I think an easy way to stop this would be for the other player to buy counting houses especially if there is a tfb or any strong trashing it seems in order for this to work you need to be able to buy lots of counting houses more than 6

Not necessarily. It depends on when you draw your first Counting House. In the solitaire game I logged above, I got 55 victory points by turn 12 with four Counting Houses. It would have been very difficult (and counterproductive) for an opponent to grab 7+ Counting Houses in that time, unless they were employing this strategy themselves.

Feel free to check my math. I edited out some notes where I'm trying to figure out when to topdeck versus discard (it's rather obvious you always discard once this gets going but the early turns still aren't clear to me).

1. 3 coin = 2 copper, discard.

2. 4 coin = 3 copper, top deck.

3. 5 coin = First CH. SHUFFLE. 16 cards in deck.

4. 4 coin + CH (unlucky) = 3 coin, discard.

5. 3 coin = 2 copper, top deck.

6. 5 coin = Second CH (a bit of luck, I think). 19 cards in deck.

7. 4 coin= 3 copper, discard.

8. 4 coin = 3 copper, discard.

9. 3 coin + both CH, resulting in 17 coin = our 13-coin engine starts.

○ TF x6, put 2 copper in discard and the 13-coin engine on top.

10. 4 coin + CH, resulting in 23 copper = 1st Province.

11. 4 coin + CH, resulting in 27 copper = 2nd Province + 2 copper

12. 4 coin + CH, resulting in 33 copper = 3rd & 4th Provinces

13. 4 coin + 6th CH, resulting in 37 copper = 5th & 6th Provinces + 2 copper

14. 4 coin + 7th CH, resulting in 43 copper = (8th CH) = 7th-9th Provinces

TheEmerged, I would have played out the end slightly differently. If I follow the log correctly, you have 7 cards in your deck on turn 9. I would start by buying a Province immediately and got to 8 Provinces on turn 13.

9. 3 coin + both CH, resulting in 17 coin = buy Counting House, Province, Copper, top-deck. <- 10 cards in deck

10. 3 coin + CH, resulting in 20 copper = buy Counting House, Province, 2 Coppers, top-deck <- 9 cards in deck

11. 3 coin + CH, resulting in 23 copper = buy Counting House, Province, 4 Coppers, top-deck <- 10 cards in deck

12. 4 coin + CH, resulting in 27 copper = buy Counting House, 2 Provinces, Copper, top-deck <- 9 cards in deck

13. 1 coin + CH, resulting in 28 copper = buy 3 Provinces

It might have been worthwhile to discard some of the gained coppers on turns 9 or 10, to liberate more of the coppers in your deck.

As for buying the second Counting House pre-combo, I have mixed feelings. On the upside, it eliminates the chance of drawing your only Counting House with an empty discard pile and it will result in the combo beginning earlier in the third shuffle (on average). On the other side, it's almost impossible to take advantage of a Counting House in your deck once you begin the combo, and the opportunity cost is 3 coppers in your deck and one more Counting House in the pile. I can't decide if it makes more or less sense to get a second pre-combo Counting House if they are contested.