"Last Train" is a term used in bidding, in the context of slam bidding, it is a bid to show more interest in slam - "I do not want to sign off, I have interest - do you have a bit extra and can bid on?".
When does it apply?
Once both sides have found a fit, and are cue bidding, so for example.
*4♦ was a splinter, showing 4 card support and 8-11 good points, and 0-1 diamonds
*4♥ is "last train" - the final bid available before our contract of 4♠.
Why do we use it?
Put yourself in this position, you have interest in slam, but don't quite want to commit to it. You want to let your partner know you are interested though - however, you don't want to go past game and end up unnecessarily on the 5 level.
So, in the above auction, at this point
Here North only has 4♠ or 4♥, just two bids. It is in this particular situation that we assign 4♥ as "last train".
How do you respond to it?
Let's reuse the first example, and decide what to bid with south.
We have a nice hand, the maximum end with 10's, 9's. Overall a very respectable splinter. Partner is looking for middle to high range of our bid, since we are comfortably there we can push on and bid 4NT, RKCB.
A lot of partnerships have this rule
The bid just before game is always "last train".
So take this example, very similar to the first one
Partner made the bid directly before game, 4♥. As our partnership rule states, that is always "last train". Partner is telling us they are interested in slam as they did in the previous example, however this ALSO denies a diamond control. Partner's overall message is "I can't cuebid diamonds, I don't have 1st or 2nd round control, however I am bidding "last train" because I am very interested in slam if you have diamonds controlled".
Again we have a perfect hand to continue.
4♥ is not a natural cue bid in these auctions, so the cost of last train is a heart cue bid. Something I will discuss more in future, but that is a meaningful downside which can cause issue in some auctions.
Recommendation
Last train is a useful tool that I do recommend but would not get caught up on, hand evaluation and more general bidding tools such as understanding cue bids in general, should all take priority before thinking about Last Train too much.
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