LG John

I’ve been going through a spate of messing around with poker maths again and given maths is a weakness of mine, I have been getting myself in a muddle. I’d appreciate some input on ‘Expected Value’ and whether a) I have calculated it correctly in the examples below and b) if there is an easier way to achieve the same result.

I’m on the turn and contemplating a semi-bluff* all in. I’ve estimated that the times my opponents call he we will win approximately 65% of the time and I will win 35% of the time. I do not foresee a tie as a possibility given the board texture.

*semi-bluff is where you are bluffing with the back up of a draw (i.e. even if the bluff doesn't work you still have a chance to win)

I also estimate that my opponent will fold 25% of the time to my all in.

The pot is £115 and I push all in for £95 and want to calculate my expected value.

We therefore know the following:

25% of the time my opponent folds and I gain £115
75% of the time my opponent calls:
Of that 75%, 65% of the time he wins and I lose £95
Of that 75%, 35% of the time I win and I gain £115+his call(95)=£210

Is the following method correct:

Lets examine 100 cycles of this play-

25x we win £115 =£2875
48.75x we lose £95=-£4631.25
26.25x we win £210=£5512.5

Total for 100 hands = £3756.25
Total for 1 hand =3756.25/100

Expected Value = £37.56

Is this correct? Is there a quicker or easier way to calculate expected value?

One other possible method might be a situation where we are to call a river bet. We estimate that we tie with villain 10% of the time, beat him 30% of the time and lose to him 60% of the time. The pot after his bet is £175 and its £75 for us to call.

Pot if we call will be £250

If we are splitting then we are effectively both getting back our £75 so we are splitting what was in the pot before villain bet (£100) thus:

10% winning £50 (£100x0.50) = £5
30% winning £250 = £75
60% losing £75 = -£45

Total Expected Value is £35

In short both these plays are nice and profitable

Another one I'm struggling to get my head round is pot equity.

Say the pot stands at £100 and its £25 for me to call. To calculate pot equity I understand that its risk/net reward x 100 thus 25/125*100 = 20%.

This seems right to me since in fraction terms 25:100 can be expressed as 1:4 and to convert a ratio to a percentage is 1/(4+1)*100 = 20%.

So if I know my 'pot equity' is 20% would I be correct to say that any outcome with a chance of winning that is higher than 20% will be +EV and any outcome with a chance of winning lower than 20% would be -EV?

TopBanana

Don't people like you have special places to post this sort of stuff?

STi wanna Subaru

iTrader: (1)

I stand by my comments in the past that you think too much

David Lock

I think I will stay with house prices

LG John

LOL, I know, I know! I just need to get this straight in my head. It's one of those things whereby you have to do 100% of the learning to use 5% of the knowledge on a 'day to day' basis. Notwithstanding, you can't get away with not knowing it. Hope that makes sense.

sti-04!!

SB - A legend at Risk assessments

richardg

thats' what all the muffled chatter at planning committee meetings is all about then! the members and planning officers are all quielty playing poker under the tables!!

TopBanana

Well exactly. I'd imagine the probabilities depend very much on who you're playing and what mood they're in! The best it can do is give you a better feel for things.

And as with any system you also need to work out the drawdowns you'll experience and their likelihood. I've never been into poker, but spent some time looking at 'systems' in financial markets. Even if you have a winning system, it's the drawdowns that'll get ya

LG John

It's a fair point.

Judgement is an integral component of poker. The better your ability to estimate these situations the better you'll do. It's no different to any other form of variable odds betting.

EV on a roulette table is fixed - the structure of the game is such that you cannot achieve +EV. In poker the EV from situation to situation changes but that doesn't mean you can't calculate your EV based on your estimations.

First of, there are situations where your EV is fixed. In other words when you know your opponent has a certain type of hand but you have the nut draw and know the probability of making that draw. The rest of the time you have to plug in some assumptions about his hand and your chances of winning the pot.

TB, I'm not familiar with the term 'drawdowns' - I'd guess it refers to standard deviation? In poker this is a very big consideration in determining your likely 'swings'. There are a number of calculations you can run with your SD figure and your average win-rate to determine what bankroll you'll need relative to x% risk of ruin. At the moment I'm crawling out of a 16 buy in downswing - a personal record!!