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Dan Barlow:

If I play the 10 and he has a 5, I've allowed him to peg out. If I play the 9 and he has a 6, I've also blown it. Since I can see a 5, it's more likely he has a 6. On the surface, this makes the 10 the best play if my sole goal is to keep him from winning right now. But not so fast. If he has a 5 or 6 I don't like my chances whether I guess right or not. After all, he didn't toss me a 5, and he probably didn't toss two face cards (if he was going to toss two faces, one of them would have been the K). I'll be lucky to find eight points in the crib. Even if I do, I'll probably lose if it's 114-119* going into the last hand. So perhaps I should be less worried about his having a 5 or a 6, and more worried whether he has a 9 or a 10. If he has 4-5-9-K, I can afford (barely) to give him two holes. If he has 4-5-10-K, letting him pair my 10 puts him at 119*, and a very good chance of pegging out next hand. So I play the 9.

DeLynn Colvert:

This is a very subtle play. You see a 4-5-K on the table, and at that point pone needs ten to win. With a J cut, if pone holds a 10, leading your 10 gives him the game. If you lead the 9 and he holds a 6, you also lose the game. But pone did not play a 6 to run the count to 30 — he played a 5 for 29. I would assume he doesn't have a 6, so I would play the 9. Both plays can be losers, but usually a player will play as close to 31 as possible, and he would certainly want to keep a 5 for last to get his needed peg. If successful, you may catch him in the stinkhole, and a possible sixteen crib gives you the game.

George Rasmussen:

Lead the 10. Pone has played three of four cards. Those are 4-K-5. Since pone did not pair the A with the count at 24 (even though it would appear the A was dumped), but instead took a go with the count 29, I would conclude that pone does not have an A to go with 4-K-5. The next most likely card to be retained would be the 6 or possibly a 3. The 9 lead (after viewing 4-K-5 and knowing that an A is not present in pone hand) would lead to the score of 15-2 in a high percentage of cases. The lead of the 10 would not result in a score if pone were holding either 3-4-5-K or 4-5-6-K. If pone is holding 4-5-5-K, you lose the game with the J cut if pone scores a go, and that has already happened. If this is the case, it was not the lead of the 10 which resulted in the loss.

Michael Schell:

This would be a straightforward endgame two-on-one problem if pone was one point further along. In that case, you'd just lead the 9, fearing a 10. As it stands though, you have a dilemma. It's extremely unlikely that pone has a 9, since your own 9 wasn't paired and since 4-5-9-K without a flush would be a bizarre hand for her to keep at this game score. And it's clear that if pone's last card is a 5, then she has the game won regardless of what you do. But if her last card is a 6, she'll end up in the stinkhole unless you lead the 9, and if it's a 10, she'll fall four points short on your 9 lead, but only two points short on your 10 lead.

The classical play is to lead the 10, since it cannot cost you the game outright, and since pone is statistically more likely to be holding a 6 than a 10 (since you're already holding one of the latter). But nowadays most experts would probably lead the 9, figuring that the game is as good as lost anyway if pone has a 6 (if she doesn't peg now, she'll deal the next hand from the stinkhole and surely peg out), whereas if pone has a 10, the two extra points she pegs on a 10 lead, compared to the two extra points you would have pegged by leading the 9, could be critical. That's probably how I'd approach it if I had to make this decision over the board.

What's easy to miss, though, is that you'll have a sixteen-point crib if pone tossed you J-K or Q-K. That can't happen if her last card is a 10 (she'd have kept the pair of Ks instead of 10-K), but it could be the case if her last card is a 6, since she might have started with 4-5-6-J-K-K or 4-5-6-Q-K-K. How likely is that? Given the ten cards you've seen so far, there's a 0.42% chance that pone started with either hand, and thus a 0.42% chance that leading the 9 will blow a sure win.

So let's take a closer look at leading the 10. If pone can pair it, it means she was holding 4-5-10-K after the cut. What might she have tossed to the crib to keep this particular hand at this game score? If she's a competent player, I think you can pretty much rule out her throwing an A, 3, 4, 5, 6, 10, J or Q, since any of those cards would be an improvement over the retained K. You can also rule out her tossing a second K in preference to the 10. It's conceivable that she could have tossed 7-8, 8-9 or a pair of 2s, 7s, 8s or 9s. But a more realistic assumption is that the possible discards are limited to 2-7, 2-8, 2-9 and 7-9, indicating that she must have started with one of four possible six-card hands: 2-4-5-7-10-K, 2-4-5-8-10-K, 2-4-5-9-10-K or 4-5-7-9-10-K. There's a 1.25% chance that this happened, in which case your crib will be worth three points. In these variations leading the 9 puts you at 111-117* where — and now the guesswork comes in — I estimate you are a 31% favorite to win. Leading the 10 instead makes the score 109-119* (remember there's a four-point net pegging swing) where I estimate your winning chances are only 7%. The cost to your winning chances of having your 10 lead paired are thus 1.25% · (31% - 7%) or 0.30%. This is 0.12% less than the cost of giving up a 15-2 on a 9 lead, thereby making the 10 lead technically correct, at least against an opponent who knows how to discard in the endgame.

What's interesting to me is not so much that the natural-looking 9 lead is theoretically wrong by a miniscule amount, but how incredibly unlikely it turns out to be that pone is holding a 10.

Phyllis Schmidt:

Play the 9. There's less chance for a 9 match. If pone had a 6, I think he would have played it earlier to make the count 30, saving the 5 for last.

Peter Setian:

In this exact position, I would lead the 9 instead of the 10. First of all, if the pone is played to have the 6 for a nine point hand, that's already too much. Pone will be in the dead hole and will of course automatically peg one hole on his or her next deal, unless my crib contains sixteen points. The chances of this are very slim. I suppose J-K or Q-K could have been thrown by the pone, but this is remote given the cards already known; and no other combination of two face cards (or 5s) would be tossed by a sober player (if holding 4-5-6-K and needing eleven points). I'll play for a possible eight-point crib and the pone needing two to four more points after counting the hand.

HALSCRIB:

It took them a while, but the humans all seem to have figured out that leading the 10 nails you if pone has a 10, while leading the 9 nails you if pone has a 6. There are two reasons why leading the 10 is better. First, leading the 9 can kill you outright, whereas the worst you can do leading the 10 is to reduce your prospects from "bad" to "really bad". Second, your opponent is more than twice as likely to be holding a 6 than a 10, both because you've already seen one 10 (whereas there are four unaccounted-for 6s) and because 4-5-6-K is generally held more often than 4-5-10-K.

Panelists

Dan Barlow won the 1980 National Open Cribbage Tournament, and made the 1985 All American Cribbage Team. His cribbage strategy articles appeared in Cribbage World for many years, and can be seen on the ACC Web site. He also provides strategy tips at MSN Gaming Zone. He has written seven books on cribbage, two of which have been glowingly reviewed in Games Magazine. All, including his latest book Winning Cribbage Tips, are available at The Cribbage Bookstore.

HALSCRIB is widely regarded as the world's strongest computer cribbage player. Its opinion was solicited using a special analysis version of the program. Since HALSCRIB only speaks binary, its thoughts have been translated into English by Michael Schell and its creator, Hal Mueller, a retired mathematics professor and eight-time ACC tournament winner. For more information, see the HALSCRIB home page.