MiketheExpert says: I suspect computer program HAL may opt for the (4 5) toss today, which would seem to best "conform" to the recommended opening strategy, but we'll see...

JQT says: Yes, I agree with MiketheExpert (above), and I've often said it here in these pages, that when we have such close discard choices, as long as we picked any one of them, it will probably then be the pegging that affects the game much more than this particular discard choice. Let's look at the difference between the top three choices: we see that it involves a minuscule 0.06 points, and while the win/loss percentages have a higher variance, these are also not correlated with the highest totals, nor do they convey much information at the initial position, since Dealer begins with a win rate of circa 56% before the cards are even dealt or looked at! To put it another way: trying to see the win/loss rate accurately ten deals ahead is like measuring the change in the flow of a stream and trying to guess the weight of a deer wading in the current fifty meters upstream! (Believe it or not, these are the kinds of physics that advanced weapons' labs are working on with powerful computers and big data and who knows, maybe even quantum algorithms!) Anyway, if we can gain 0.06 points as the Dealer and do it seventeen times, it will net us One Point. Since an average game is Nine Deals, and we are Dealer half the time, we can at best add this illustrious One Point to our ledger if we perform such a task (and do it correctly every time) over the course of two complete games! Meanwhile, if we make a routine error while pegging, and give up a PAIR instead of getting said PAIR, this costs us a whopping 'swing' of Four Points!! And this is just one of many such possible pegging errors that can and often does occur during EVERY DEAL. For example, in one of the annotated games in "Play Winning Cribbage," DeLynn Colvert advises that the Dealer with 5-6 should 'Play Off' on Pone's "X" Card Lead and play the 6 Card, and then if Pone plays another "X" only then do we collect the Two Points with our 5 Card with (31=2). This tends to avoid the frequent comeback by Pone in PAIRING our 5 Card if we grab the early (15=2), and of course this is all in keeping with Colvert's "Twenty-Six Theory" of playing Positional Cribbage. DeLynn figured, since we already have the Dealer Advantage, why squander it by allowing Pone to easily parry us when it's entirely preventable at this early juncture? And whether a player agrees or disagrees with this particular adaptation or implementation of this well-known theory, it should be clear that time spent here, on the aspects of these types of nuances during the pegging, is where we can really find ways to improve our game.