8c mentioned above, and you have the As-Js with the given flop. The small blind bets out and everyone including the cutoff calls to you. What is your best course of action and why? The game has been loose on the flop, and people tend to call another bet if they have already called once.


Question # 3: Now assume that only the cutoff, you and the big blind called before the flop. The big blind checks and the cutoff bets. You look and see that the big blind is going to fold… you are 100% certain. What should you do?


If you are having some troubles post a question, and I will try and help you out. I will post my solutions later.


Derrick Ashworth

n/t

For Question #1) making it on the turn only is 8/47 = .17 or 17%. The ratio; .83/.17 = 4.9:1


Flop to River:


X-F 39/47 * 8/46 = 312/2162 = .14


F-X = .14


F-F 8/47 * 7/46 = .03


added up: .14 + .14 + .03 = .31 or 31%


Ratio .69/.31 = 2.2:1


I'll try the other two later, I need some sleep.

"Question # 2: Assume there are 6 people in the pot for 1 small bet each including the SB and BB. You are the button and the cutoff has the 8d and the 8c mentioned above, and you have the As-Js with the given flop. The small blind bets out and everyone including the cutoff calls to you. What is your best course of action and why? The game has been loose on the flop, and people tend to call another bet if they have already called once."


I guess I'd raise even if I knew he had the pocket eights since I'm getting five for every one I bet(which is better than 2.2:1).


[One thing I find confusing is this: when do I take only the odds from the flop to the turn into consideration, or just the odds from the turn to the river? Or do I always weigh the flop-to-river odds against the pot odds? For example(from your question # 2, except let's say I don't know I'm up against pocket eights): I raise the flop, everybody checks to me on the turn after a card hits that doesn't help or potentially hurt me(paired board). There are 6 big bets in the pot. The flop-to-river odds are 1.85:1, but the turn-to-river odds are something like 46/9 = 5.11:1. So do I now ignore the flop-to-river odds and take into account the turn-to-river odds when deciding whether to bet the turn when it's checked to me?(I didn't mean for this paragraph to be so long).]

Hint #1: Since you are 100% certain the cutoff has a set you actually only have 45 (not 47) unseen cards.


Hint #2: You have to calculate the odds of completing the flush with out having the board paired. Cards that give you a flush that do not pair the board are: (3s, 4s, 5s, 6s, 7s, 9s, Ts, Ks) You were definitely on the right track when you said 47/8...


<table> <tr><td>X1-F1</td></tr> <tr><td>F2-X2</td></tr> </table>


Note: X1 is any card that doesn't complete your hand AND doesn't pair the board. It is actually a little more involved than this because if you get an A or J on the turn, you still have 8 outs on the river, so F1 will change depending on how X1 is accomplished.


X2 is the probability that the board doesn't pair on the river assuming F2. X2' would be the probability that the board pairs on the river assuming F2. If you were trying to calculate X2' how many cards pair the board after F2 has been completed?


I will put up the solutions in a bit...


Derrick

First, if you have 9 outs with 46 cards remaining 46/9, this is not 5.11:1. X:Y is the ratio of the good cards to the bad cards so 9 outs with 46 cards remaining means 9 cards help and 46-9=37 don't help. Your ratio is 37:9 (divide both sides by 9) 4.11:1.


When do you consider your odds from the flop to the turn and turn to the river separately from flop to river? After the turn card comes, ALWAYS reevaluate your chances of winning. Your chance of completing the flush draw is about 1.85:1 with 2 cards to come. Once you miss your chances are about 4.11:1.


I tend to consider only my flop to turn bet odds in P/L poker because I often won't continue with a hand if I miss. This also applies to my long shot draws in limit. For instance if I am drawing to a 4 out gut shot on the flop 10.75:1 from the flop to the turn (1 card), but is ~5:1 if you consider 2 cards to come.


IE. If there are 11 SB in the pot and I take one off with a gutshot there will be 6 BB on the turn. I still need over 10:1 to complete, so I probably will not call here (barring a lot of callers). So I tend to consider my flop to turn outs separately when I probably won't continue if I miss.


Derrick

Assume you have As-Js, and the flop comes Qs-8h-2s. From the solutions to quiz # 1 we have determined our chance of completing the flush draw by the river was 35% or 1.86:1. However, sometimes making your flush draw will pair the board.


Question # 1: What would your chances of winning be if you were 100% certain that the player to your right (the cutoff) held the 8d and the 8c (a set)?


