8 Feb

The Illusive 29: Best Hand in Cribbage

What is the best Cribbage hand, and just how rare is it?

The Illusive 29: Best Hand in CribbageEveryone knows the best poker hand is the Royal Flush, the best blackjack hand a natural two-card 21 (A+10), and the best thing ever to come from SquareSoft labs was Final Fantasy X. [Okay, that last part might be a matter of (highly popular) opinion, but let’s not dwell on such inconsequential details.] What few people outside of hard-core Crib fans know is this:

What’s the absolute best hand to be dealt in Cribbage?

Just being familiar with the rules of the game isn’t going lead to a direct answer. You need to have a perfect memory and quick recall of the scoring system. Or you could just continue reading, where you’ll soon discover how and why…

The Best Cribbage Hand is 29

The illusive 29… It’s often whispered about in veteran Cribbage circles. Some boast that they’ve been dealt this miraculous hand, but not all are to be believed. It is the rarest of all hands, awarding the highest possible amount of points.

How do you achieve a hand value of 29?

To do this—by traditional Cribbage scoring rules—you’ll need to be dealt a very specific arrangement of cards. The up-turn card must be a 5 of any suit, while your hand must contain the other three 5s, and the Jack of the same suit as the up-turn card. It should look similar to this…

What is the best Cribbage hand, and just how rare is it?

How to Score J-5-5-5 +5 to 29

Applicable Cribbage scoring to make the all-but-mythical hand of 29 includes points for pairs, a combined total of 15, and Nobs (Jack of the up-turn card’s suit). Let’s examine:

There are 6 ways to create a Pair of 5s, worth 2 points each = 12 Points

There are 4 ways to combine three 5s for a total of 15, also worth 2 points each = 8 Points

There are 4 ways to combine the Jack with a 5, also for a combined total of 15, and again worth 2 points each = 8 Points

Holding the Nobs is worth = 1 Point

12 + 8 + 8 + 1 = 29

How Rare is a Hand of 29 in Cribbage

The short answer to that question is 1 in 216,580. If you prefer the long answer…

There total number of 6-card hands that can possible be dealt are:

(52*51*50*49*48*47/720) = 20,358,520

Now, you’d have to be dealt three 5s and the Jack of the other suit, plus any other two cards. The total number of qualifying 6-card hands is:

4*(47*46/2) = 4,324

Finally, we need the up-turn card to be the other 5. There are 46 cards left, the odds of which are:

1/46

Now, if we divide the total of qualifying hands by the total of 6-card hands, and the probability of that last 5, we get:

4,324 / 20,358,520 / 46 = 1 / 216,580

The “30 is Better than 29” Debate

Some players have debated that the dealer can actually score 30 points, 1 higher than 29, by being dealt all 5s, with the Jack as the up-turn card.

The argument is that, since the dealer receives 2 points if the up-turn card is a Jack, then his hand total would come to 28, plus 2 points for the up-turned Jack; a total of 30 points. And as we can all agree, 30 is higher than 29.

The problem with this argument – and the reason those who advocate for 30 always lose – is that this hand is still worth only 28 points. Yes, the player has pegged 30, but the “hand total” remains 28. And the legendary score of 29 constitutes the ‘best possible hand in Cribbage‘, not the best possible score for a single round of play.

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