Game theory and raising

Lets assome you are playing in a 10 player game where each player is given a random number between 1 and 100.
The betting structure is the same as the first betting round in a poker game, where you can either fold, call or raise.
Think about what numbers you would raise or call with as your position changed around the table.
What numbers do you call a raise with?
What numbers do you reraise with?
What is the difference in your relative number value if other players have limped in, as opposed to when it is folded to you?

Now after we have considered this, how does hold em differ from this game preflop?
The most obvious difference to me is relative hand values in holdem change depending on the number of players you are up against.

Think about the hands KQs and A8o. Which is a better hand at a full table and why? How do these values change when you are heads up?
The "worst" hand in hold em most players know to tell you is 72o. But heads up if you had the choice between 72o and 23s to run hot and cold, which would you choose?

Since hand values change with the number of players, and with position, how should your raising standards change as it is folded to you based on the number of players yet to act?

without taking any psychology into consideration u aren't going to make the best decision. sure math and theory is an essential part of the game. but when u throw away or don't raise a medium/strong hand from middle position when the players behind you are obviously not interested in getting into the pot you've made a huge mistake.

Quote:

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Originally Posted by RiverGhost

without taking any psychology into consideration u aren't going to make the best decision. sure math and theory is an essential part of the game. but when u throw away or don't raise a medium/strong hand from middle position when the players behind you are obviously not interested in getting into the pot you've made a huge mistake.

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So using a branch of mathmatics that takes away an opp.'s (of which you deem of equal or greater skill) edge (or even making it impossible for them to make any move on a hand that is +EV for them, which is my favorite) isn't as important as the Psychology of poker? The Psychology of Poker applies moreso to post-flop play (in Hold'em games anyway) than to Two-Card Bingo (in which mathmatics and creating +EV situations is the best)?

I'll have to wait until later to make a better post on the subject as I understood it from TOP et al

There are no implied odds in a 1-street game, only pot odds.

Are there blinds? If there are no blinds and no rake, you should just fold everything <99.

EDIT: Actually that will not maximize your EV... I think the following will

From the last two positions, you should raise any number >50 if everyone else has folded. From 3rd position... I think you raise 100 - N-/100 where N is number of players remaining.

Assuming it's folded around to you:
[code]
N = Players Remaining. Formula = 100 - N/100
N=2 50
N=3 67
N=4 75
N=5 80
N=6 82.5
N=7 86
N=8 87.5
N=9 90

72o is much better than 32o heads up (in poker)
KQs is better than A8o vs many players... but I'm not sure where the breakeven point is.

Unless demonstrated otherwise, assume the other players know the above formula. Then, if someone else enters the pot first, you should only call/raise if your number is higher than their minimum raising standard.

I'm pretty sure you should never call... but I could be wrong.

If everyone plays by these rules, then you should never bluff. If players are tighter than this, you can bluff (by some formula exactly cancelling their excess tightness).

If there are blinds (like in HE), I think you lower all the requirements slightly to account for the dead money. (i.e., it folds to you with 5 remaining - with no blinds need an 80 or better to open - for an even money bet. You can actually open for a sligtly lower number - probably some formula you can calculate by the ratio of your bet size to blind size.

Note that this is very close to HOH1 - with some misdirection and suitedness thrown in.

If icould understand most of this math it would be fun!
But it would appear to show that you should be opening the pot for a raise or folding yes?
(we take from that the idea that pps have implied odds and are therefore slightly different)

Quote:

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Originally Posted by zenbitz

Unless demonstrated otherwise, assume the other players know the above formula. Then, if someone else enters the pot first, you should only call/raise if your number is higher than their minimum raising standard.

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This isnt quite correct. You need to bet when your number is higher than their AVERAGE raising standard and fold otherwise.
Say they will open with 100-80 and you hold 81. You should definatly fold because the only card they could have that you beat is 80 whereas 100-82 (18 cards) are ahead of you So you would need pot odds of at least 18-1 to call.
i.e. they would have to bet more than you.

If you call only with cards 91 and above there are 10 cards worse than you (80-90) and (9 cards better than you) This makes calling profitable as you are now getting 10-9 odds of winning at 1-1 pot odds.

If you assume he will call with all hands he raised with then raising is better than calling. If he will fold all but hands 80-90 then the situation changes again and you should just call since the only time your extra bet even makes a difference is when he calls/raises you and you win.
The reason calling is better than raising here is because there is no chance he can draw out on you (like the river in holdem) and because you know his exact range and betting patterns.

It only becomes profitable to raise when he will call with more hands that lose than hands that beat you.

I agree, I didn't think it through very deeply.

I guess in general, if you are getting exactly even money or are likely behind but have pot odds (say you are last with a 93, UTG open raises, everyone else calls) you should call - otherwise raise.