Mathematical Analysis Help Needed Please

Ladies and Gents:

In my efforts to improve my stagnant ring play, I am trying to get right into the mathematics of the game. I need some help, though, to get me kickstarted.

Here are a couple of hands. Undoubtedly, you will find them grisly examples of poker, but I want to start analyzing them mathematically in terms of EV, and that's all. I've read a lot of articles and books the past few days, months and years but I just cannot start in on analyzing my own hands. I am hoping that a step by step example will help me to understand how to do it. If someone would be so gracious as to take the time to illustrate how I should do so, that is.

Hand one:

Paradise Poker No-Limit Hold'em, $0.10 BB (10 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

UTG ($31.00)
UTG+1 ($36.35)
UTG+2 ($25.00)
MP1 ($36.90)
MP2 ($10.00)
MP3 ($21.10)
Jiggus ($23.90)
Button ($19.00)
SB ($10.75)
BB ($22.45)

Preflop: Jiggus is CO with K, J. MP2 posts a blind of $0.25. SB posts a blind of $0.10.
2 folds, UTG+2 calls $0.25, 1 fold, MP2 (poster) checks, 1 fold, Jiggus raises to $1.4, 3 folds, UTG+2 calls $1.15, MP2 folds.

Flop: ($3.40) 2, 8, A (2 players)
UTG+2 checks, Jiggus checks.

Turn: ($3.40) K (2 players)
UTG+2 bets $3.8, Jiggus raises to $7.6, UTG+2 calls $3.80.

River: ($18.60) T (2 players)
UTG+2 bets $16, Jiggus folds.

Final Pot: $34.60

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My assumption at the flop is that the opponent would hold anything from AA-22, AK-A2 off, and any suited. I think that totals up to 284 hands, no?

I reckon he'll call 50% of the time. He'll fold 25% of the time and he'll raise 25% of the time. Or maybe that's not right? In fact, this clown will probably call a pot-sized raise 100% of the time. Oh dear, this is where my "analysis" starts going flat.

So, now where do I go?

A second hand, which I haven't tried to analyze at all is this:

Paradise Poker No-Limit Hold'em, $0.10 BB (7 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Button ($6.15)
SB ($15.65)
BB ($20.40)
UTG ($18.55)
MP1 ($61.07)
Jiggus ($24.40)
CO ($6.90)

Preflop: Jiggus is MP2 with T, T. SB posts a blind of $0.10.
UTG calls $0.25, 1 fold, Jiggus raises to $1.2, 2 folds, SB (poster) calls $1.10, BB calls $0.95, UTG calls $0.95.

Flop: ($4.80) 2, 4, J (4 players)
SB checks, BB checks, UTG checks, Jiggus bets $2.8, SB folds, BB calls $2.80, UTG folds.

Turn: ($10.40) 4 (2 players)
BB checks, Jiggus bets $6.5, BB calls $6.50.

River: ($23.40) J (2 players)
BB checks, Jiggus checks.

Final Pot: $23.40

Thank you.

Jigs

Originally Posted by Jiggus

I reckon he'll call 50% of the time. He'll fold 25% of the time and he'll raise 25% of the time. Or maybe that's not right? In fact, this clown will probably call a pot-sized raise 100% of the time. Oh dear, this is where my "analysis" starts going flat.

You need to make assumptions (and express them in chance percentages) about how your opponent will react, otherwise you can't really do any math.

One quick mistake I can see though is that you forget to incorporate how he hit the flop.. ie let's say 5% of his range makes TP.. then he'd do (something), 15% of his range makes a draw, then he'd do (something else) etc.

Btw, fwiw, these calculations you want to do are very complex and time consuming.. and I don't think they're all that necessary..

I think precise mathematics are largely inapplicable in a deepstacked (>/=100bb) nlhe ring game. Implied odds make most calls profitable. As far as calculating percentages of ranges, thats mostly feel based.

What the other two said:

Originally Posted by Jiggus

Turn: ($3.40) K (2 players)
UTG+2 bets $3.8, Jiggus raises to $7.6, UTG+2 calls $3.80.

Here is a simple case where the math does matter. You min-raise, now he has to call $3.80 into a ~$14 pot. He is getting ~3.5:1 odds, and A, the flush draw etc are calling this bet.

You need to make the raise to $14 minimum if you want him to consider folding a weak A or have bad odds to chase the flush.

I will confess to being both disappointed and glad. Disappointed because I wanted to see how to do the complicated calculations, but glad because you say it is largely irrelevant.

I knew it was a lot to ask, however, but was still hoping for the math whiz (or two) here to give it a go.

I understand that one needs to make assumptions -- I have read a lot on the subject -- it's just that I, for one, cannot understand how subjective assumptions will lead to anywhere near accurate mathematical analysis. Perhaps that's why it is irrelevant, and all the scholarly articles out there are just over-complicating an already complex game.

Nonetheless, thanks -- as always -- for taking the time to reply.

Jigs

Originally Posted by Jiggus

I understand that one needs to make assumptions -- I have read a lot on the subject -- it's just that I, for one, cannot understand how subjective assumptions will lead to anywhere near accurate mathematical analysis. Perhaps that's why it is irrelevant, and all the scholarly articles out there are just over-complicating an already complex game.

I think it's done mainly as an exercise to prove a point. I don't agree that the author is making the game more complicated. I think that analyzing the game at a higher complexity gives you a better understanding and actually makes the game simpler when you are playing at the table. You intuitively make more complex decisions.

I don't think the hands you picked lend themselves to analysis. So, for example; look at calling a bet vs. raising, with the nut flush draw (a classic). You have an equation that uses FE combined with the chance you make your hand. If villain is a calling station, (a read) clearly raising is a bad idea, similarly if villain is a nit, raising is a great idea (and both can be shown mathematically). If villain is a tough solid player, now the math doesn't help as much.

Not sure if this is a useful post, but it's typed so you have to read it anyway.