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Cribbage Stratagy - Jacks

Cribbage Jacks

How Do I Account for Jacks in Cribbage?

If you’ve ever played cribbage, you know that a jack comes with a bonus: if the cut card’s suit matches your jack, the jack is worth 1 point when you count your hand. For this reason, you should avoid putting a jack in an opponent’s crib if you have a different option that’s otherwise equal.

It’s obvious that a jack is, in this respect, worth more than a 10, queen, or king. But how much more? When are some times that you should put a jack in an opponent’s crib? Does this affect play in any way other than the discard? And what about the possibility of cutting a jack?

How Does a Jack Compare to Other Face Cards?

A jack is equal to all 10-value cards at making 15s. There’s no nuance there.

It is more useful than a queen or king at making runs. When you think about it, all runs with a queen or king must include a jack, but not the other way around. There are many runs with a jack that don’t have a king or queen, so jacks are more likely to be part of a run, on average.

This logic works in the other direction too, somewhat; a 10 is a tiny bit more valuable than a jack at making runs, because a jack can’t serve as the lowest card in a 4-card run, but a 10 can.

Aside from the value in making points the common way—with pairs and 15s and such, like all cards do—how much is the possibility of “his nobs” worth? About a fifth of a point (0.2) on average, as it turns out. That’s close enough if you want a rule of thumb.

If you want more depth, it varies with the cards in your hand. You can have 0 to 5 cards that share the jack’s suit, and it affects the probability and theoretical point value (expected value, or EV) thusly:

Jack Suit in Hand Chance of Nobs Expected Value (EV)
0 26.09% 0.26
1 23.91% 0.24
2 21.74% 0.22
3 19.57% 0.20
4 17.39% 0.17
5 15.22% 0.15

This extra 0.15 to 0.26 point is virtually the only thing that separates jacks from other 10-value cards.

When Should I Discard a Jack to an Opponent’s Crib?

If your hand will have fewer points if you keep a jack, dump the jack. Always. It’s never worth sacrificing guaranteed points outside of longshot endgame situations.

In all other cases, measure the jack’s nobs potential accordingly. Holding the jack is always:

The approximate EVs for these four types of draws, in order, are 0.05, 0.26, 0.52, and 0.70. The most noteworthy is gapped run potential, which has the exact same EV as the nobs draw—but only when there are none of the nobs suit out. If even 1 nobs out is gone, the gapped run draw is worth more.

The big picture is clear: almost all draws are better than nobs draws. You should not throw away any draw that can be completed with a single card just to hold onto a jack for nobs potential.

Notice that the only draw worth less than nobs potential is drawing a 5-card flush from 2 suited cards, which is a longshot parlay outcome, as it requires drawing not just 1 but 3 needed cards.

Should I Put a Jack in My Own Crib?

You certainly won’t hand any points to the enemy by putting a jack in your own crib. That 0.26 point or whatever is yours either way. But you should expect fewer jacks in your crib than other cards, since most opponents will avoid discarding a jack to you. This supports the idea that, against the vast majority of opponents, you should favor holding onto a jack on your own deal if all else is equal.

This also means to expect your opponent’s hand to be slightly richer in jacks, on average, than in other 10-value cards, to the same slight extent as you expect to see them less in your crib. This should inform your pegging in a small number of cases.

For example, if you have JJQQ (neither is cut) and your opponent opens an 8, reply with a queen rather than a jack. Your opponent can safely pair you, and it’s more likely he has a jack than a queen.

For the same reason, opening a jack to set up trips (including setting it up for round 2, as in the JJQQ example above) is a better option than doing the same with any other 10-value card.

When you’re pone, this only applies if your opponent disfavors putting jacks in his own crib—which many opponents may not even think about. In general, it matters a lot more when you’re dealer.

What About a Cut Jack?

Most of the time, a cut jack will just be a random event that you don’t think about in advance—a passive, background thing that only rarely factors into decisions.

It might matter in a tight endgame situation where it’s the only thing that makes a victory possible, in combination with a particular hand score or pegging situation. The rest of the time, it’s a chance event that doesn’t force your hand one way or the other.

The table shows the probability of cutting a jack, as well as the expected value of the cut in points, depending on how many jacks you’ve been dealt.

Jacks in Hand Chance of Jack Cut Expected Value (EV)
0 8.70% 0.17
1 6.52% 0.13
2 4.35% 0.09
3 2.17% 0.04
4 0.00% 0.00

As you can see, a decision would need to be razor-thin for this possibility to factor in.

Have you ever changed your discard choice based on the chance of a jack cut?

Author - Jim Donahue


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