Game Theory Quiz

[Lmn55d]

doesn't he have to bet with either the trey or the ace? There's a 50% he was dealt either. Theres no poit in checking the ace because hero will know he is ahead and will bet either the deuce or trey. Theres no point in checking the trey either because hero will never bet the deuce after it is checked to him because only a trey will call.

[Jazza]

just making sure before i take a stab at it, the deck has only 3 cards in it so both the players cannot have the same card, yes?

[jason1990]

[ QUOTE ]
just making sure before i take a stab at it, the deck has only 3 cards in it so both the players cannot have the same card, yes?

[/ QUOTE ]
correct

[jason1990]

[ QUOTE ]
doesn't he have to bet with either the trey or the ace? There's a 50% he was dealt either. Theres no poit in checking the ace because hero will know he is ahead and will bet either the deuce or trey.

[/ QUOTE ]
When the opener has the ace, he can either check-fold or bluff. Do you think he ought to always bluff and never check-fold?

[ QUOTE ]
Theres no point in checking the trey either because hero will never bet the deuce after it is checked to him because only a trey will call.

[/ QUOTE ]
Maybe, maybe not. As the opener, if I have the trey, I may want to sometimes check in order to induce a bluff from my opponent when he has the ace. If he has the ace, he will certainly fold if I bet, so I gain nothing by betting.

Edit: I agree the dealer will never bet the deuce after it is checked to him. But when the opener has the trey, there is a chance the dealer has the ace, in which case the opener may wish to check. So I do not agree that it is obvious that "Theres no point in checking the trey." It may or may not be true (I won't say yet), but it's not obvious.

[Jazza]

okay, here's my guess:

1) 1/3
2) 1/3
3) 1/3
4) 1/3
5) whatever the hell you want it to be, as long as it's the same probability you bluff with an ace and 3 times the probability you bet with a trey

edit: not sure about 2), lemme check...

edit: yeah 2) looks good

3-edit: now i'm not sure about 2) again

capped-edit: okay i think 2) is right

[Slade]

1)(p=1/3) You would need to call 2/3's of the time to make it so a bluff is not profitable. Given that you will be dealt a three half the time when the opponent has an ace, then you need to call 1/3 of the time when you hold a 2.

2)(p=1/3)If you always bet or always check then you hold no advantage over if your opponnent knew what you hold (assuming they know your strategy). If you bet with p=1/3 then you will make 1/3 of a bet on average (over checking) any time you are dealt an ace or three.

3)(p=1/3)If your opponent is calling one 1/3 of the time with a two and always with a three then you will be break even bluffing 1/3 over checking with an ace. However this makes sure the opponent keeps loose calling standards with his deuces so that you gain value when he you have a three and he is dealt a deuce. Either way an opponent tries to adjust from this is -EV.

4)(p=1/3) If you bet 1/3 if the opponent always or never bets a 3, then it wont matter if you dont know if he has one.

5)If you are betting all threes then you should call with 2/3's of deuces. If you are betting none then you should call with 1/3 of deuces. You want to make the amount of deuces you call with an amount so that you call a total of two thirds of the time, so it depends on your betting strategy.

Overall I think the second player should make 1/18 bets per hand.

[kevin4011]

1) p = 1
2) p = 1/3
3) p = 0
4) p = 1/3
5) ran out of time

[Paul2432]

1) 1/3
2) 5/9
3) 1/3

Still thinking about last 2.

Paul

[alThor]

[ QUOTE ]
1)(p=1/3) You would need to call 2/3's of the time to make it so a bluff is not profitable. Given that you will be dealt a three half the time when the opponent has an ace, then you need to call 1/3 of the time when you hold a 2.

2)(p=1/3)If you always bet or always check then you hold no advantage over if your opponnent knew what you hold (assuming they know your strategy). If you bet with p=1/3 then you will make 1/3 of a bet on average (over checking) any time you are dealt an ace or three.

3)(p=1/3)If your opponent is calling one 1/3 of the time with a two and always with a three then you will be break even bluffing 1/3 over checking with an ace. However this makes sure the opponent keeps loose calling standards with his deuces so that you gain value when he you have a three and he is dealt a deuce. Either way an opponent tries to adjust from this is -EV.

4)(p=1/3) If you bet 1/3 if the opponent always or never bets a 3, then it wont matter if you dont know if he has one.

5)If you are betting all threes then you should call with 2/3's of deuces. If you are betting none then you should call with 1/3 of deuces. You want to make the amount of deuces you call with an amount so that you call a total of two thirds of the time, so it depends on your betting strategy.

Overall I think the second player should make 1/18 bets per hand.

[/ QUOTE ]

[schafdawg]

1. 1/2
2. 1/2
3. 1/4
4. Not sure yet- something between 1/4 and 1/2 (would be 1/4 if you knew he checked the three, like #3, and would be 1/2 if you knew he bet the three, like #1).
5. 1/2