I’ll set an example

Turn pot is 100 and v then bets 66.6 all in into it. I have 20% equity and I incorrectly call.

Now is my mistake expressed as a percentage a) I risked 28% of the total pot when I could only risk 20% therefore my mistake is that 8% difference. So an 8% mistake

Or b) my ev is -20 chips therefore my mistake is 20% because it’s 20% of the turn pot

Or c) my mistake is 20 chips of the 66.7 chips I risked therefore I call my mistake 30%.


Ultimately I’d like to charge a 10-15% fee for people’s flush draws so which of these 3 metrics should I use to do that?

and yes I realise you should never think in terms of specific draws rather a range of possible draws but let’s just simplify it for this occasion or think of it as I assume his range equity is 20% in a spot and I’d like to charge v a 10-15% fee.

You are getting 2.5:1 (28.57% equity required) and have only 20% equity.

You had a 30% disadvantage on money wagered.


Reward * probability = return.

350 * .2 = .7

So you return only 70% of what you wagered.

Ok so to test if I’m using your way correctly if turn pot is 100 and I call a half pot bet all in with 20% then it would like this:

3* .2 =.6 therefore my mistake is 40%? Did I do that right?

In your first example you wagered 66 in a pot that was 100 before the betting round.
In your second example you wagered 50 in a pot that was 100 before the betting round.

Do you see why your mistake in the second example can’t be bigger than in the first?

FWIW, if you call 50 to make the pot 200, you would need 25% equity instead of the 20% you have. It doesn’t really matter how you want to quantify that percentage-wise. But it’s an important first step to understand the difference between percentage and percentage points.

When a pot is raked it is raked on percentage points right? 10 percentage points of the final pot for example.

I’d like to be able to charge 10 percentage points in a similar fashion for someone to complete their draw. I guess that would mean using my a) way in the original post

If I bet 80% of the pot all in and they called with 20% equity then this would theoretically charge them a 10% rake on their draw. I think this sounds about right.

Rake would be 10 percent in that example.

A percentage point is the actual amount of change between two percentages. Percentages measure the rate of change.

A simple example:
The difference between 50% and 55% is 5 percentage points (because 55-50 = 5) but 55% is 10% higher than 50% (because 50 * 1.1 = 55).

Yep so by me betting 80% of the pot it’s 80 of 260 is about 30% which is 10% percentage points higher then the 20% equity draw. Therefore that excess 10% they pay is like my rake or fee that I’m charging them for their draw

Why?

But this might be wrong in that by the time they actually win the pot they will have paid that 10 percentage point excess 5 times. Which really means I charged them 50% rake not 10%

As mentioned not specifically flush draws I just meant 10% excess on my guess at what their equity is. Reason being is that 10% seems like a sweet spot that isn’t too high and not too low. If people thought 10% was too high then they’d never pay a standard rake on a sit n go so psychologically this number is pretty attractive

The formula I use to measure the "exploitability" of a solver solution is:

dEV / pot

Where dEV is the change in the expected value.

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20% of the time you'll win 166.6 chips: +33.33
80% of the time you'll lose 66.6 chips: -53.33

I would use b) "my ev is -20 chips therefore my mistake is 20% because it’s 20% of the turn pot". This metric has the advantage of working in more complex scenarios, beyond simple pot odds calculations.

Yeah that was my second one b).
I was using this for a long time and it might well be the best way. The problem with using the method of dividing ev against the risk as a percentage is you can end up with really high numbers very easily like 2225% when someone either checks or bets very lightly. I really don’t like a metric that has such wild numbers like that.

The metric you like never has numbers like that in a typical poker setting which is good. I’m gonna experiment more with penalty % from total pot as opposed to penalty % as a relation to the turn pot because if this system works for the house then it should work for us players too.

Tombos I know we are both speaking the same language here so I’ll ask this. What you’re measuring is a 20% deviation from the path of breakeven ev. The new way I’m experimenting with is I’m suggesting that 8 excessive % points are being paid 5 times. He is calling 28% with 20% equity. This is measured as a 40% mistake. Or 40% of the final pot is missing after it is ran out 5 times. Essentially the made hand has charged a 40% rake. What are your thoughts on using this as a scale?

