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Rake adjusted cube handling

When playing online, the house takes a fee (rake) from the winner of the game. So I was wondering if that can change the proper cube decision of some positions. We will look at two simple bear offs, in one position we can offer a double in the other we are offered a double and have to decide if we take.

Doubling

Let's take position 574 as an example. We will assume you play $10 a point and the rake is 5%, with the winner paying 10% (also paying the 5% for the loser), a very common setting in today's backgammon online industry. The following calculations are based on the assumption, that you have at least $80 at the table, the maximum amount you could win or loose, when you decide to double.

Take or Pass

As an example we will look at position 594, you are white and have to decide, whether you should take or pass.

In a regular money game this is an easy take.