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Too much disadvantage for player who draws second
The player who draws first has imho a fair advantage for winning a game which is not balanced by the 1 gold that the player who draws second gets automatically.
I explain:
In the first draw the player in turn has a 50% chance to generate 4 gold. If there is a good card that is 2 or 4 gold he will draw it. If there isn't such a card he will swap a 1-gold card versus a 2 gold card which will be placed in his cool down stack.
The second player has also a 50% chance to generate 4 golds with his/her cards which yields 5 gold. If there had been a 4 gold card initially the other player would have drawn it and the second player needs some luck to get also a good 4 gold card. The chances are identical that a 6 gold card pops up in the tavern which exceeds in most cases the capabilities to buy for the second player (only 25% chance at best). If there is no card to buy for the second player he will do a card swap using the bank.
As the first player had the opportunity to either buy a good card or swap a 1 gold card first the chances are about 20% that he will get this good card or the 2 gold card in his third draw while for the second player the bought card or the 2 gold card is still in his cool down stack. This advantage remains during the first draws and will only diminish with time.