Gatherer text:

"Whenever a Samurai or Warrior you control attacks alone, untap it. If it's the first combat phase of the turn, there is an additional combat phase after this phase."
https://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=548545

Keyword: "...first combat phase..." The second clause should only trigger ONCE, and ONLY if it is the first combat phase of the turn, not the 2nd, not the 3rd, not the 4th. It doesn't say "first combat phase after this card comes into play, just first combat phase." Period.

This is significantly different wording from Combat Celebrant.

https://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=547615

C.C. allows an 'unqualified' additional combat, when exerted, with no check for which combat phase/step number the ability is triggered during.

Putting a Helm of the Host on a Combat Celebrant and exerting the token is a legit infinite-attacks combo, but putting it on Raiyyu, Storm's Edge should only render a single "second" extra attack phase, not a 3rd, 4th, 5th, etc. During the second attack phase, the ability should not trigger an extra attack phase since it is not the "first" attack phase of the turn.

However, in the game I just played, someone got infinite attacks out of Raiyyu, with a Helm of the Host on it, by attacking with their Bruenor Battlehammer, losing me the game and not letting me progress to my next turn where I might have been able to turn it around with a Timetwister into possibly some other stuff from my Oracle of the Alpha.