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"third draw set"...? Is that what you kids are calling it these days. I'm so out of the loop.
On the set: I'd probably play the 3 up top, since Hero is IP and can see Villain has played a pr of 3's.
As played:
On 7th street: Looks good
On 9th street: Looks good
On 11th street: Def. play J on bottom and secure FL. Now the goal is to avoid foul.
If you play the A to the mid, you foul. That leaves A up top or T to the mid or T up top.
Whether you play the A or the T up top, it secures the top vs your opponent, and leaves 1 each of { A, 3 } as your potential foul cards. Since you discard a card on your final draw, you only foul if you draw both of them (~0.85%). Either of these plays makes you 99.15% to avoid foul.
If you play the T to the mid, that leaves 6 potential foul cards { A, K, T, T, T, 3 }. You have two open hands (top and mid) so you only foul if you draw in such a way that you are are forced to play an A, T, or 3 to the mid. (You can play AKT without foul by playing A up top, K to mid and discard the T.) You only foul if you draw exactly { ATT, AT3, TTT, TT3 }. There is no draw with the K in it that forces a foul. Your potential foul cards are really { A, T, T, T, 3 } and you only foul if you draw 3 of them (~0.34%). You are 99.66% to avoid foul.
So the best play on 11th street would be to play J on the bottom, T in the mid. However, it's a relatively moot point since once you play the J on the bottom, any choice is over 99% to avoid foul.
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