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In most sets of rules for Cribbage [1], you score a point for playing the last card.

My first impression is this tends to nullify the "point for go" - if you manage to win "1 for go", probably the other player then has an extra card than you and is going to get "1 for last card". Of course if you get "2 for 31" you come out ahead.

Then I wondered if the point of forcing go is perhaps you get to play at least two cards in succession (e.g. you have a pair of twos, 2H and 2D; you arrange it so you plays 2H for "28"; opponent is blocked so "go"; now you can play 2D for a pair). But the the opponent would have the same advantage at the end when they get last card (admittedly they will have played some cards before you forced go so have less chance of this opportunity.)

So, I have got as far as "if you don't have the '1 for last card' rule, it is worth winning 1 for go, and 2 for 31 is even better; if you have the rule, it's just more difficult to score over the opponent.

But I imagine there is more to it? So my question is What is the effect of the "1 for last card" score on tactics in cribbage?

[1] Closely related question - to my limited research it seems '1 for last card' is less common in British books than American books or websites. Is it a regional variation, or more a 'house rules' thing? Or are rule sets missing this rule just wrong?

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I believe you are misreading the rules. As this set points out, the one for last card is just an alias for the minimum go guaranteed to Dealer for playing second.

Update:
Tactically, the guaranteed go for Dealer really only affects end-play as both players approach 121 points. at other times in the game, worrying about a single point is just not important enough.

For example: Consider a situation where Dealer is at 106 and Non-Dealer at 112 with 7 points in hand. Non-Dealer would like to peg at least two points to guarantee the win with first count, but must be wary of sequences that allow Dealer to peg a 2+12, followed by the guaranteed go. Non-Dealer should not lead with a low pair hoping for a triple, as the 6 is insufficient compared to Dealer's possible 2+12. Better to try to get a 15 and give up a possible 6 to Dealer, as that is enough with first count.

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