To all those saying Tryndamere's chances to crit you 3 times in a row are 35% * 35% * 0.35 ~= 4.3%

Old timer tryndamere veteran here.

This is how the pseduo rng of league works:

Every successive critical strike will reduce the chances of the next attack being a critical strike-- the reduction is based on how much critical strike chance you have. More critical strike chance equates to a lower reduction; 100% critical strikes chance means 0% reduction. The reduction as a function of critical strike chance is non linear. It probably depends on how long the string of crits is too.

Every successive basic attack that isn't a critical strike will increase the chances of the next attack being a critical strike-- the increase is based on how much critical strike chance you have. More critical strike chance equates to a greater increase; 0% critical strike chance means 0% increase. The increase as a function of critical strike chance is non linear. In fact it probably depends on how long the string of non crits are so far too.

This means the chances of actually critically striking 3 times in a row with 35% crit chance are less than 0.35 * 0.35 * 0.35 = 4.3%, because your effective critical strike chance will be reduced for each successive crit. It is probably closer to 0.35 * 0.3 * 0.2 = 2.1% (not sure about the exact coefficients since those aren't public and I haven't tried to collect data to fit the curve myself)

However-- and here is the important bit, if your critical strike chance CHANGES, the algorithm will reset.

So an experienced and informed Tryndamere player will not spin on you at full fury; instead he will try to walk up to you with around 85 fury. He has a 29.75% chance of doing a crit assuming no critical strike items or runes. If he manages to get a critical strike with 85 fury, it will bring him up to 95 fury. His fury has changed so the algorithm has reset. His chance of critically striking you at 95 fury is 33.25%. Regardless of whether he critically strikes you or not, his fury will change again, resetting the algorithm.

So his chances look more like 0.2975 * 0.3325 * 0.35 if he games the system and crits three times in a row.

If he crits twice in a row and misses the third crit, his chances of getting three crits out of four attacks look like 0.2975 * 0.3325 * X where X is GREATER than 0.35, because his third attack DOESN'T change his critical strike chance because he's already capped on full fury, but the fact that it wasn't a critical slightly increases his chance of making a crit on the next attack.

Generally a very good Tryndamere will try to use Spinning slash to help him game the system too, because it grants 2 fury per target it hits-- therefore resetting the algorithm.