Pineapple discard test

Here's something I stumbled on while using Poker Probe to work on a completely different problem...


NL Pineapple, throw one after the flop. You are all in with JcJdTd. You know your opponent has AA and will discard the kicker regardless of what comes.


1. The flop is 9d6c3h. Which card do you throw?


2. The flop is 9d6c3c. Which card do you throw?

Why aren't you folding?

Mack - If you keep JdJc with flop 9d6c3h, and if the aces are any suits, and if opponent has non-J as kicker, then you need a jack without an ace. There are 2*41 = 82 ways to get a jack without an ace. However, if your opponent started with a J as kicker, then you have about half that many chances (1*42 = 42).

The weighted average of these is 80.14 chances to beat the aces.

You’re an underdog by about 10.27 to 1.


If you keep JdTd, you also know location of 9d6c3cJc.

Opponent could have started with a variety of aces and kickers, the weighted average of which is 85.3 chances. (7506/88 = 85.3)

You’re an underdog by a bit less than if you keep the pair, about 9.59 to 1.


Thus you should keep JdTd and throw the jack of clubs.


I don’t see how the result would be any different if you substitute 9d6c3c for 9d6c3h as the flop, except in this case it wouldn’t much matter which jack you threw.


Since you didn’t give specific information regarding the kicker or the suits of the aces, I took a weighted average. Kind of a tedious counting and averaging problem (16 different cases) and I easily could have an error somewhere.


What are the results from Poker Probe?


Buzz

I ran this against AsAh, kicker unknown.


JdTd won 10.36% (8.65:1) against both boards.


JdJc won 8.56% (10.68:1) against 9d6c3h but


JdJc won 13.21% (6.57:1) against 9d6c3c.


I assumed that this increase is because it picked up the runner-runner flush draw. To check, I put an Ac in the opponent's hand (a 50% likelyhood he has it). It went right back to 8.56%. I averaged the two and got 10.885%, a whopping 0.5% over JdTd with the same board. Not much to write home about, but I found it interesting.