What SHAL we talk about today?

Harrington calls it Structured Hand Analysis. I call it my maths insanity forcing its way out of my brain (MadYank was once a Nuclear Engineer you know).

Here is hand that The Irish Guy (Derek of Gutshot) posed out as a question.

Tournament Last night N/L Hold’em with lots of runners
Down to the last 10 – playing 10 at the table
Next out gets €920 – 9th gets €1250 – Winner gets €17,000
Biggest stack has 220k – smallest 12k – I have about 90k
Blinds – 3000/6000

I’m in fifth position with one caller before me.
I look down and find AcAd. I make it 20k to go.
Two callers with one of them being the big stack, (on the button) and the other had me covered, (on the BB).
Flop Ah-Jh-10h First to act, (the big Stack), checks –BB pushes all-in

OK lets ignore the position discontinuity of The Big Stack and attack the issue of ALLIN guy.

We have top set here though we could be behind. Well if he has flopped a royal flush then were the never coming back kind of behind. ANything else we got chances.


OK Lets Look at The Pot.
Preflop:
SB put in 3K and folded
BB put in 20K and saw the flop
Limper Puti in 6K and folded
Button put in 20K and saw the flop
Derek put in 20K and saw the flop
Total Pot preflop = 69K

From the action described: BB moves allin (covering you) ergo the pot is now 139K (69K + 70K) (that part of his stack that you can call) if you call the pot is now 209K.

So you are being offered 1.96 to 1 odds on the pot and possibly more if the big stack chappie decides to call.

What mix of hands does the allin bettor have to have to make folding correct here?
If he has KhQh your proper fooked and win 0% of the time but I'll discount that hand (just for now) for the simple reason that he has moved in with 2 reasonable stacks to act behind him and a "raiser friendly" flop that is likely to get at least a continuation bet out of the original raiser.

Hands that are beating you on the flop
If he has KhQx (or KxQh) hes ahead with his straight But you win 33.83% of the time.
If he has a made flush Lets say 78h(I would suppose its not the Kflush (back once again to the why allin question)) hes ahead But you win 33.48% of the time
If he has KhXh you win 33.43% of the time
If he has KxQx (both non hearts) hes ahead with a straight but you win 37.12% of the time

Ok those are the possible scenarios where you are behind on the flop.

other likely hand holdings that would move allin here.
and near nut flushdraw with gutshot straight draw
KhJd hes behind and you win 63.08% of the time
AsQh hes behind and you win 62.27% of the time

Pair of Kings with the Kh
KhKx hes behind and you win 64.04% of the time

Pair and other flush draw
As9h hes behind and you win 69.59% of the time

Other Set
JsJc hes behind and you win 92.62% of the time
10s10c hes behind and you win 92.62% of the time

Open end LOW straight draw and flush draw
9h8x hes behind and you win 58.28% of the time

Crazy Brave underpair with a flush draw
9h9c hes behind and you win 70.40% of the time

OK. Those seem to be the reasonable range of hands this player could have BOTH called the preflop raise AND pushed allin on the flop.

Now we have to assign some probability to each hand grouping.
KhQh (ok I said I dismiss it but you can't can you) I'll give it 10%
KxQx 10%
KhQx (KxQh) 25%
KhXh 10%
7h8h (other made flush) 10%
KhJd (AsQh) 10%
KhKx 10%
JJ or 1010 10%
9h8x 2.5%
9h9c 2.5%

OK quick maths
10% of 0 = 0% wins
10% of 37.12 = 3.71% wins
25% of 33.83 = 8.46% wins
10% of 33.43 = 3.34% wins
10% of 33.48 = 3.35% wins
10% of (63.08 + 62.27)/2 = 6.27% wins
10% of 64.04 = 6.40% wins
10% of 92.62 = 9.26% wins
2.5% of 58.28 = 1.46% wins
2.5% of 70.40 = 1.76% wins
summing up 0 + 3.71 + 8.46 + 3.34 + 3.35 + 6.27 + 6.40 + 9.26 + 1.46 + 1.76 = 44.01% wins

You win 44% of the time based on my assumptions which conservatively put the allin bettor ahead 65% of the time when he moved allin. Personally I would put a higher weighting on the pair and draw hands, but I wanted to heavily weight the ahead hands to demonstrate that it's still a trivialy easy call here with the top set. Even if the bettor had KhQh 20% of the time and NEVER had JJJ or 101010 then you still win 35% of the time and it is now an almost EXACT mathematically correct call.