In our last post we said that scoring an extra point per game will add an extra 1.7% on top of your win rate. Today we’re going to talk about how to discard to score that extra point. Discarding is such a ridiculously exciting topic that we’re not even going to give an overview. Let’s just jump right into the data!
Dealer discard tableThis table shows the average number of points you can expect in your crib, based on the two cards you put in your crib.
You can use this table when you’re having a tough time figuring out what to toss in your crib. For example, you’re holding 2-3-5-6-J-Q and it’s your deal. You probably want to give yourself either the 2-3 or the 5-6, but it’s not obvious which. You’ll end up with 4 points in your hand either way, so what should you put in your crib? Discard table to the rescue: if you toss the 2-3 in you’ll average 6.9 points in your crib; if you toss the 5-6 you’ll average 6.4 points. Keeping the 5-6 in your hand and tossing the 2-3 gives you a 0.5 point advantage in your crib. (5-6-J-Q is also a better pegging hand, but that’s a topic for a future article).
Michael Schell put together some good articles describing how to choose your discards using a discard table. I recommend using his technique, but with our discard tables. (We believe ours is more accurate, since it’s based on a very large sample of hands from actual human play, rather than a smaller sample or computer simulations).
Here’s a visual display showing how those discards stack up with each other. Pairs show up in blue, and cards totalling 15 show in red.
As expected, 5-5 is far and away the best discard. Also unsurprising: 10-K, 9-K, and 9-Q show up at the bottom of the rankings.
You’re probably not going to split up a pair or a 15Hypothetical scenario: you deal yourself 3-3-6-7-J-J, and you’re not sure what you should put in your crib. Looking at the discard table you see that 3-3 will get you 5.9 points (on average), 6-7 will get you 4.9, and J-J will get you 5.1. It looks like 3-3 is the best discard, but the discard table is a little misleading here. You’ll get the “pair for 2” for the 3-3 or the J-J whether or not they’re in your crib, as long as you don’t split them, so you probably don’t want to consider those points when evaluating the discard. The entry in the table for the Jacks has even more built in points -- between the two Jacks you’ve got about a 50% chance of scoring “1 for his nobs”, for an extra 0.5 points or so on average.
If we ignore those extra points, let’s call them the “intrinsic points,” we see that 3-3 and J-J are actually poor discards, averaging 3.9 and 2.6 points respectively. The 6-7 is probably the right discard, beating out 3-3 by a full point.
Here are updated versions of the charts, with pairs in blue and cards totalling 15 in red. The left chart includes the intrinsic points in each average, while the right chart exclude those points. Note that Jacks have an intrinsic value of around 0.25 points, and we’ve accounted for that on the right chart, too.
Removing the intrinsic points changes everything. 5-5 is no longer the top of the heap. 2-3 beats it by almost half a point. And K-10 is no longer at the bottom, since it does better than pairs of 10s, Jacks, Queens or Kings!
Except for 5-5, the pairs look like pretty bad discards. It’s more important to throw yourself cards that add to five or could turn into a run.
Pone discard tableHere’s the corresponding table for pone, showing average number of points in dealer’s crib based on pone’s discard:
Of course you should subtract the values in this table from your hand value when trying to decide what to toss into your opponent’s crib. As before, Michael Schell’s articles do a good job explaining the logic.
Here’s the visual layout of the average crib scores based on pone discard: