:) just between you and me I had to check the analysis twice over as I suddenly had a horrible thought that A other D might wreck my entry...but all is well! Your question also raised an interesting issue on penalty doubles: some use very direct assessment- how many defensive tricks (like mum taught) and others seem to use variety of proxy methods: how many cards in their (inferred) suit bid and an old one from Silver Bull with different but apparently equally robust proxy ideas....so I’ll do some more BBO research and then look out for a useful hand: I’m use to the room here so it would be my first posting there! Meanwhile thank you again for such a stimulating question :) x. 0deary. (0ooops old name)