9-high is the worst doable hand that may nonetheless win, so long as you’ve got 3 or fewer opponents to beat at showdown.
All through this reply I am simply assuming that flushes are usually not thought of; it is vitally straightforward to give you a set of 9 playing cards the place you have no 5 of the identical go well with.
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Your hand: 2,6
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Opponent hand: 2,5
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Neighborhood playing cards: 3,4,7,8,9
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Your finest 5 for the showdown: 9,8,7,6,4
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Opponent’s finest 5 for the showdown: 9,8,7,5,4
You win with the 9-high, 6 kicker.
This case applies as much as there being 4 folks at showdown, since all 3 opponents might have the identical hand.
Might your hand be any worse? No.
First off, 8-high is routinely an unattainable hand to have. You’ve 7 accessible playing cards to make your hand, and should you can’t have any duplicates, then you definately’d want 7 distinct playing cards which might be 8 or decrease, and people solely exist if the playing cards are 2-8. This implies you’d even have 4,5,6,7,8 for a straight.
So to have a look at doable worse arms of 9-high:
Of the 7 playing cards accessible to you, there are solely 8 distinctive numbers from 2-9 to select. Should you depart 2 of these numbers out, then you definately solely have 6 distinctive numbers to fill 7 slots, so by the pigeonhole precept you’d have not less than a pair. Thus there’s a single quantity unnoticed. If that quantity have been 2-4, then you definately’d have a 5-9 straight. If that quantity have been 7-9, then you definately’d have a 2-5 straight. Thus the lacking quantity should be both 5 or 6. This solely leaves you with 2 doable units of seven playing cards:
- 2,3,4,6,7,8,9
- 2,3,4,5,7,8,9
When you’ve got the primary set, that’s the resolution proposed above. When you’ve got the second set, that’s what your opponent had. There isn’t a different worse hand that may be made for 9,8,7,5,4 to beat.
There are different variants the place you’ll be able to change the two with any of the neighborhood playing cards and nonetheless find yourself with the identical consequence. All that issues is that you’ve a 6 whereas your opponent has a 5, and that the opposite card you’ve got is identical as your opponent’s different card.
