Re: odds questions
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what are the odds of the board pairing with 2 cards to come? and with 1 card to come?
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Bill - The odds in an Omaha-8 game (or any poker game) depend on your vantage point. They’re different for somebody standing on the rail who can’t see anyone’s hand than they are for the players in the game.
And the odds are different for different players in the same game who are looking at different hands.
For example, if you hold 2345 and the board is 6789, then from your point of view, there are 12 cards (out of 44 missing cards) that could pair the board. In that case, the odds against the board pairing are 32 to 12.
But from another player’s viewpoint who holds 2399 with the same board (6789), then there are only 10 missing cards that could pair the board and the odds against the board pairing are 34 to 10.
For someone who can’t see anybody’s individual cards, the odds are against the 6789 board pairing are 36 to 12, And finally, for someone who can see both player’s cards, the odds against the board pairing are 30 to 10.
So the odds against the board pairing depend on your perspective, and when you are playing in the game and thus can see your own hand, the odds against the board pairing depend on the board cards and also on the particular cards you hold yourself. If you don’t have any cards the same rank as any of the cards on the board, the odds of the board pairing, from your perspective, are greater than if you do.
It gets more complicated if you try to put your opponent on cards and figure the odds from there. (But let's not go into that at this time).
You asked about after the flop. When you hold 2399 and the flop is 789, the odds against of the board pairing are 643 to 347, or about 1.9 to 1. The odds against of the board pairing on or beneath your set are not quite that good: 673 to 317, or about 2.1 to 1.
When you flop bottom set, and it’s a high bottom set, for example when your hand is A2JJ and the flop is KQJ, an opponent in a full nine player game will have been dealt a pair of queens or kings about three times out of ten - and a loose player in a loose game who has seen the flop will thus have flopped a higher set than you about three times out of ten. In this circumstance, you’re screwed whether the board pairs or not (unless you make quads). An additional problem is that an opponent may have flopped two pairs. Someone probably has flopped a straight and so you want the board to pair, but it’s probably worse for you if you the board does pair. (But you didn’t ask about that).
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say you have A23Q and the board comes K59 what are the odds against you making a low?
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About 3.1 to 1 against.
You need one of the following two-card combinations:
A4, A6, A7, A8, 24, 26, 27, 28, 34, 36, 37, 38, 46, 47, 48, 67, 68, 78.
There are a total of 240/990 ways for the turn/river to be one of these combinations. Therefore the odds are 750 to 240 against you making low, or about 3.1 to 1 against. Note that an opponent might make low on an A2, A3, or 23 two-card combo on the turn/river (a total of nine more two-card combos that don’t help you for low).
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say the turn is a 4 what are the odds then?
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Almost even. (23 to 21 against).
(Any low card other than a four or a five makes you the nut low. You’re looking at 3 low cards (that aren’t fours or fives) and 3 high cards. There must be 21 unseen low cards that could make low for you, 17 unseen high cards that don’t and also 6 unseen fours and fives that don’t. Does that all add up to 44? If so it checks. The odds are thus 23 to 21 against low.)
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say you have A2KK and the board is QQ3, what are the odds of making a low?
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Odds against you making low are about 5.3 to 1 (against).
10*16 = 160 ways to make low out of 990 possible turn/river combos.
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say the turn is an 8 what are the odds now?
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About 7 to 4 against.
The river has to be a 4, 5, 6, or 7. That’s any one of 16 out of 44 possible cards. The odds are thus 28 to 16 against it, or about 7 to 4 against.
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thanks so much for the help hope this wasn’t too confusing!
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You’re welcome. Your post wasn’t confusing. Your questions were very straightforward. They’re questions I had at one time myself.
Sometimes the way you phrase an odds question has to focus on the particular viewpoint from which it should be answered. Otherwise you don’t necessarily get the answer you’re seeking.
Just my opinion.
Buzz
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