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#1
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If I'm dealt one ace in the hole, what is the prob I will make trip or quad aces on the flop? I calc 0.002449 by 3*2*48/(50*49*48). Is that right?
Then, if I miss on the flop, what odds by turn and river? |
#2
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[ QUOTE ]
If I'm dealt one ace in the hole, what is the prob I will make trip or quad aces on the flop? I calc 0.002449 by 3*2*48/(50*49*48). Is that right? [/ QUOTE ] No, it should be: (3*2*47*3 + 6)/(50*49*48) = 0.007245. There are 47 non-aces left, not 48. Then you need to multiply by 3 since the non-ace can occur in any of the 3 positions, and since your denominator counts all possible orders of the 3 cards. Then add 6 for the 6 ways to order 3 aces to make quads (3*2*1). I would normally do it this way with combinations: (3*47 + 1)/C(50,3) = 0.007245 where C(50,3) = 50*49*48/6 is the number of flops ignoring order. Then there are 3 pairs of aces that can combine with 47 non-aces, plus 1 flop that gives quads. [ QUOTE ] Then, if I miss on the flop, what odds by turn and river? [/ QUOTE ] It depends on whether you got an ace on the flop. If you got no aces on the flop, then it's 3/47 * 2/46 = 0.28% that you get aces on both the turn and the river. If you got 1 ace on the flop, then it is 2/47 that you hit on the turn. If you miss the turn, then it's 2/46 that you hit on the river. It is 2/47 + (45/47)*(2/46) = 0.84% that you hit on the turn OR miss on the turn and then hit on the river. |
#3
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Thanks, Bruce. Here's the specific problem I'm working on (between hands) - Pacific is offereing an $88 bonus if you win a hand with 888 and $888 with quad 8s. If I'm dealt 8-rag, when should I stay in the pot? Ideally I'm looking for a number to add to the pot and then use pot odds to decide.
I'm roughing up some calcs and will post them soon, but I thought I'd give you the whole problem in case you or anybody else wants to work it out while I'm stumbling around on it. |
#4
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Damn! Just missed. Held A8o to the turn against the normal pot odds, hit an 8 on the turn, another on the river, but then lost the hand to 4s full of 8s.
BTW, I'm playing .50/1, you'll have to know that for the calcs, so the bonuses are 88 and 888 BBs. |
#5
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[ QUOTE ]
Damn! Just missed. Held A8o to the turn against the normal pot odds, hit an 8 on the turn, another on the river, but then lost the hand to 4s full of 8s. BTW, I'm playing .50/1, you'll have to know that for the calcs, so the bonuses are 88 and 888 BBs. [/ QUOTE ] What happens if you split? |
#6
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Don't know. It says "hands won" so I'd assume the worse and say splitting isn't winning, so no bonus.
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#7
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Okay, see if I'm on the right path - I calculate I should add 3.28 BB to the pre-flop pot when betting to see the flop.
There are 3 outcomes that add value over the regular value of my hand: flop comes 888, odds 1/19600 to make $888, thus value of $0.045 flop comes 88x, odds 3*47/19600 or 0.72% to make $88 AND have 1/47+46/47*1/46 chance of another $800 if it hits quads by the river, total value $0.878 flop comes 8xx, odds 3*47*46/19600 or 33.09%, to have 8.4% chance of making trips by the river, total value $3.39 I left out as insignificant the chance of 8xx flop ending in quads, and of xxx flop ending in trips. Then I have to discount the value for 2 factors. First, my biggest number of $3.39 from flopping 8xx will sometimes be worthless because the betting will be such that I won't continue. I'll put that at 80% and thus value that piece at .8 * 3.39 or 2.71. Second, even if I hit trip 8s I could lose the hand, let's call that a 10% chance. So 2.71+0.88+0.05 = 3.64 * 90% = 3.28 add to pot. |
#8
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For the flop:
favorable combinations for trips or quads: (AAx) - C(3,2)*46=138 (AAA) - C(3,3)=1 Totally, you have 139 favorable combinations from C(50,3) = 19600 possible. So, the odds are 139/19600=0.70% If you miss the flop (no ace at all): favorable combinations for turn+river cards (this means the "or" event) to generate trips (quads not possible): (AA)- C(3,2)=3 from C(47,2)=1081 possible. This means 3/1081=0.27% odds. |
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