I think, though ... you are guaranteed a psi dude the first time you put people in the chamber?
I recall this not being the case. You're just really likely to have someone with high will by the time the Psi Lab is unlocked, and thus very likely to have your first testers be psis.
I'm going to assume the odds are skewed until you get your first one though. I often play Classic Ironman with the second wave psi reduced option, and I always get my first PSI easily, and then take forever to get another, despite the fact that my later entries to the PSI chamber almost always have higher willpower (thanks to getting around to purchase Iron Will and generally having more top-ranked units).
Much like the aiming thing, where on most difficulties every shot missed increases your odds of hitting with later shots, I'm guessing the game is cheating in your favour in regards to that first Psi unit. Maybe not guaranteed, exactly...
Edit: Okay, found the actual equation.
Odds are based on the
number of psionic soldiers you already have. This is the single most important factor determining whether or not you will get a PSI unit. So yes, your odds are significantly better until you get your first PSI solider, and then it plummets.
iChance = int(float(iTraineeWill) / class'XGTacticalGameCore'.default.SW_RARE_PSI);
iChance /= float(1 + BARRACKS().GetNumPsiSoldiers());
return Roll(iChance);Note that this is with the second wave option enabled. This is less important for "normal" mode, in which case units of the third rank have by far the highest chance of being gifted, while your average higher ranked units have a lower chance (although those with high will are a bit better off) and rookies have a slightly higher chance than the average top ranked soldier but less variance. Never ever test a soldier of rank 6 or 7 - they have lower will AND no bonus whatsoever.
See:
iTraineeRank = arrCandidates.Find(kSoldier);
if(iTraineeRank >= 0 && (iTraineeRank < 6))
{
iChance += Max(0, 75 - iTraineeRank * 20 - iGiftedSix * 40);
}There are 8 ranks, and units below rank 6 get a significant bonus to their PSI chances. This additional bonus does NOT apply when the second wave option is enabled.