Quiz: 989 to 1 draw
From Dave's book:
"Recently, in a local poker tournament I was eliminated when my opponent made a 989-1 draw."
1. What is an example of such a draw?
2. Can you give a complete description of such draws?
3. Besides drawing dead, is this the worst possible (i.e. biggest longshot) draw someone could have in holdem? If so, why? If not, what's an example of a worse draw?
4. Besides drawing dead, is this the worst possible draw someone could have in poker?
ScottyZ
"Recently, in a local poker tournament I was eliminated when my opponent made a 989-1 draw."
1. What is an example of such a draw?
2. Can you give a complete description of such draws?
3. Besides drawing dead, is this the worst possible (i.e. biggest longshot) draw someone could have in holdem? If so, why? If not, what's an example of a worse draw?
4. Besides drawing dead, is this the worst possible draw someone could have in poker?
ScottyZ
Comments
This is when on the flop you need two perfect cards to come on the turn and river and those two cards are all that will save you. I once calculated this to about 1000-1 so I'm assuming this is the situation
An example of this would be when you have a pocket pair and an opponent has already made trips or filled up with a higher pocket pair. Assuming no flush or straight is possible to split the pot, you will need your two remaining equally ranked cards to come runner runner to give you quads.
ie - opponent has AA
You have 44
flop comes A96 rainbow.
the only way you can win is to catch two running 4's.
Regards
Brad S
I don't actually have this book. Are the answers in it?
989-1 draws in holdem are relatively common (having them, not making them) The set vs underpair example was a good one. 2-outer followed by 1-outer... so the draw is 2/45 * 1/44 = 1 / (45*22) = 1 / 990 so the odds against it are 989-1. Another example would be a flush vs a runner-runner straight flush draw (with only 1 way to make the straight flush... eg flop AhKh vs 2h3h on a flop of 6h Jh Qh... the only way the 2h3h can win is to catch the 4 and 5 of hearts). Unless if you count a 989-1 draw to chop (eg 9h8h vs 23 and a flop of AhKhQh, or AA vs 23 on a flop of AKK), this is the worst possible draw you can have in holdem, since it calls for 2 precise cards and you have to catch both of them (anything worse is drawing dead)
As for the worst possible draw in poker... I guess that would depend on the game. In stud you can need a runner-runner-runner perfect-perfect-perfect draw, eg (AA)AA vs (KK)2h3h. The second hand needs to catch the 4h, 5h, 6h to win (note that the Ah is in the 1st players hand). Odds of that (assume playing heads up, so no other cards are in play) are 3/44 * 2/43 * 1/42 = 1/13,244 = 13,243-1 against.
You could have worse draws, depending on your definition of "poker". Consider a version of 7 card stud where all deuces, and the 3 of hearts, are wild (and 5 of a kind beats a straight flush). Now, consider this draw:
(22)22 vs (3h4)56. The 1st hand is guaranteed to make 5 of a kind. The only way that the 2nd hand can win is to make a better 5 of a kind. There are 3 ways this can happen:
1. The 2nd hand catches 444 (probability = 1/13,244) AND the 1st hand catches 333 (probability = 1/13,244). Total probability = 1/175,403,536
2. The 2nd hand catches 555 (probability = 1/13,244) AND the 1st hand catches only 3's and 4's (probability = 20/13,244) Total probability = 20/175,403,546
3. The 2nd hand catches 666 (probability = 1/13,244) AND the 1st hand catches only 3's, 4's, and 5's (probability = 84/13,244) Total probability = 84/175,403,536.
So the 2nd hand only wins 105 times out of 175,403,536. In other words the odds are about 1.67 million to 1 against. Now THAT'S a bad beat.
Include a 3rd hand in the mix and it can get worse. Give the 3rd hand (56)56 and now the 3rd hand is drawing dead, and the 2nd hand only wins about 1 time in 1 hundred million (1 time in 97,614,400 to be exact). This is almost exactly 7 times worse than your chances of winning the lotto 649 jackpot with 1 ticket. If you dealt this hand out one time a minute, 24/7, you would only expect the 2nd hand to win about once every 186 years.
Note that this is the ULTIMATE runner-runner-runner draw... you need to catch 3 exact cards (the three remaining 4s), AND have your opponent catch 3 EXACT cards (the 3 remaining 3s), in order to win.
Keith
ScottyZ
Isn't that part of the grade 3 multilplication and division tables?
There are at least 4 more cases (from holdem) I can think of other than the cases already mentioned.
So far we've got:
(a) Flopped set vs. underpair, quads draw
(b) Flopped higher flush vs. lower flush, straight flush draw
Of course, the fundamental fact that you need to go runner-runner for two exact cards put forth by AleoMagus and MiamiKeith is the correct main idea.
ScottyZ
(c) flopped quads vs higher pocket pair, quads draw
Oh. I considered the fact that you need to go runner-runner for 2 exact cards to be a complete description. But if you want them enumerated:
Similar to (a) is flopped quads vs an overpair (eg KK vs AA, flop KK2). Also similar is a flopped full house vs an underpair (eg AK vs 22, flop AKK). Similar to (b) is a flopped straight flush vs a higher straight flush draw (eg 2h3h vs 9h10h, flop 4h5h6h). There is also a straight flush draw vs flopped quads/full house (eg AK or KK vs 10h2, flop AhKhKd)
Did I miss anything?
Keith
Actually, you got one I didn't think of too: the made straight flush versus the higher straight flush draw.
ScottyZ