Always start with EV. That's the only metric that really matters. I only know two "correct" methods for measuring EV:

a) Measure the EV directly (i.e. -20 chips, +5bb, 8.2bb/100, etc)

b) Measure the EV as a percentage of pot (EV / pot).


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The method you are proposing is (actual equity - required equity). I don't think this method makes sense.

Original Example: So your actual EV loss is: ((20% * 166.6) - (80% * 66.6)) = -20 chips.
As a percentage of pot: -20 / 100 = -20%
Loss as measured by your method = -8.57%

If we ran this spot 5 times, you'd expect to lose 100 chips.

Your loss as measured as a percentage of pot is (-20% * 5 times) = -100%. You would lose 100% of the 100 chip pot, which is 100 chips.

Using your method: (-8.57% * 5) = -42.86%? I don't really know what this 42.86% represents. It doesn't seem to have anything to do with your actual EV loss. I don't think your formula is multiplicative, but I could be wrong.

You're not dividing against the risk, you're dividing against the pot. You should almost never see numbers like that using EV/pot. That would mean your gain/loss was 22.5x bigger than the pot.

As with most things .. I want to look at this from a slightly different direction ... Before establishing a method we need to know what your goal is. I think you want to 'charge' for a Player's draw, we all do for our value. You just need to determine what you want to be the basis, either the calling amount or the total of the pot. I think the introduction of 'rake' may have swayed the conversation ... at least for me.

Back to your original example ... What's EV=0?

100 in pot and a calling Player with 20% EV needs 4 to 1. So 100 x 4/3 is 133.33. If Hero bets 33.33 all-in on Turn, then this spot is break even in a vacuum.

So if a Player is all-in for 66.66, not 33.33, how much did he 'charge' for the draw? Or from a caller's viewpoint, how much of a premium did they pay for their draw? One could argue that he paid a 100% premium if you base it on the bet sizing.

For a 66.66 call to be EV=0 the pot needs to be 333.3 (66.66 x 5) and this pot only ended up being 233.2 ... that's a pretty big deficit! But how do you quantify that for 'study'? (Note that this matches the 100 chip 'loss' mentioned above.)

If we take a look at the pot sizes, in the example the calling Player received 2.5 chips per 'calling chip' when they really needed to receive 4 chips per chip, so that's a 40% deficit from the caller's viewpoint? If you work with % 'only' IMO you miss out on what's real, which is actual BB or chips involved in your decisions.

That's a lot of chatter that may not contribute anything .. but without knowing exactly what you are are trying to track (and from either the bettor or caller's viewpoint) I'm not sure it was of any help at all.

I think there's probably a few different ways to establish a good/bad trend here. And as long as you know what your basis points are it's going to work for you. This issue is the opinions of others as to how valuable that information is ... And for me, as long as I can get to the EV=0 point it's pretty easy to see whether it was a 'good or bad' play in the long run. GL

Very interesting replies thank you for sharing insight.

I personally feel like the disadvantage to using ev divided by turn pot to get a % deviation from the breakeven line is it can sometimes be deceptive and I’ll provide an example:

Say you have a ten seated game similar to an sit n go but for study purposes we’ll say everyone has a perfectly even chance of winning the 100% pricepool money.

Say everyone pays $10 and then the house takes $10 for itself. So essentially you are getting 8:1 with a 9:1 draw.

If we use our % deviation from breakeven line method we can see that if we make the decision to play this game we are making a -1.4 ish% mistake. You might be tempted to think -1.4% ain’t so bad and nothing to fuss about but in reality that’s a 10% rake.

This is the dilemma that really stumps me.

My goal is to be able to charge a 10% house rake in a uniform manner and the reason why I like this idea so much is because 10% is a psychologically inviting penalty % rate that has worked on gamblers since forever.

Ok legends, some hours have passed since my last post here and through trial and error I’ve solved my goal.

