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What’s wrong with this picture?

This may have been covered numerous times in various places already – it’s about 4 years old now – but I only just got round to starting to watch the World Poker Tour box set, so – as usual – I’m just a little bit behind the times.¬† In any case, it’s still just wrong.

When I was watching this with Claire, we diligently paused the DVD to work it out ūüôā¬† I said at first that you’d be about 70% favourite, whilst she said about 75% and I said, well actually yes that’s probably more like it.¬† You’re clearly a favourite as over half the deck improves you hand and there are two cards to come.

So, according to WPT you have any heart (9), 7 (3 non-hearts), 9 (3), J (3) or Q (3 non-heart) to win.¬† But you can also win with¬†the other 3 10s, and somehow they’ve missed this!¬† As if 21 outs wasn’t enough, you actually have 24.¬†

There’s so many outs here that the rule of four isn’t close to accurate, and the full house redraw¬†to lose or running pair to win¬†makes it pretty tricky to work our from first principles, even if you can divide numbers into 45 and 44 in your head!¬† The rule of four would make you a 96% favourite on the hand, and with that logic the universe starts to falls apart.¬†

However I couldn’t believe that you’re only 2-1 here so I had to plug it into a calculator to find out if they got that wrong too…¬† but alas no, the answer was just over 69% –¬†a bit better than 2-1 but not as far ahead as I thought.

What use this is I don’t really know, although it’s made me – somewhat compulsively – check out how the open-ended straight flush draw looks against various other hands.¬† You’re in pretty bad shape against an opponent holding 88 or 99, of course.¬† But you’re also behind to any overpair, the worst situation being QQ with the Q of hearts where you’re actually worse than 40% to win, and even ace-rag of hearts is just¬†beating you.

Here’s what I didn’t consider and have subsequently learned, thanks to the WPT’s mistake!¬† The pair on board with two cards to come gives an opponent with any pocket pair a 17% chance to make a full house.¬† So even if you do improve to a straight or flush, you’ll still lose this hand one time in six.¬† If the board is not paired, you’ll only lose to a full house one time in 35.

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