[MarkGritter]

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Interesting tidbit demonstrated: It is always incorrect to play an ace as the kicker to two pair in front. Do you see why?

Mark, can you explain this better? Thanks

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I should have said "to two pair in back", sorry. I confirmed that this is still the case in the latest 1M-hand iteration (which has some bugs fixed.)

If you have two pair in back, the difference between a lower kicker and an ace kicker is less than 1%. Putting the ace in front instead always increases the strength of the front hand by more than this.

For example, 51.1% of fronts are QQK or worse, while 53.9% are QQA or worse. Now look at this example with two pair in back:

two pair Threes and Deuces Four kicker , 1 , 0.084274
two pair Threes and Deuces Five kicker , 4 , 0.084278
two pair Threes and Deuces Six kicker , 3 , 0.084281
two pair Threes and Deuces Seven kicker , 3 , 0.084284
two pair Threes and Deuces Nine kicker , 25 , 0.084309
two pair Threes and Deuces Ten kicker , 79 , 0.084388
two pair Threes and Deuces Jack kicker , 172 , 0.084560
two pair Threes and Deuces Queen kicker , 132 , 0.084692
two pair Threes and Deuces King kicker , 9 , 0.084701

Here the kicker makes < 0.1% difference.

two pair Kings and Jacks Deuce kicker , 421 , 0.217500
two pair Kings and Jacks Three kicker , 363 , 0.217863
two pair Kings and Jacks Four kicker , 366 , 0.218229
two pair Kings and Jacks Five kicker , 284 , 0.218513
two pair Kings and Jacks Six kicker , 317 , 0.218830
two pair Kings and Jacks Seven kicker , 254 , 0.219084
two pair Kings and Jacks Eight kicker , 304 , 0.219388
two pair Kings and Jacks Nine kicker , 278 , 0.219666
two pair Kings and Jacks Ten kicker , 221 , 0.219887

The difference in kickers is still less than 1% in hand strength. Note that there were no examples found where a Q kicker was played, either!

And of course it doesn't make any sense to play xxyyA ..... zzA, since you should pair the aces.

If you don't have a pair in front, then ace-high is again much better than any other high-card hand, so it outweights playing the aces as a kicker.

If you have trips in front, then you can't have two pair in back so the situation does not occur.

However, there are some hands where you must play two pair, ace kicker, in the middle.