Heads Up Game Theory exercise

[jay_shark]

There are two players in a game . Hero posts the sb and villain posts the bb . There are only two choices for this game . You may either raise 3X the bb ,or fold .

The object of the game is to select a card from a deck with numbers 1,2,3,...100 and raise if you think your number is the highest . Your opponent can either call you or fold . Since there is only one deck , your opponent's card must be different in rank than yours .

What numbers should hero raise with ?
What numbers should your opponent call you down with ??
What is your bluffing frequency ?

[jay_shark]

Part B )

Suppose instead of raising 3X the BB , you are allowed to raise up to 10X the BB or fold .

Now answer the same questions as before .

[Nichomacheo]

This is really hard no?

[jay_shark]

Actually the first problem is very easy .

If you're familiar with SAGE then you probably know the answer to the first problem .

[omgwtfnoway]

edit: i see that the bb cannot raise, i'll be back when i've thought about it some.

[dippy111]

you are risking 3bb to win 1.5 if im not mistaken in the definition. Therefore you should raise top 1/3 of numbers = 67+. Knowing that you're raising this range, villain should call with top 1/2 of your range = 83+? Then again, that doesnt account for bluffs. Hmmm...

[Schpacko]

I guess you should raise 51 and above, or is this too easy?

So villain is getting 1:2 for a call. Has to be ahead 33%, so he should call (or raise?) with the the top 33% of the top 50% -> top 16.6%, right?

But i really suck @ things like that, this is probably abolutely ridiculous [img]/images/graemlins/smile.gif[/img]