Does the dealer always peg one point?

Jay Boysun asks via email:

I had a quick question regarding pegging and am hoping you could provide some light being shed upon the subject. My Grandfather taught me the game when I was younger and I thought I remember him telling me that if you are the dealer you will always have at least one point in the peg although you would not necesarrily reciev any points in the hand or crib. The subject came up tonight when my family was playing cards and this talked about. I am just curious if this holds true in 2 handed cribbage as well as 3 or 4 handed play.

We referred this question to Professor Plum, Cribbage Corner's resident maths and statistics expert. Professor Plum:

Jay,

Your grandfather was quite right. In two player cribbage, the dealer must peg at least one point. Here's why. You both have the same number of cards. Your opponent plays first. When you play your last-but-one card, either your opponent can go or he can not. If he can, you get a point for last. If he can't, you get a point for Go.

This is not necessarily true in the 3 or 4 player game as someone else can score the Go.

Thanks, Professor! And thanks Jay, for asking the question.

Re: Dealer always Pegs 1 Point

Hello Professor,
Could you explain how in a multi-player (more than 2 player) cribbage game how the dealer would not peg at least 1 point. I don't see a way the dealer would ever have less cards than all other players (including the dealers partner) if the dealer was not previously awarded a 'Go'. Having the last card pegs 1.

4-handed

Because the dealer may be holding cards that get eaten up during pegging especially if they are low cards, they might not peg one point. Say the dealer holds A, 2, 2, 3.
The play goes like this 10, 10, 6 then dealer plays a 2 and another player plays a 3 for 31. The dealer in 4-handed is not guaranteed to be holding the last card and they don't have to peg one point.