Surely there is a way of working this out mathematically though

Yeah there is. Work it out. Hint: You need to make villain's EV = 0 when he has the worst hand in his range at the point at which the river card is dealt - i.e. BEFORE you bet or check.

Tbh, whilst working out the exact number is interesting/good practice, precise accuracy is not especially important. You just need to be in the right ballpark. If the correct answer is that you should be calling with 36.27% of your checking range, it does not matter too much if you in practice are calling with 30% or 40%. The trick is not to be calling with 10% or 60%. In game you are going to be making intuitive estimates anyway, and your job is not to seek to get the perfect % (this would be impossible), it is to try to get it closer to correct than the average bear.

Conceptualising the spot correctly is the most important thing. You said 66% because you had conceptualised it incorrectly - you had not taken into account the fact that you had an option to bet prior to being put in a call or fold situation after checking. However, once you correctly conceptualised it (which you have), who cares if you do not bother working the exact % out - just as long as you know that it is going to be WAY less than 66%. If you are 5-10% out either way, no big deal - you'll still be much closer than most (even very good) players. Just don't be 20-30% out! Many of your opponents will be this far out in many spots, even opponents you consider good.

BTW, I view the exploitative bit in the opposite way to you. I would call a LOT here. This is due to the turn play. I would expect your average villain to jam all his two pair or better hands on the turn given SPR and the texture of the board (two flush draws, straight draws etc). So I'd imagine that villain is extremely air heavy when he jams the river. Ofc I realise a straight has come in, and some one pair hands will have become two pair by the river, but I'd still call MORE often that whatever theory says I should do.

People DO bluff!

Obviously I could be completely wrong about this, so make your own reads/adjustments and go with them.

You're not quite correct in the exact details, but that doesn't really matter cos you are correct in the overall conceptualisation.

Villain is ALLOWED to have a (somewhat) +EV bluff with all his air once we check - i.e. we don't need to defend anywhere close to 66% of our checking range. The reason for this is that he only gets this +EV spot when we check, and we are only going to be checking some % of the time.

2/3 of the time

Can you explain why you believe you should (theoretically) call with 66% of your checking range?

Edit: Actually ofc I know why you believe this. It is because villain is laying himself 2 to 1 on the bluff so you believe you should call 66% of the time to prevent him profitably bluffing with his entire air range, right?

But this is incorrect. Can you tell me why?

Clue: You are defending a range that has CHECKED.

How come Neil Channing isn't in the WSOP Legends list?

Lol. He's in the Team GB list though.

WSOP Main Event prediction pools at http://stakesandladders.com.

£200 guaranteed for £2 entry and overlaying

honeybadger is your man on here if you have questions....

Thanks for mentioning this Tighty.

There is still 25 mins left to enter, and currently a 100% overlay...

Still 25 minutes to get in the WSOP Main Event pools. Currently a 100% overlay in the £2 to enter Lucky 7 fantasy pool.

It's more of a case of I know what I should roughly call in this spot if villain is playing theoretically sound but in your experience, are they?

So just out of interest, what % of your river checking range do you think you should theoretically (i.e. GTO-wise) be calling with? And why? I'm asking you this just to check your understanding of the theory in these spots.

Also, how do you approach making exploitative adjustments from 'theoretical play'? If you have a tentative read on an opponent (or a tentative population read) do you think you should radically adjust your ranges based on that read? Or do you think the amount you adjust should roughly correlate with the strength of the read?

Unfortunately you're probably not gonna get a response cos your post is pretty intimidating! I did consider putting all your ranges into flopzilla or crEV and looking at them/doing some maths etc, but it just seemed like so much hard work...

Also, no idea if there are FDs on the flop/turn cos your HH does not show suits. This is kinda important for ranges as you know.

We have three different types of pool open for the WSOP Main Event. 24 hours left to enter. We've guaranteed the £2 fantasy 'lucky 7' pool at £200 and there is going to be a big overlay, so come take advantage of the free money.

Yeah VC are the worst. I have had 3 accounts closed, and all three have been closed after my FIRST BET lol! And each time before the race had even run! They said they would honour the bet each time though... and all three bets lost lol. The first one was sort of fair enough because I was naive and made a pretty big bet. But the other two my bets were both only £100. I bet from an ipad using 3G on the second two accounts so it is not like they were tracking my IP address or PC or anything and could tell it was the same person.

Okay thanks. I will show him what you wrote when he tells me I am a terrible dad for not allowing him to buy them!

Why do you want Stars to go after players VPN'ing to play poker?

I personally have no real issues with people VPN'ing to play poker from the USA. Refusing to accept a stupid and unfair law that was passed in an underhand manner by the US government does not seem a particularly bad crime to me, even if it is officially against Pokerstars T&Cs. Provided they are playing using their own accounts it seems reasonable to me.

I guess one 'selfish' reason why players would like Stars to take action to stop this is because players using VPNs make the games tougher - it's not like your average recreational player is going to ever do this - pretty much every player using a VPN is going to be a good player.

As Boba Fett says, a less self-serving reason would be that it is unfair on those who have had to relocate to continue to play. Why should A, B and C have to move to Canada away from their families and friends in order to play but X, Y and Z just think "screw that, I am going to stay here and play illicitly through a VPN".

Also, guys from the USA playing via a VPN are dodging taxes/money laundering or whatever. Although this seems a bit pedantic in some ways.

Haha, two bits of completely different advice

So now I do not know what to do lol.

Got 3 or 4 times more coins than for the same price through XBox/EA/FIFA (whichever one the recognised route is).

Does this mean I can buy them from an 'official' site then? i.e. from a site where it is allowed rather than against the T&Cs? Cos I was under the impression that you could only buy coins from third party sites...

it's a world I'm not that familiar with.

Yep, same here. I have no clue what it is all about tbh. For example, I have no idea at all what this means:

The whole reason EA/FIFA changed the Ultimate team transfer market to having player values (lower & upper limits) was to stop coinsellers from being able to easily ply their trade like they were able before when the market wasn't capped on any player/consumable.

Does anyone know anything about these? My son wants me to buy him some, it seems you buy them from 3rd party websites. I did a bit of googling and it seems they may be against the T&Cs of EA (the makers of FIFA) and your account could get barred if you buy them. Is this actually the case, and if so what is the realistic risk involved? Also, are these third party sites reputable or is there a risk of getting ripped off? Any recommendations for which site to use? Basically any info from anyone whose kids are into FIFA and have bought these coins would be great...

[I don't see anything improper, deceptive or unethical]

Since online poker first came into being, people have been playing on other people's accounts in order to get action they might not get on their own account. I don't see anything improper, deceptive or unethical about it.

Well it is clearly deceptive. Whether it is improper or unethical is down to your own point of view on these things I guess. You make an interesting comparison with the punter vs bookies battle, which does make logical sense in many ways.

Since stuff like this is fairly subjective, I choose to see a person betting through someone else's William Hill account as okay by me since they are fighting the nasty, evil bookies who try to fuck everyone. Same with someone, say, being a card counter at Blackjack - it is not allowed by the casinos, but I consider it perfectly ethical since the card counter is battling the big nasty casinos. But this is my personal (biased!) way of seeing these things, and I respect yours even if I do not see it in the same way.