1. One Yes share in every option is equal to 1 mana
   • Because we know exactly one option will resolve Yes, and the 1 Yes share in that option will be worth 1 mana, no matter which option is chosen.
2. One No share in an option is equal to 1 Yes share in every other option
   • Because the 1 No share pays out 1 mana in exactly the cases as the Yes shares — when any other option is chosen.

Exercise for the reader

Use the above two identities to turn 1 No share in each of first n-1 options into Yes shares of the last option plus mana. This conversion is needed when the user buys Yes shares of an option!

Solution

Apply the second identity for each No share. You will get n-2 Yes shares of every option except for the last, for which you will have n-1 Yes shares.

Apply the first identity n-2 times. You now have n-2 mana plus 1 Yes share in the last option! Hooray!

But what do we do with excess mana created as a by-product of this conversion? We use it to buy you more Yes shares in your requested option, of course.

In our arbitrage system, we buy up to a much larger amount of No in each option so that after conversion to Yes shares plus mana, you are on net down by the originally provided amount of mana.