Now we're talking. A board full of weak cards is at its most dangerous when your opponent plays a wide range. There are plenty of hands he could have that just improved dramatically – fishing for two pair or sets with low cards can be viable in some games – but checking on this board strongly suggests that he has nothing.
Shiro is four to a flush with no overcards, and the purely mathematical odds of her making the hand on the turn or river are 35%. If she makes it, she has the nuts – if this guy had an ace of clubs hand, he would've continued betting on the flop – so if it goes to showdown and he has a pair or better then those are her odds of winning.
Purely Mathematical Odds of Improving After The Flop
Hand |
Improvement |
Outs |
Turn Odds |
River Odds |
Flush Draw + Outside Straight |
Flush/Straight/Pair |
21 |
72.32% |
47.73% |
Flush Draw + Outside Straight |
Flush/Straight |
15 |
54.10% |
32.60% |
Inside Straight |
Straight/Pair |
10 |
38.40% |
21.70% |
Four Flush |
Flush |
9 |
35% |
19.60% |
Outside Straight |
Straight |
8 |
31.50% |
17.40% |
Three of a Kind |
Full House |
7 |
27.80% |
15.20% |
Any Non-pair |
Pair |
6 |
24.10% |
13% |
Pair |
Two Pair/Three of a Kind |
5 |
20.40% |
10.90% |
Two Pair |
Full House |
4 |
16.50% |
8.70% |
Inside Straight |
Straight |
4 |
16.50% |
8.70% |
Pair |
Two Pair |
3 |
12.50% |
6.50% |
Pocket Pair |
Three of a Kind |
2 |
8.40% |
4.30% |
Three of a Kind |
Four of a Kind |
1 |
4.30% |
2.20% |
'Outs' are the number of unseen cards left in the deck that could improve the hand.
These odds can be combined with the odds of all opponents folding to calculate hand equity. While the odds of getting a fold have to be made with incomplete information, the odds of improving your hand can be known with certainty.
However, poker is not a game of pure mathematics. Especially not against unsophisticated players. The optimal raise for maximizing profit against a rational opponent, considering this man's range and stack-to-pot ratio, are completely irrelevant. What she wants is a bet that will combine her odds of winning with his odds of folding for something that works out to positive expected value, and right now she's worried that a sufficiently large raise will scare him off.
She thinks for a bit, then raises 150. Not a huge raise, but still over half the pot. If he wants to stay in this hand, he needs to be sweating for it.