Final scenario here (with the team that wins the cup and also picks first overall) is especially delicious. I might try to ballpark just how outlandish it is tomorrow. https://twitter.com/DownGoesBrown/status/1275217359448539137

First of all, @DownGoesBrown's article is great and you should read it. At the risk of spoilers, I thought I'd take a hand at computing the probability of the outlandish scenario at the end. It's less outlandish than I expected.

First, suppose that the Rangers win the cup. I'll be putting out full playoff chances later this week, but at the moment I have this at 2.94%, using my predictive model(s).

Now, if the Rangers win the cup, that means that Carolina lost to them in their play-in series. Let's also imagine that Toronto loses their play-in series against Columbus. Toronto is slightly favoured there, so I give the chances of them losing the play-in as 48%.

For today's purposes, we're gonna treat those two events (rangers win the cup and columbus beats toronto in the play-ins) as independent events, which they very nearly are.

Now, Carolina and Toronto are both play-in losers. What is the chance that Carolina wins the first lottery, and that Toronto wins either the second or third lotteries? Here the calculation breaks into three pieces.

First, we need two or three play-in losers to win their lotteries. So the play-in losers (remember the lottery happens before we know who they are) have to pick 1-2-not3, 1-not2-3, or 1-2-3. Those probabilities are 4.29%, 4.73%, and 0.96%, respectively.

Next; /after/ the play-ins, we need Carolina to win the first overall spot, for which the chance is 1/8, and then we need the 2-or-3 play-in lottery winner to be Toronto, which is 1/7 for the first two scenarios and 2/7 for the third scenario.

So, a seventh times 4.29% + 4.73% plus two sevenths times 0.96%, all times an eighth, gives 0.195%, the chance that Carolina's first overall pick is #1 and that Toronto's first overall pick is #2 or #3, given that Carolina and Toronto are both play-in losers.

Now, this is important because the Toronto first was traded to Carolina, but with top-ten protection. Toronto's pick can't be top-ten without them winning a lottery.

So, according to the conditions of the Marleau trade, the Leafs would keep this #2 or #3 overall pick, and give the Hurricanes their first /next/ season. The Hurricanes only have one first-rounder now, and it's first overall! How lovely!

Except, the Hurricanes traded a first overall to the Rangers this year, in the Skjei trade, and now they only have this one to give them. The rangers win the cup, and also get the first overall.

Probability of all of these things coming to pass: 2.94% times 48% times 0.195%, which is to say, 0.00275%. Odds of about 36,328 to 1 (against).