Solution # 1:


F1 - X1


X2 - F2


X3 - F3


Let F1 be the probability that you catch your flush on the turn and it doesn't pair the board


Let X1 be the probability that a card comes that does not pair the board assuming F1 has occured


Let X2 be the probability that the turn card matches one of your hole cards (A or J).


Let F2 be the probability that a flush comes that does not pair the board assuming X2 has already occured.


Let X3 be the probability that a card comes that does not pair the board, is not an A or J, and does not make a flush.


Let F3 be the probability that a flush card not pairing the board comes assuming X3 has occured.


Then the odds of winning, disregarding your remote straight possibilities would be P(total) = F1*X1 + F2*X2 + F3*X3


F1 = 8/45


X1 = 34/44


X2 = 6/45


F2 = 8/44


X3 = 24/45


F3 = 7/44


P(total = 8*34 + 6*8 + 24*7 = 488 / 1980 = 24.65% or 1492:488 = 3.06:1


Note: had you not noticed that drawing an A or J on the turn changed your answer, you would get P(total) = 482 / 1980 = 24.3% or 3.11:1 (basically the same number)

"Hint #1: Since you are 100% certain the cutoff has a set you actually only have 45 (not 47) unseen cards."


Oh, I have to omit the two eights I've seen! Duh, I've always been horrible at word math problems.

I looked to it quickly, so I could be mistaken, but have you considered the possibility that both turn and river are flushcards and dont pair the board?


Regards

I said, "Let X1 be the probability that a card comes that does not pair the board assuming F1 has occured"


If the board is a flush card on the turn that does not pair the board, I considered it in this total. As you can see X1 is 34/44 because if a flush card comes on the turn 10 cards will pair the board... 34 will not. In that 34 some cards are flush cards...


So, yes I have considered this in my calculations.


Thanks,


Derrick

nt

Was already getting late.....


Regards

Question # 2: Assume there are 6 people in the pot for 1 small bet each including the SB and BB. You are the button and the cutoff has the 8d and the 8c mentioned above, and you have the As-Js with the given flop. The small blind bets out and everyone including the cutoff calls to you. What is your best course of action and why? The game has been loose on the flop, and people tend to call another bet if they have already called once.


Solution # 2: There were 6 SB in the pot before the flop. On the flop there are 5 more SB to you bringing the total to 11 SB. You know your opponent has a set of 8's. From solution # 1 we have determined that we need just over 3:1 to call. I would mainly consider 3 things here when raising, what are the chances that I will get at least 3 callers (3:1) back to me? 2. Since I am on a draw, what are my chances of getting a free card on the turn if I miss? 3. Are there other draws that are not as good as mine that I am getting equity from?


The chance of getting 3 callers really depends on what the SB does. He lead out on the flop and everyone called, so a bet here may cause him to 3 bet immediately behind you. Even then at least 1 weak player will call, and the set of 8's isn't going anywhere. Ideally it would be great if the SB had a set of Q's, or 2 pair. This would lessen the fullhouse draws against you. The 8's will probably 3 bet anyway (they should, but IMO they should have raised right away). If I was 3 bet by the 8's I may not cap it because I don't want people to fold for small bets.


Your chances of getting a free card are relatively small, and it depends on the action your flop raise gets. If everyone just calls to you the set of 8's is either a very timid player or a very greedy player and wants to make it 2 BB on the turn. If I had waited to raise until the turn if I was the set of 8's I would have a lot of trouble not leading out on the turn for fear of missing a turn bet all together. If you are playing a cutoff who likes fancy moves he may check to you hoping to check raise.


The weak draws against you are definitely there. There is a Q-8 on the flop, so someone could be drawing to a 3 out gutshot. Remember one of their outs pairs the board. Someone may have top pair, and he is drawing almost dead to the set of 8's. Also, weaker flushes are drawing dead.


No matter what, with this weak field, you have to raise for value here.


Derrick

I received this email from someone:


Why do you have to consider turn cards that match your hole cards when you know you're up against pocket eights? What I mean is that the remaining aces and jacks don't help you (even if you hit runner runner aces), so I would assume they are the same as a card like the 4 of clubs which is neutral. [I hope that made sense]


The only reason you care if the turn is an A or J is because the number of cards that will give you a flush on the river differ. If, on the turn you get an A or J, you will have 8 flush cards to hit on the river. If on the turn you hit a blank that isn't an A or J, you will have 7 flush cards to hit on the river.


Make sense...


Regards,


Derrick

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