Another Game Theory Quiz

[Jazza]

Inspired by jasson1990's quiz i have made one of my own

The game is pot limit 1-card, the deck consists of 5 cards, the A,2,3,4 and 5.

The ace is low, so the 5 is the nuts.

You each ante $100. There are two betting rounds. It is pot limit, so to start off you can be anywhere from $1 to $200 since you both have $100 each in the pot to start.

Now suppose you are playing some one heads up, you are last to act in both betting rounds, and before the first round your opponent decides to have a little fun and flip his card face up, it's the 4.

What's your strategy, and what minimum EV does your strategy guarantee?

[jogsxyz]

Much too complex a problem. Simplify. Solve this one.
Three card deck. The cards are high, middle and low.
Only a half a round of betting. Dealer vs. opp. Opp may bet or check. If opp checks, it's a showdown. If opp bets, dealer may call or fold.

1. Who does this game favor? Or is it a zero sum game?
2. What's the expected value for each player?

Hint: What is the betting maxtix?
2nd hint: What does opp do with the middle card?

You must first walk before you can run.

[Jazza]

dude, no offense but what's with the hijack?

your question does seem simpler than mine, but i don't think it's extremely helpfull

i've solved my question, and i'm not the smartest person here, so i reckon people can go straight into the 'running'

[eurythmech]

Why are there two betting rounds dude?
You freak me out.

[jogsxyz]

You couldn't answer Jason's simple question correctly. You have no chance of getting your complex question right. Too many variables. Two rounds of betting. Spread limit bet size. Do you even know maxtrix algebra? Have you even heard of maxtrix algebra? Why do you think that even now the experts have no clue what's optimum strategy in no limit hold'em. If it were that easy, computers would have solved this game years ago.

[Jazza]

[ QUOTE ]
You couldn't answer Jason's simple question correctly. You have no chance of getting your complex question right. Too many variables. Two rounds of betting. Spread limit bet size. Do you even know maxtrix algebra? Have you even heard of maxtrix algebra? Why do you think that even now the experts have no clue what's optimum strategy in no limit hold'em. If it were that easy, computers would have solved this game years ago.

[/ QUOTE ]

gimme a break dude i got 4 out of 5, and i'm pretty sure a simple algebraic mistake caused my wrongness on 5, i didn't double check it

and as for you slandering my math skillz, well at least it's a refreshing form of flaming, i think my math skillz are ok, yes i know what matrix algrebra is

are you a betting man? if so put your money where your mouth is, i'll give you even odds that i have figured out the correct answer, and we'll have jason1990 as an arbitrater if he's willing, he's a smart dude

[Jazza]

[ QUOTE ]
Why are there two betting rounds dude?
You freak me out.

[/ QUOTE ]

there are two betting rounds because most pot limit games have multiple betting rounds

an application to pot limit holdem is that UTG has KK, and he is so predictable that CO knows he has KK by the turn, so far the board is 2378r

and UTG has narrowed CO's hand range to AA-TT

so there's two betting rounds left, and little chance that the river will improve either person's hand (although there will be a fair chance that the river is above a 9, which will make a difference, but hey, this is a first approximation)

[DarkKnight]

[ QUOTE ]
are you a betting man? if so put your money where your mouth is, i'll give you even odds that i have figured out the correct answer, and we'll have jason1990 as an arbitrater if he's willing, he's a smart dude

[/ QUOTE ]

I'll take that bet - $100 ?

[Jazza]

sure, but it's only fair that i you let you know that i've posted this in the probability forum, and some one has already got the right answer

[NLSoldier]

[ QUOTE ]
sure, but it's only fair that i you let you know that i've posted this in the probability forum, and some one has already got the right answer

[/ QUOTE ]

Haha, I think it would have been perfectly fair to take the bet without telling him that.

Also, that other guy who tried to hijack is a complete tool.

[marv]

As stated, your problem looks too large (because with an initial pot of 200 the game tree is just too big).

Let simplify:
Pot Limit
ante = 5 dollars, no blinds
max number of bets/raises = 3
chips = 10000 (i.e. enough for 3 pot limit raises)
ncards = 5
one betting round

This is solvable.
The second player has an advantage of 0.33 dollars.

Part of a game-theoretic optimal strategy for the first player is: with a 5 (the nuts), he should pot-raise 61% of the time and check 39% of the time.

Marv

[Jazza]

well, i have to admit i'm a little dissapointed, i view questions like this as solid poker theory, but didn't get any attempts at an answer

if you want the answer it's in the probability forum, i crossposted

jason1990 got lots of replies to his quiz, is this because this question is uniteresting, too hard, i'm not as respected as jason1990, or a combo of the 3?