Game Theory Quiz

[A_PLUS]

[ QUOTE ]
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.

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You say that the Hero will bet a 3 or 2 in the 1st sentence, and that the Hero will never bet a 2 in the 2nd.

[schafdawg]

Editing my #1 response:

You should never bet with the deuce:
-If he has the ace, he'll never call, knowing that he's lost the hand.
-If he has the three, he'll always call, knowing he's won the hand.
So it's impossible to get more money out of him and win, while it is possible to lose more money yourself.

[schafdawg]

Yeah, I'm silly- I reread the post wrong the second time and corrected myself... Thought the opener checked when I have the deuce. I think you should call everytime, p=1 (for #1)

[JoshuaMayes]

[ QUOTE ]
I think you should call everytime, p=1 (for #1)

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If hero called everytime villain bet, then villain could exploit hero's strategy by never bluffing. This would net villain 1 additional unit when he has the trey and lose him nothing when he has the Ace. Thus, villain would have an EV of +1/2 unit everytime hero was dealt a deuce.

[JoshuaMayes]

Here is my answer to question #1 and my reasoning. I will try to answer the rest later.

To figure out the neutral calling percentage, I balance Villain's EV if he bluffed everytime with his EV if he never bluffed. This should yield an unexploitable calling strategy.
If the villain never bluffs, he will win the antes 1/2 of the time (when he holds the trey) plus one bet everytime that you call (P). Thus,

Neverbluff(Villain)=1/2(2+P).

If villain bluffs every time, 1/2 of the time (when he holds a trey), he will win the antes plus one bet each time you call (P). The other half of the time (when he holds an ace), he will win the antes every time you fold (1-p) and he will lose one bet everytime that you call (p).
Thus,

Bluffeverytime(Villain)= 1/2(2+P)+1/2(2(1-p)-p).

Bluffevertime(Villain)=Neverbluff(Villain) when 1/2(2(1-p)-p)=0

solving for p,
1/2(2-2p-p)=0
1/2(2-3p)=0
1-3/2p =0
1=3/2p
2/3=p

When P=2/3:Neverbluff(Villain)= 1/2 (2.6)= 1.3
Bluffeverytime(Villain)=1.3+1/2(2*.3-.6)=1.3

I conclude that hero should call 2/3 of the time when villain bets and hero holds a deuce, if hero knows nothing of villain's tendencies.

[Slade]

[ QUOTE ]
I conclude that hero should call 2/3 of the time when villain bets and hero holds a deuce, if hero knows nothing of villain's tendencies.

[/ QUOTE ]

This would be true if the hero was dealt the deuce face up.

[JoshuaMayes]

[ QUOTE ]
[ QUOTE ]
I conclude that hero should call 2/3 of the time when villain bets and hero holds a deuce, if hero knows nothing of villain's tendencies.

[/ QUOTE ]

This would be true if the hero was dealt the deuce face up.

[/ QUOTE ]

Why is it false if the deuce is dealt face down? Please explain how villain could exploit this calling strategy.

[Slade]

[ QUOTE ]
Why is it false if the deuce is dealt face down? Please explain how villain could exploit this calling strategy.

[/ QUOTE ]

If the villain is bluffing with an ace then he doesnt know if hero has a deuce or three. Since hero will always call with a three, he only needs to call with probability 1/3 with a deuce to achieve an overall probability of calling of 2/3 that he needs to make a bluff unprofitable.

[JoshuaMayes]

Thanks for the help [img]/images/graemlins/smile.gif[/img]. I see my error.

[stonebluff]

1. 1, if he has the 3, its 50-50 he will slowplay or not, assuming u dont know how he plays. same thing for ace except substitute bluff for slowplay. therefore the probability of u winning is 1:2. Your pot odds are 1:3, so you get good pot odds whenever u call.
2. 1, he doesn't have the trey, as said, so he must have the deuce. Again, u dont know his strategy, so it's 50-50 that he will call a bet. That means when bet u have a 50-50 shot at winning when u bet. The pot odds are 1:2, so it is correct to call.
3. 0, It's a 50-50 chance he has a 3, in that case you'll lose when you bet. If he has a 2 it's a 50-50 chance he'll call. that means all in all, you have a 1 in 4 chance of winning. the pot odds are 1:2, so in any 1 given spot, it is incorrect to call
4. 0, first off, it is 50-50 he has the deuce or trey. with the deuce the prob. is 1 that he will check. If he has the trey, he will check half the time. that means his check means it is 2:1 odds he has the deuce. If u bet, and u have a 1 in 3 chance of him folding (1 in 3 chance of trey, 2 in 3 of deuce, divide chance of deuce by 2 since he will call half the time). The pot odds are 1:2 so it is incorrect to bet
5. 1, this is practically the same situation as problem 1

As an afternote, if the villain realizes your strategy and exploits it, simply quit playing, by then, you should have built up a win total.