Clarity around MDF calculation vs how often we need to be right when calling

[yanader]

Hi everyone, hope you're all well.

I'm trying to make sure I am comfortable with these two calculations and they seems slightly different and I think I've only just spotted it.

On one of the quizes I was completing there was a situation where, with a pot size of 3575 we are facing a bet of 1600 and I was looking at calculating how often we need to be correct to call.

"It's pot odds = bet/(bet + pot) = 1600/(1600 + 5175) = ~24%"

So in this case, the denominator includes the bet twice, once because it is the bet and once because it is part of the pot. So this gives 1600/6775 which is approx 24%


Different from that is the MDF calculation which, as I understand it (and as it shown in today's 30 day challenge video):

1 - (bet / (bet + pot))

in Jonathan's example he is looking where there is a bet of 8 into a pot of 10 and then calculates through to get:

1 - (8 / (8 + 10)) = approx 55%


If we apply that calculation to the numbers from the first example:

1 - ( 1600 / ( 1600 + 3575)) = approx 69%


So that is to say, facing a bet of 1600 into a pot of 3575 our minimum defence frequency is 55% and when we call we need to be right around 24% of the time. The minimum defence frequency can be more because it can include raises (either as a bluff or for value) and the 24% we need to be right to call is also an absolute minimum so the numbers don't HAVE to match.



Am I thinking about these correctly? TIA

[LondonImp]

MDF is to stop us being exploited.

Let's take your simplified example.

The opponent is betting 8 into a pot of 10 - so risking 8 to win 18. This means if he wins the pot because you fold >44% of the time then he instantly profits. 8 / (8 + 10) = 44.4%.

This means that if you fold over 55.6% [1 - 8 / (8 + 10)] of your range then he profits immediately with any two cards. So the 55.6% is the minimum percentage of your range that you need to defend with to stop help being able to do this.

What's very important to remember is that MDF is only applicable when the villain is balanced.

Let's say he bets 8 into a pot of 10 on the river but you know he only does this with the nuts. Then MDF goes out the window.


Pot odds are far more useful against weaker opponents who are less likely to be balanced.

Lets use the same example where the villain bets 8 into 10 on the river.

If he does this with 3 nutted hands for every 1 bluff then he has you beat 75% of the time meaning we win 25% of the time.

What odds do we need to call? We need to call 8 into a pot that will be 26 (our call + villain's bet + original pot --> 8 + 8 + 10).

We can do 8 / 26 = 31%.

So we need to win 31% of the time to break even but we will only win 25% of the time. Therefore we fold.




Does that make sense? Hopefully it helps and I haven't muddied the waters further. Let me know if you want me to go into more detail for you.

[yanader]

yeah, it's definitely useful to see how one is really applicable against balanced opponents and the other will help us figure out whether a call is literally profitable or not.

I think part of my problem is the slight change in the calculations. Where one divides by 18 and the other by 24. Like, I can understand in a general sense why the calculation can be different but it really hasn't solidified in my head in a logical way yet and that's blurring the lines a little bit.

Thanks for your comment though, that's definitely useful.

[LondonImp]

Haha okay mate, if nobody else has chimed in by the time I'm on my lunch break I'll try and explain again

[LondonImp]

Perhaps you are finding it confusing because you are trying to relate the calculations to each other.

They are completely different and need to be treated differently.

Pot odds
When we are calculating pot odds we are doing a risk versus reward calculation.

The two parts of the calculation can then be broken down as so.

The first section is what we have to risk. Our "bet" which in poker terms is a named a call. In gambling terms we are still placing a bet on a possible outcome.

The second part is what we get back when we win which is our bet (our risk), our opponent's bet, and the pot.

So that calculation is: our call / (our call + opponent's bet + pot)

I assume this is what you mean by: the denominator includes the bet twice? You are correct because it is counting both the opponent's bet and our own bet (i.e. a call).

MDF
You might find it easier to think of MDF from our opponent's point of view.

They too are making a risk versus reward calculation. Their calculation is bet / (bet + pot)

The first part of their calculation is what they have to risk i.e. their bet.

The second part of the calculation is what they get back when they win the pot which is their bet and the pot. Notice this time you have not called and so there is only 1 bet included in the second part of the calculation.

So that calculation for them is: their bet / (their bet + pot),

So if they bet 5 into a pot of 10 then their calculation is 5 / (5 + 10) = 33%.

All we need to do is 1 - minus the answer (so 1 - 33% = 67%) to work out how often we need to defend to stop them profiting with any two cards.


Is that any clearer?

[yanader]

Yes! that's amazing, thank you. I was definitely treating them as linked but now I can see why those calculations are logically constructed in the way they are that makes a tonne more sense. Thanks so much for taking the time to do that

[LondonImp]

No problem buddy