Hello,
thanks for your interest, below I will answer your questions:
- As I have understood, if you can't follow suit but still have trump, you must cut, is that correct ?
Yes, this is correct. Cutting is mandatory.
- Are you allowed to undercut ? For example, if trump is hearts, if there are the queen and the jack of heart on the table, am I allowed to play the 10 of heart even if I have the ace ? Or I must play the ace in that case ?
Yes, undercutting is allowed, but pay attention that in this game, the 10 is always stronger than the king, so playing a 10 over a queen isn't undercutting. That being said, with your example, playing a 9 of heart would be perfectly legal, although probably not benefitial in most cases, since you may allow the other player to change the trump by declaring a different marriage.
- Am I allowed to play a king or queen and announce a mariage directly in the first trick ?
No. Before announcing a marriage, you must win at least one trick, and must be leading the next one. So it can be announced in the second trick or any other one, as long as you are the one leading that trick (playing the first card of the trick). Since that point that suit becomes the trump.
You also must have both the king and the queen in your hand at the start of that trick. For instance, if player 1 starts a trick with an ace of heart, and player 2 had a king and a queen, but played the king on the ace, they have basically lost the ability to declare it as a trump.
- Does something special happen if, as a defender, I make more points than the declarer ? Does it necessarily make the declarer to fail his bid ?
Under the original rules no, you simply win those points. If the declarer made his bet anyway, he will win that bet. I'm not sure if a variant proposing this also exists…
- What happens if nobody make a bid ? Is the pack just reshuffled and redealt ? Or is there a special kind of desesperate mode where there's no declarer and where you hav to make as few points as possible ? For info, that kind of variant exists with tarot and belote.
I haven't heard of such a variant, but in this game somebody essentially has to make a bid. Typically, the player next to the dealer starts the first bidding phase. He has to bet at least 100, and can't just pass and say 0. After that 100 bid, you are then allowed to pass.
When trying this game for the first time, I largely considered this rule unfair, because my opinion was that the person next to the dealer always has to play a bet even if they don't have good cards. In practice however, other players will rarely let you play such a small bidding round, because it is in the interest of whoever has a good hand to overbid you and possibly see the contents of the kitty.
Essentially, the game starts with someone dealing the cards. if we imagine that you are next to the dealer, you are the first to play. Your possible bids are 100, 105, 110, 115 and 120, if you don't have any marriages in your hand. If you do have at least one, you can increase it further. Once you choose one of these bids, the next player can simply pass, or overbid you if they can.
Regarding the game name, yes I thought of this confusion with 1000 miles as well. However, since the points in this game are always rounded up to 5 (there is an optional variant where they are rounded to 10 instead), some special care will need to be taken if you plan to allow adjusting the score limit, especially considering the fact that if you are 120 points below the score limit, you are on the barrel and have 3 rounds to win, possible only by declaring a bet that would take you to the victory. You don't win any points while on the barrel, and if those 3 rounds pass, you lose 120 points and are off the barrel, then your points go as usual.
Researching an alternative name, apparently Wikipedia uses Russian Schnapsen
as a name for this game. I was a bit confused myself since "Schnapsen" on its own is a completely different game (possibly also a good candidate), but currently I don't know of any other alternatives. I've asked a friend who has a bit more experience with the game so he may comment a little later.
Hopefully that helps address your questions and makes things more clear.