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We magically knows that he has a busted draw: This makes the question a bad idea to consider. Let's say he's playing 66 and hits his set on the river and wants to get paid - it's as consistent with his line as a busted draw if not more so. If for whatever reason we assume that a busted draw is the whole of his range we're making a critical mistake. I know it's the very basis for this thought experiment, but entertaining that type of thought experiments teaches us to ask questions in situations where the questions themselves are flawed. Getting in the habit of asking and answering questions with this kind of perspective or bias makes it more likely that we'll just assume an opponent is on a busted draw without considering that he could actually be holding a nut hand and make costly mistakes as a result. Learning is not just about learning lessons well, it's also about learning the right lessons.
Better to put him on a realistic range with nut and air hands both and try to calculate based on that whether we're good to call. Mathematically we need to be good about 30% of the time for calling to be correct.
If we go with the exercise that I disagree with what is a 'busted draw'? It's not specified any further, and since the villain is unknown we don't know if he'd be playing Tc2h etc or whether you count 7h6h as a 'busted draw' since the draw didn't complete, but the hand still improved to beat us. It could be perceived as a busted draw and the opponent might think that he's bluffing with a busted draw even though he just made the best hand. The question as posed is really really vague and not really conducive to analysis or math imo. What draws are being played here? Flush draws? 8-out straight draws? 4-out straight draws? Unpaired high cards (like KJo could be considered a drawing hand hoping to hit a pair on the flop or a pair/straight on the turn). Is he the most unlikely of villains who thinks top pair is weak and who is playing Ahxh hoping to hit his flush and betting the river in frustration as a 'bluff'?
Let's examine the busted draw concept most closely - we'll define it as hands that were draws and which did not in any way improve to beat anything - hands for which the turn and river were both blanks.
32: Flopped straight - not qualifying
Qx: Turned pair - not qualifying
6x: Rivered pair - not qualifying
Pairs: Not draws - not qualifying (not even 22/33 which are technically also gutshots)
87, 73: Rivered straight - not qualifying
Hearts: Qualifies
The only straight draws that qualify as busted on the river are the gutshot kind - the 2x and 3x hands. No higher gutshot works because it will either contain a 6 and make a pair or hit the straight with the 6. As I'll do with the suited discussion I'll basically rule out all 3x and 2x hands as having not reached the flop.
This leaves us with hearts. Ace of hearts is out because it gives a pair - same is the queen, 4 and 5 of hearts are out because they're on the board. 6 of hearts is out because it hits a pair on the river. This leaves the hearts with which he could have had a draw that by the river is busted at these: Kh, Jh, Th, 9h, 8h, 7h, 3h, 2h
Total combinations of these:
KhJh, KhTh, Kh9h, Kh8h, Kh7h, Kh3h, Kh2h
JhTh, Jh9h, Jh8h, Jh7h, Jh3h, Jh2h
Th9h, Th8h, Th7h, Th3h, Th2h
9h8h, 9h7h, 9h3h, 9h2h
8h3h, 8h2h
7h2h
I don't think it's realistic that all these hands have seen the flop, so we should rule out the more unlikely ones such as 7h2h, 8h3h, 8h2h, 9h3h, 9h2h, Th7h, Th3h, Th2h, Jh7h, Jh3h, Jh2h, Kh3h, Kh2h.
This leaves us behind:
KhJh, KhTh, Kh9h, Kh8h, Kh7h
Splitting with:
JhTh
Ahead of:
Jh9h, Jh8h
Th9h, Th8h
9h8h, 9h7h
So by calling against that range we're winning about 54% of the money and since we need to win 30% of the money for calling to be breakeven then yes.. given these ranges it is correct to call.
But honestly it is NEVER realistic to put an opponent on 'busted draw' as narrowly as I have defined it in this post. It's just bad thinking. Any reasonably wide interpretation of 'busted draw' will contain enough 22/33/6x hands that still beat us that we're -EV to call.
Edit note: Not to mention that it never said that our opponent had a draw on the flop. Any KJ, KT, JT hand is also a busted draw as it's a gutshot on the turn and KJ and KT are 12 hand combinations each.
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