Go for quads IIa: 3K with kickers

[Minn. Fatz]

Kicker effects complicate the rules of thumb given in "When to go for quads" Part I, but the results are still not that difficult to calculate at the machine. The mathematics are similar so the detailed explanations have been left as an exercise for the interested reader.

Breaking FH with 2 kickers: Draw one to 3K and one kicker only if the possible payoff is more than 44 times the difference between your FH and 3K payoffs.

Draw two to 3K only if 3/4 of the 4K with no kicker payoff plus 1/4 of the 4K with kicker payoff is more than 21 times the FH - 3K difference.

To choose between these two draws when both are better than holding the FH, compare:
9 times the 4K, no kicker payoff plus 5 times the FH payoff
3 times the 4K with kicker payoff plus 11 times the 3K payoff
If the first is greater, draw two to 3K; otherwise, draw one to 3K with a kicker.

Breaking FH with one kicker and one odd card: Draw one to 3K and a kicker only if the payoff is 43 times the FH - 3K difference.

Draw two to 3K if 7/10 of the 4K, no kicker payoff plus 3/10 of the 4K with kicker payoff is 21 times greater than the FH - 3K difference.

To choose, compare:
12 times the 4K, no kicker payoff
4 times the 4K with kicker payoff plus the FH payoff plus 7 times the 3K payoff
Draw two to 3K if the first is greater and one to 3K with a kicker otherwise.

Breaking a FH with no kicker: Draw two to 3K if 1/3 of the 4K with kicker payoff plus 2/3 of the 4K, no kicker payoff is more than 21 times the FH - 3K difference.

Part IIb will cover 2P situations...

[Minn. Fatz]

Just noticed something: for "Breaking FH with one kicker and one odd card" above, which makes no sense, read "Holding a kicker with 3K;" also, the "Breaking FH with 2 kickers" calculation also applies to holding a 3K and kicker from a hand like 4442A.