rush

You do start out with all ten houses. The houses you have for the next round aren't necessarily going to be your top eight, but rather the eight you ranked highest that also chose to ask you back or whatever number under eight asked you back. Let's say that I ranked the houses like this after round 1: Kappa, Tridelt, KD, Theta, Pi Phi, Zeta, Chi O, AXO, ADPi, AOPi. If every house asks me back, I don't have to go back to ADPi or AOPi and I cannot get a bid from them. If only Theta and Pi Phi cut me, then I still have to go to ADPi and AOPi and have them in the running for a bid, but I still go to the maximum number of houses. If Tridelt also cuts me, then I only go to seven houses.

This continues to apply as you move through the rounds. If my pref night from that initial list has me going to KD and Zeta, those obviously weren't my top two but I will get a bid to one of them so long as I indicate that I would accept a bid to either.

you are not guaranteed a bid. it is ONLY guaranteed if you get to pref and then if you put down every house you went to on pref on your card, then you're guaranteed one of those two.