VP Return Table Calculations

Here's a question for the math guru's (which has probably been asked before). For a given VP game like JoB, why do the number of possible combinations for a particular hand (say a RF) change with the pay table? For example, the combinations for a RF in Job 9/6 is 493512264, while in Job 9/5 it is 496237776. It would seem to me that the number of combinations for a hand like a RF is a fixed number for a standard deck of 52 cards. Thanks in advance for your feedback.

It's not the same because the optimal drawing strategy changes based upon the paytable.

For example, lets say you have Ac Kc Tc 6c Qd.

In 9/6 JoB, holding Ac Kc Tc 6c is the optimal play. Generally 3 to a Royal is correct vs. 4 to a flush, but this hand has a flush and a straight "penalty" for the royal flush draw that make the 6 for 1 4 to a flush draw a better choice here. "Penalty" means a card that you discard that would help you complete a draw.

But in 9/5 JoB, holding Ac Kc Tc is the optimal play because a flush is only worth 5 for 1.

This example and other scenarios makes a Royal Flush in 9/5 JoB a little more likely.

But if you never adjust your strategy based on the paytable, then the probability of you making a Royal would not change.

Quote: joseph2356

Here's a question for the math guru's (which has probably been asked before). For a given VP game like JoB, why do the number of possible combinations for a particular hand (say a RF) change with the pay table? For example, the combinations for a RF in Job 9/6 is 493512264, while in Job 9/5 it is 496237776. It would seem to me that the number of combinations for a hand like a RF is a fixed number for a standard deck of 52 cards. Thanks in advance for your feedback.

The two different numbers, 493512264 and 496237776, would automatically tell me that there are strategy differences between the two games.

It appears that the root of the issue is that I did not understand what was meant by the term "combinations". I thought that it referred to the total number of ways that a particular winning hand (i.e. RF) could be achieved. Based on the posts here, I now understand that it means the number of ways a winning hand can be achieved by playing the correct strategy. Thanks for the help.