How dominant assurance contract fix free rider problem? Dominant assurance contract is a proposed solution to free rider problem in crowdfunding. It pays more money to payers (for example 105%) in case of failure of campaign. Is it make paying a dominant strategy? I think not.

Suppose a city need a road that make 100\$ benefit for each person. It costs 8000\$ and entrepreneur offers 5\$ in case of failure for every 80\$.


normal strategy (paying 80\$):


in case of failure: 5\$ benefit
in case of success: 20\$ benefit

free rider strategy:


in case of failure: 0\$ benefit
in case of success: 100\$ benefit



That shows a free rider can risk on the success probability (that helping does not affect it so much) and make a higher profit. Where I am wrong? Is there any additional hypothesis that dominant assurance need to work?
It was established in the comments that the source of this claim is Tabarrok: The private provision of public goods via dominant assurance
contracts via Wikipedia.

Tabarrok writes


  assume that a plain is flooding and that a dike must be built to hold back the river. It
  is known with certainty that the flood will be averted if the dike reaches 6ft.
  If the dike doesn’t reach 6ft then the river overflows and the builder’s efforts
  are wasted. Assume that the agent’s choice is binary, he can help to build the
  dike or not.  [...] 
  note that the game really consists of two distinct elements [...] Consider column one; the problem in this column is not free
  riding. [...] The problem in column one is that the agent doesn’t want to waste his effort
  in building a dike which won’t hold the river. Each agent lacks “assurance”
  that the others will contribute in the event that he contributes. 
  The problem in column 2 is quite different. In column two each agent
  assumes that the public good will be provided regardless of his actions. Each
  agent, therefore, wishes to “free ride” on the others.  [...] 
  The assurance problem can be overcome via an assurance contract. 


[emphasis by me]

So assurance contracts are not claimed to overcome the free riding problem.