Are the odds one in a million?

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This is a from a card game call Magic the Gathering
And my question is regarding this video during a tournament match (best of 5). One in a million. You dont need watch the video I will explain the scenario here, but is very exciting.

In this match, player Gabriel Nassif is at 9 life.
And player Patrick Chappin cast 5x copies of Ignite Memories targeting Nassif

Ignite memories: select a card a random from player hand and deal damage equal to that card convert mana cost or CC for short.

Nassif have 3 cards in hand at that moment.

Ignite Memories CC = 5
Grapeshot CC = 2
Rite of Flames CC = 1

Dont be confused because the 5x Ignite Memories are from Chappin. But Nassif also have one Ignite Memories in hand. In Magic this is call a mirror match because players are using similar strategies

So if a single Ignite Memories is select from Nassif hand, Nassif will loss
1x 5 CC + 4 * {1 CC or 2CC} >= 9 life

If select 5x Grapeshot mean 10 life, also lose.

Max damage possible is selecting 5x the Ignite of Memories for 5x 5CC = 25 life loss
Min damage possible is selecting 5x the Rite of Flames for 5x 1CC = 5 life loss

Again Nassing beign at 9 and 5x copies of Ignite Memories,
You loss if your life reach 0 or lower.
What are the odd of survive?.

At the end Nassif survive and won that game at 1 life but finish lossing the match in the next game.

I only could add 2 link so if anyone want check for the other 2 cards:
gatherer.wizards.com/Pages/Card/Details.aspx?name=GRAPESHOT
gatherer.wizards.com/Pages/Card/Details.aspx?name=rite+of+flame

I will try to add some context.
As far I can go the total number of outcomes is $3^5$
Now how count wich of those outcomes cause the player to lose can't figure it out.

Also give the motivation of because this is interesting, for a game planning the possible outcomes afect how you make the strategy.

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If he takes a $5$ hit at any time he is lost, because the other four hits are at least $1$ each. He can afford up to three $2$ hits. There are $3^5=243$ sequences of hits. The number that let him survive are $1$ (all $1$ hits) $+5$ (one $2$ hit and four $1$'s) + $10$ (two $2$ hits and three $1$ hits) + $10$ (three $2$ hits and two $1$'s)$=26$. So his odds of survival are $\frac {26}{243} \approx 10.7\%$, much better than one in a million.