Some poker maths to think about.

Lafortezza

David Sklansky on twoplustwo.com wrote:

The situation is that there is $40 in the pot in a 10-20 game. You have 32 offsuit. The flop is JJJ. You know for sure that if you bet you will be called only by pocket pairs, fours or higher.

You then say to yourself the following. "It is correct for me to bet $10 all in, if there is a greater than 20% chance I will steal the pot and incorrect if the chances are smaller than 20%."

The above quote is wrong. The correct number is not 20%. It is a bit higher or lower. Which is it and why?

So, $40 in the pot, you have $10 left. You're first to act on the flop. If you go all-in for the $10 there's a chance you will win the pot without a caller. But if you do get called you will be up against a pocket pair 44 or better.

Tis all about the +/- EV!

There's a massive thread over on the twoplustwo forums here discussing this little problem posted by Sklansky.
Just wondering what the resident maths heads think. If you read the linked thread you'll realise that there's an awful lot of intelligent people playing poker.

Iago

my head hurts

Hectorjelly

lafortezza wrote:

Just wondering what the resident maths heads think. If you read the linked thread you'll realise that there's an awful lot of intelligent people playing poker.

You wont always lose if you get called, so the figure is lower.


I preferred this question:

http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1085751&page=16&view=collapsed&sb=5&o=14&fpart=1

Lafortezza

Hectorjelly wrote:

You wont always lose if you get called, so the figure is lower.

The figure is higher apparently. Can you see why? Think about not betting the flop.

kipple

Higher

Going all in is zero EV. There is no point betting.

Rake will make it higher, even without rake you need a bet the have +EV so the answer is higher.


T.

Correct Link is:
http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1112659

Very good, I only looked at Ed Millers responses, he is a smart guy and his book is good.

Hectorjelly

kipple wrote:

Higher

Going all in is zero EV. There is no point betting.

Rake will make it higher, even without rake you need a bet the have +EV so the answer is higher.


T.

You can assume there is no rake, and I dont see how the EV could be 0.

cajun_tiger

anyone watch last night's show on card counters?

kipple

I dont see how the EV could be 0.

You are right another J makes it a chance of a split pot.

T.

DeVore

This question makes little sense to me.
I havent read the thread but there are several things that occur to me.

1. If I get called by 44 I have a number of outs to split the pot (any running pair higher then the calling pair on turn and river ie: JJJ55), however if I get called by AA that option is not available to me, therefore the odds of splitting the pot (and thus taking SOMETHING from the pot) vary with the pair that calls me. Hence my EV is dependant on the pocket pair that calls me (a small difference but this is a gedanken experiment rather then a real live situation).

2. If the case Jack pops and any card higher then the pair that calls me we split the pot: JJJJK beating both JJJJ4 and JJJJ3 for a split pot. Again the numbers now depend on the pocket pair that calls me. 44's being slightly easier to split with then QQ

3. What if I DONT bet the flop, do the odds of a call differ on the turn or river? If I let the turn come and THEN bet it hoping noone has paired it and scare them into thinking *I* have. Need more data here. Anyone betting out on the flop probably doesnt have the J (or is a total moron). An all in on the river has a lot more "scare" about it.

4. If I check and get raised, even if the guy is bluffing I cant call and I lose. What are my odds of getting raised if I check because that effects my decision to check and try a bluff later. Any bet at all is a death blow to me here.

5. WTF am I doing in a pot for the last of my cash with 32.


DeV's answer: Insufficent data if you want me to be accurate. Real life answer: I get up and buy a scotch at the bar with the tenner, mucking over everyones stack as I leave.


DeV.

Lafortezza

DeVore wrote:

3. What if I DONT bet the flop, do the odds of a call differ on the turn or river? If I let the turn come and THEN bet it hoping noone has paired it and scare them into thinking *I* have. Need more data here. Anyone betting out on the flop probably doesnt have the J (or is a total moron). An all in on the river has a lot more "scare" about it.
DeV.

As far as I can tell from the complicated 2+2 forum thread this is the reason why the correct answer is higher than 20%.
While
1) betting the flop has more EV than checking (in case your opponent bets),
2) checking and having your opponent check behind you on the flop, *then* betting the turn has better +EV in the long run.

I think.