What is proper ratio of money spent on amp/preamp/integrated vs speakers? 1:1?

Free speakers! That’s the solution! And my wife would be so much happier too!

Wife happier with no speakers.Or maybe invisible speakers.

eddie,  you will get a million answers go out
spend as much money as you can   forget about it 
 you will go nuts trying to
have fun   

@tlinkie, yes white  speakers, white background goes down really well. Helps with imagery a bit too.

As for this magical ratio, well as @mikapen said sometimes spending more = worse sound. Not all companies are like Harbeth or ATC where spending more gives a better sound. Far from it, especially for amps/cables etc. But we all know that, don't we?

Again, it all depends upon at which price point you can hear the performance flat lining.

You might have to discover where the sweet spot in a particular range might be, or else risk being forced out of your listening room by the sheer number of boxes which have almost surreptitiously taken up residence.

I have a friend whose front room looks like he's installed a console from Cape Canaveral. Seriously, reconnecting or rewiring his receiver is a two man half day job.

Rule of thumb is that speakers (including subs) should be 1/2 your budget. If buying used gear it throws it off, but still. 
 
If a $1000 speaker needs a $2000 amp to sound good, then it’s not a good speaker. 
 
How I would spend $10,000: 
 
• -$3000: Ascend Acoustics Sierra Towers w/RAAL. 
• -$1800: Dual Rythmik F12 subs. 
• -$1000: Room treatment.  
• -$1300: MiniDSP SHD. 
• -$2200: ATI AT522NC amp. 
• -$700: Cables (don’t need to spend this much, but why not).