Do you think the N64 and PS1 were competing?  How about the Gamecube and PS2?  I think these systems were competing.  Playstation kept gaining marketshare with each generation while Nintendo was losing it.  They were competing.  What kind of games did Nintendo make during this era?  3D Mario, 3D Zelda, Mario Kart, Smash Bros, Animal Crossing, etc....  They were making the types of games that are selling the Switch right now.

PS5 and Switch do not occupy a different market niche.  They will compete over the same gamers just like the PS1 and N64 did.  They make the same type of games and therefore appeal to the same type of gamers.  They most definitely will compete. 

The main thing that has changed is that Nintendo has a lot more advantages this time around:
1) The franchises I listed above are much more popular on Switch.
2) Switch is a better value than a traditional home console, because it can be used as either a home or handheld system.
3) Switch has a much bigger third party library compared to N64 or Gamecube.
4) Switch will always be significantly cheaper than PS5, which is a huge advantage in a recession (like the one going on now).

Nintendo is making the same types of games that it has always used to compete against Playstation.  That is why it will compete against the PS5.  The main difference is that Nintendo is much more prepared for this contest, and that is why the Switch will prevail against the PS5.  Same competition.  Different victor.

PS4 is been out stock in most parts of Japan but it seems that stock will be available around June 17th just in time for the last of us part II. The same is happening in Australia.

So the weeks before the last of us part II we will see low numbers for PS4

Again, you're trying to force Switch into the paradigm of past generations which it just doesn't fit due to its hybrid nature.

PS5 will fill the same market role as the PS4, so if Switch didn't directly compete against 4, there's zero reason for it to suddenly compete against 5.

Let me put it this way; no system with a direct competitor as successful as the Switch has ever sold better than the PSP. (And even then its questionable just how directly PSP and DS competed) How much do you expect PS5 to sell, lifetime?

The Switch doesn't directly compete against the PS4, because the Wii U directly competed against the PS4.  The Switch and the PS5 are both the respective successors. 

How much do I expect PS5 to sell?  There is still more info I need, because I need to know the marketshare split between PS5 and Series X.  Neither console has even been revealed yet so that is impossible to tell.  Switch is taking away sales from both systems.  I also need to know when the Switch will peak, and that also has yet to be determined.  Giving a very rough approximation though, I'd say PS5 + Series X combined will sell about 100m +/- 30m.

See this first paragraph is just completely arbitrary. PS4/5 will fill the same market niche, a mainstream AAA machine, either Switch competes against that or it doesn't, both or neither.

And I will bet you right here and now that PS5 + XSX sell more than 130 million combined. Will you take that bet?

What is the point of betting something, when you won't know the result until about 10 years later?  I don't think either of us really knows what we'll be doing in 10 years.  If you want to bet, let's wait for them to reveal their consoles, and then we'll see if we can come up with a bet that can resolved in the next year or two.

I'm willing to commit to the bet now because that's how certain I am in the outcome. This gen is looking like it'll settle with around 190 million PS/Xbox systems sold. That total is NOT going to drop by 60 million next gen because of Switch.

It's not about the certainty of the outcome.  It's more about that I doubt we will both be on this forum 10 years from now.  I've never stayed on any internet forum that long, and in fact I don't even know if this forum will be live 10 years from now.  The issue is not who is right, but that the winner probably won't be able to collect in any practical way.

Can we come up with a similar bet that can be settled in a year or two?

I for one certainly plan to stick around on VGChartz as long as the forum is online; I've been here ten years already. And I really don't think it'll take that long either, they'll probably sell 130 million in the first five years.

Not sure what parameters could really decide this within just the first year or two.

VGC has year end 2016 numbers for PS4 + XB1 as 53.5m+27.9m = 81.4m.  That is 43% of the 190m total you suggested about 3 years after launch (including all holiday sales). 

So, 43% of 130m is approximately 56m.  I'll bet that combined sales of PS5 + Series X are 56m or less combined by year end 2023 (using VGC numbers).  That should be enough time to tell which of our predictions was actually on the right track.