How to figure odds

[ozziepat]

Some regulars here like to chastise newbies. I suppose it gives then a sense of something or other I wouldn't like to mention. If you are in the wrong place, a nice suggestion to move to the correct forum would be helpful.

Regarding your question:

There are 45 unseen cards. 1 of them is the Kh. The odds of your opponent having being dealt that card at this point is 2/45, in the absence of any other information. However, you have additional information. He called a bet.

To simplify greatly, let's assume (gross simplifying assumption) for the sake of discussion he can see the flop as well as you can and would only call your bet with a flush of his own. Now, the odds are 2/8 *at worst* that he holds the Kh. Further, if he is a very tight sound player who probably would not be in this situation without two hearts including a top heart (K or maybe J), now the odds are 50-50 *at worst* he holds specifically the Kh and a smaller heart. See how that goes?

A bet on the flop and maybe turn also would greatly help clarify. Checking allows Kh any-other-card to beat you if another heart (or boat or worse) comes. Not good. Point is, I think, it's about much more than the "odds." Betting introduces a dynamic that affects the actions of others (and yourself). Checking doesn't positively advance the position, allow you to acquire information or gain you any $$ - some things to think about in the context of this particular situation. Your opponent, on the other hand, can trap until the River with much less risk if he holds the nut flush.

In the world of bridge, there is a principle called the Rule of Restricted Choice. Simply stated, a card played conveys information about what the player does *not* have, otherwise he might have made an alternative play. Something similar operates in poker. By his taking an action (calling in this case), an inference can be drawn that the player does not have one of the many hands that (logically) would not have called. Or, the range of hands he holds has been significantly narrowed and that narrow range is much more likely (given the action) to contain the nut flush holding than many other borderline or worse holdings. In other words, after the call it has become a much more likely holding than you might think, and certainly more likely than just any two randomly dealt cards happening to turn up KhXh.

[ozziepat]

Sorry. There was a Flop bet. Meant to say bet on Turn would clarify.

[AlaskaBob]

Thank you for the response.