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We introduce a type $B$ analogue of the nil Temperley-Lieb algebra in termsof generators and relations, that we call the (extended) nil-blob algebra. Weshow that this algebra is isomorphic to the endomorphism algebra of aBott-Samelson bimodule in type $\tilde{A}_1$. We also prove that it isisomorphic to an idempotent truncation of the classical blob algebra.Thus weprovide strong evidence in favor of the recent Blob vs. Soergel conjecture.

The nil-blob algebra: An incarnation of type $\tilde{A}_1$ Soergel calculus and of the truncated blob algebra