07-29-2013, 01:02 PM

Mick: you said, with South holding no aces, it's 15 out of 51. There are 81 cases (3^N, where N is the number of missing aces). Just a typo?

Flack: the order doesn't matter. Note that the cases count both (say) NNE, and ENN. The point is, this guarantees that you capture every case, and that each case is equally likely (or close enough to not really matter, for an at-the-table use). When South has 1 ace, there's only 1 case where North has 3...but 3 ways where North has 2. This makes for a very simple counting approach.

On the assumption that your data's correct...it is hard to use. The first improvement: sort it. # of aces for S is primary, then W, then N, then E. Don't make someone search through to find the cases that apply. Now you've got a storyline. If South has 1 ace and wants to reach North...bang, we can instantly find the rows. S=1, W=0, N>0. Also: for presentation, just show about 3 digits...down to tenths of a percent. There's no reason to go beyond that, as even in Monte Carlo sims, the variance of most cases should actually be larger. (In fact, the fact that your variance is much smaller, is another reason to suspect that you're just in a recycling mode....the RNG is repeating the exact same sequence.) As a practical matter, differences of even 2-3%, are just not relevant. There are situational reasons that will *swamp* that.

Flack: the order doesn't matter. Note that the cases count both (say) NNE, and ENN. The point is, this guarantees that you capture every case, and that each case is equally likely (or close enough to not really matter, for an at-the-table use). When South has 1 ace, there's only 1 case where North has 3...but 3 ways where North has 2. This makes for a very simple counting approach.

On the assumption that your data's correct...it is hard to use. The first improvement: sort it. # of aces for S is primary, then W, then N, then E. Don't make someone search through to find the cases that apply. Now you've got a storyline. If South has 1 ace and wants to reach North...bang, we can instantly find the rows. S=1, W=0, N>0. Also: for presentation, just show about 3 digits...down to tenths of a percent. There's no reason to go beyond that, as even in Monte Carlo sims, the variance of most cases should actually be larger. (In fact, the fact that your variance is much smaller, is another reason to suspect that you're just in a recycling mode....the RNG is repeating the exact same sequence.) As a practical matter, differences of even 2-3%, are just not relevant. There are situational reasons that will *swamp* that.