Part 2 Take or Pass:

For our analysis we will make the same assumptions as in Part 1:

• you play $10 a point
• the rake is 5%, with the winner paying 10%
• At least $80 are at the table

Calculations without rake

Let's start with the equity for a take when there is no rake:

Your equity is $-19.01, exactly the value, the software displays (+0.951 x -2 x $10)

That means, on average you would loose $19.01 by taking in this position. Your alternative is to pass the 4 cube and that means losing two points, $10 each, for a total of $20.

Taking saves you $0.99 on average and is the correct decision.

Calculations with rake

Now we do the same calculation, with the difference that your payout is just 90% (100% - 10% rake).

Your equity for taking is $-20.62.

That means that on average you would loose $20.62 if you take in this position. Once more, your alternative is to pass the 4 cube and that means losing two points, $10 each, for a total of $20.

Taking costs you $0.62 on average and is a mistake (eg:-0.031).

Rake adjusted Take point:

The basic take point of 25% in money games is calculated as follows:

You compare the equities for pass versus take. If you are doubled to 2 you can either pass, losing one point on average or take. The equity for the take is calculated qas follows: Let "p" be the chance that you win. Then the chance that you don't win is 1-p. So your equity is:

2p - 2 x  (1-p) this can be reduced to 2p -2 + 2p or 4p - 2

So we can take when 4p - 2 > - 1 (= the one point we lose when we pass)  , that transforms to 4p > 1 or p > ¼ or p > 25%

Please note this formula does not take into account that you could redouble, so this calculation is only valid for a dead cube.

No we do the same calculation, but introduce the new variable "r" that is the rake in percent. So as the winner pays for both players instead of 1 point he will receive only 1-2r points. We still lose one point when we pass, but when we take our calculation looks different:

2p x (1-2r) - 2 x (1-p) = 2p -4pr -2 + 2p = 4p - 4pr - 2

So we should take when 4p - 4pr - 2 > -1 or 4p - 4pr > 1 or p (4 - 4r) > 1 or

p  > 1/(4-4r) or p > ¼(1-r)

The following table will give you an idea on how the rake affects the take point.