Ah Ha!
If Rho held
Jxxx
AKxxxx
Q
xx
then he could defeat me by playing, at tricks 1,2,3, the A, K and another heart.
So: Either he doesn't have this holding or he did not realize how it would go.
Even if it is
Jxxx
AKxxx
Q
then playing A, K and another heart forces me to guess what to do with the clubs early on.
The idea is this. Playing AKx of hearts forces a ruff on the board since I can hardly ruff in my hand when Rho has four trump. So I pitch a
from hand and ruff on the board. But now the
J doesn't drop and I no longer can finesse the T so Rho gets his J.
After riffing, say I play a
and then take the Q. It would be good to pitch a losing
on the long
but entries are in short supply. If I take the two trump on the board and come to hand with a
and play a top
, perhaps hoping trumps are 3-3, I find that they are not 3-3/ I then play a high
, Rho lets it hold the trick. Then a small
, Rho ruffs and plays a
I ruff, I am in my hand, with only
cards left.
In the second case I listed, where Rho is 4=5=1=3, being in hand will be fine if Lho holds
Qx. But that but who says that's the way they are. My guess is that if this began A,K,x in hearts I ruff on the board, try the 1D suit, and when the Q comes up I either play for
to be 3-3 or else I play for the
Q to be on my right.
I thought it surprising that Rho did not cash the
AK at tricks a and 2, but it just now occurred to me that if he had four spades to the J he might have then played a third
as well.
So that's is some evidence that Rho holds three spades, not four.
Ok, coffee please.
Oh. I can't resist this addendum. If we agree that Rgo would play AK and another heart whenever he held Jxxx in spades, then of course we will not take the finesse. But wait. If we do not take the finesse here because "obviously" Rho does not have Jxxx since he did not begin with AKX in hearts, then he does not have to play AKx because we are going to not take the finesse and so he gets his J anyway, without him having to give the sluff ruff.
Oh my.
Also I can see why maybe Rho switches at T2 if he started with only five hearts. So I think the switch is evidence for him holding five.