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The Upper Hand


In the upper hand tool today, I had a scenario that doesn't make sense to me. I understand it's all based on very specific math, but I'm confused by this one completely.

This one has no board, it's just hand against hand. My hole cards are Qc10h.

The opposing hands are 4s4c and 3c3h. The 4s are ahead with 51% and the 3s are behind <50. I have the logic that since the 3s have flush blockers with both cards, they would be in the same winning range-ish as the 4s. The pairs themselves are basically the same considering they don't have any straight blockers for my hole cards.

I realize the % difference is minuscule, but do any of you have any insight?


  • 1warlock
    edited May 2018

    Qc10h vs 3c3h: 49.86% to 49.13% with a 1.02% chance of a tie

    Qc10h vs 4s4c = 48.93% to 50.28% with a 0.79% chance of a tie

    I am going to venture out and say the differences are all due to the 44 hand having a flush possibility (with the 4s) while the 33 hand doesn't. In the 33 hand, board diamond and spade flushes chop the pot. Both club and heart flushes are won by the Q10 hand. In the 44 hand, only the diamond flush chops. If the board has 4 spades, the 4s would make the flush to win. If the board has 5 spades, in cases where the 2s or 3s are present, the 4s would still play to win the hand. All other cases of 5 spades would chop.

  • eselspiele

    Also 3's can be counterfeited slightly more often than 4's.

  • LoosieDoosieL

    Thanks guys. I did it with the odds tool with the 3's being the d and s and the 3s were 50.52%. You are completely correct and I was thinking of it backwards.

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