For me to charge a 10% rake for someone’s draw firstly you workout what a break even bet for them would look like. So if turn pot is 100 and they have 20% then a breakeven bet for them would be 33.3%. Then you look at what the total pot would be if you did that and it would be 166.6. Now you simply find 10% of that and get 16.6. Now it’s a matter of arranging a bet that will charge him negative 16.6 chips in ev.

So if turn pot is 100 and we charge him 60 then his ev will be -16 and wallah you have successfully raked him 10% on his draw.

Another example would be if you assume he is calling with nothing but a pair and he has an 11% chance of it improving to 2pair or trips then you could charge him 33% of the pot and once again he’ll be paying a 10% rake for this draw.

Thanks guys for helping me solve this

A) Wouldn't you 'bet' 50 in the 20% case? 33.3 + 16.6 (10% of 166) = 50, not 60

B) Pot=100 .. 11% .. EV=0 bet is 11, 'would be' Pot=122 ... 11 + 12 (10% of 122) = 23 bet

A quick look shows that even though you're risking 2x chips in A (50 v 23) you only 'make' 38% more chips in your 'rake' (16.6 v 12). GL

Ok answer I love that you are challenging me like this and you might be right lemme tell you why I chose to do it my way.

In the ten seater sit n go example where everyone chucks in 10 and the house takes $10 out for itself and then an open hand is played and the winner gets the $90.

Look at the mechanics of that situation. A breakeven risk reward is $10 risk for a total pot of $100 (includes your risk in it). The house then takes out its $10 or 10% and this creates the overall 10% rake.

I have copied this format. So I figure out a breakeven total pot and get 166.6. I remove the 10% (16.6) so I arrange a bet that involves 16.6 chips that get removed from the breakeven total pot and a bet of 60 does this.

If I bet 50 (33.3 +16.67) then only 10 chips will be removed from the final breakeven pot so it’s not enough.

Make sense?

I'm not there yet ... and maybe farther away from what your end goal.

I agree the break even pot is 166.6, and in order to achieve this EV=0 spot 'someone' needs to bet 33.3 since there's already 100 in the middle.

I lose you at 'removing' 16.6 (from what?) and ending up with a bet of 60. If you bet 60 the pot will become 220 if called, which is 53.4 more than break even. That's a number that hasn't come up in this thread as of yet ..

If you are ahead and trying to charge a 'fee/rake' for another player to draw, wouldn't you 'add' chips to the break even bet of 33.3?

I'm viewing you as both the Player and the House in this spot. As a Player you want to make sure you 'charge' at least 33.3 to make the spot EV=0. As the House you need to add on the fee/rake (value as a Player) at your determined percentage of the total.

If we want to separate the Player and House in this spot and determine the 'gross' bet needed for a Player to break even at 10% House rake (Australia) then we would 'simply' take the 166.6 and divide by 0.9, getting 185. So we need to bet at least 42.5 in order to make our 'net' profit EV=0 since the House is taking 18.5 chips in rake if we get to Showdown. (185-18.5=166.5) Using this data anything bet over 42.5 would be the Player's fee/rake/value ... Which would come out closer to the 60 that you're talking about. (42.5 + 16.6 = 59.1)

So at 10% rake for the House AND the Player I would agree that the bet needs to be 60.

If I somehow got to where you wanted this discussion to go, then WOWo ... GL

Ok I read your post twice. I can see how this got complicating because in a real game there is an actual real rake too. The ideas I was using did not factor in a real PokerStars type rake at all (in the case of the betting 60 into 100 pot example) so the numbers I used in my example might be skewed a bit cos I left it out.

For study purposes let’s assume we are playing in the park with no actual house rake.

A breakeven total pot would be 166.6. If I bet 60 and he calls then the ev of this call is equal to -16. If we measure -16 against what a breakeven pot of 166 would be we can see that it’s equal to 1 tenth of a breakeven final pot.

If I had I’d bet 75 instead of 60 then the ev would be -25. -25 of that total pot of 250 is 10%.

Is that ^ the bet I should be making to achieve my goal of charging a 10% penalty for someones draw?