This is a theoretical question about poker-type games. I'm not going to specify the rules. You can consider No Limit Texas Hold'em or some simple theoretical model, where each player holds a number from the $(0,1)$ interval. We only consider playing heads-up, i.e., when two players play.

Playing against Darth Vader is quite tough because he can read your mind, and thus he knows your hand. You don't know Darth Vader's hand, but you have no hidden information.

Should you ever bet against the Dark Lord?

In games where cards are revealed at later stages, like Texas Hold'em, the answer can be yes, but even there it seems that you should bet/raise at most once after each time a new card is revealed. I'm interested in any sort of related results, which is why I haven't given precise definitions.

This is a theoretical question about poker-type games. I'm not going to specify the rules. You can consider No Limit Texas Hold'em or some simple theoretical model, where each player holds a number from the $(0,1)$ interval. We only consider playing heads-up, i.e., when two players play.

Playing against Darth Vader is quite tough because he can read your mind, and thus he knows your hand. You don't know Darth Vader's hand, but you have no hidden information.

Should you ever bet against the Dark Lord?

In games where cards are revealed at later stages, like Texas Hold'em, the answer can be yes, but even there it seems that you should bet/raise at most once after each time a new card is revealed. I'm interested in any sort of related results, which is why I haven't given precise definitions.

Update. After Douglas's examples, the following interesting question is left open.

If you bet/raise, should you always go all-in in a No Limit game?

This a a theoretical question about poker type games. I'm sure I don't have to explain the rules - you can consider No Limit Texas Hold'em or some simple theoretical model, where each player holds a number from the $(0,1)$ interval. We only consider heads-up, i.e., when two players play.

Playing against Darth Vader is quite tough, because he can read your mind, and thus he knows your hand - practically, you're playing with an open hand.

Should you ever bet against the Dark Lord?

In games where cards are revealed at later stages, like Texas Hold'em, the answer can be yes, but even there it seems that you should bet/raise at most once after each time a new card is revealed. I'm interested in any sort of related results, which is why I haven't given precise definitions.

This is a theoretical question about poker-type games. I'm not going to specify the rules. You can consider No Limit Texas Hold'em or some simple theoretical model, where each player holds a number from the $(0,1)$ interval. We only consider playing heads-up, i.e., when two players play.

Playing against Darth Vader is quite tough because he can read your mind, and thus he knows your hand. You don't know Darth Vader's hand, but you have no hidden information.

Should you ever bet against the Dark Lord?

In games where cards are revealed at later stages, like Texas Hold'em, the answer can be yes, but even there it seems that you should bet/raise at most once after each time a new card is revealed. I'm interested in any sort of related results, which is why I haven't given precise definitions.

This a a theoretical question about poker type games. I'm sure I don't have to explain the rules - you can consider No Limit Texas Hold'em or some simple theoretical model, where each player holds a number from the $(0,1)$ interval. We only consider heads-up, i.e., when two players play.

Playing against Darth Vader is quite tough, because he can read your mind, and thus he knows your hand - practically, you're playing with an open hand.

Should you ever raise against the Dark Lord?

In games where cards are revealed at later stages, like Texas Hold'em, the answer can be yes, but even there it seems that you should raise at most once after each time a new card is revealed. I'm interested in any sort of related results, which is why I haven't given precise definitions.

This a a theoretical question about poker type games. I'm sure I don't have to explain the rules - you can consider No Limit Texas Hold'em or some simple theoretical model, where each player holds a number from the $(0,1)$ interval. We only consider heads-up, i.e., when two players play.

Playing against Darth Vader is quite tough, because he can read your mind, and thus he knows your hand - practically, you're playing with an open hand.

Should you ever bet against the Dark Lord?

In games where cards are revealed at later stages, like Texas Hold'em, the answer can be yes, but even there it seems that you should bet/raise at most once after each time a new card is revealed. I'm interested in any sort of related results, which is why I haven't given precise definitions.