It turns out that the correct answer depends on the pay schedule -- that is, how much you receive for a full house and how much you receive for a flush. In the 10/6 version (that is, full houses return 10 for 1 and flushes return 6 for 1 -- perfect play on this game returns 100.07%), the best play is KT. In the 9/6 version (returning 99.98%), KT4 is the best play. And in the 9/5 version (returning 97.87%) holding the solitary K is the best play.

Liam W. Daily and I discovered this hand while we were preparing our Winner's Guide for this game. This "king ten and a baby" hand is the only one that we've come across where the top three pay schedules of a game give three different plays. The idea that there is ANY such hand is surprising news to many players. After all, most players use a fairly standard strategy for all video poker games -- and many don't pay attention to the pay schedule.

Let's see why the plays are so different. The enclosed table lists the expected value, in coins, for each combination assuming a 5-coin bet. If we are playing for dollars, then we can read these numbers as dollars and cents.

	KT5	KT	K
10/6	2.1092	2.1126	2.1039
9/6	2.1092	2.1070	2.0958
9/5	1.9010	2.0706	2.0899

The first thing to notice, perhaps, is that the value of all three combinations is very close -- at least when flushes return 6.

In 10/6, the higher pay for full house makes KT the better play. The return on full houses doesn't affect KT5 at all. It has a slightly greater effect on the bare king than it has on the suited KT.

In 9/6, the value of KT is decreased by a half cent over what it was in 10/6, and that's enough to make a difference. The value of KT5 is only dependent on the return on high pairs, two pair, 3 of a kind, and flushes, and none of those changed when we went from 10/6 to 9/6.

In 9/5, the lower value of the flush affects all three combinations -- but it affects the 3-card flush by considerably more (20.8˘) than the 2-card flush (3.6˘) than the 1-card "flush" (0.6˘). Since the K is reduced the least by the reduction in the return on a flush, and the three combinations had very close values at the higher pay schedule, it should be no surprise that the K is the preferred play.

What about 8/5 DDB? This is a 96.79% game and nobody with a clue should ever play such a poor game, but let's see if we can determine what the correct play on the hand in question should be.

We know that the KT5 will have the same return in 8/5 as it does in 9/5, so we know that number will be 1.9010. Since the value of KT decreased by 0.56˘ (2.1126 -- 2.1070 = 0.0056) when we reduced the return on full houses from 10 to 9, it is reasonable to assume that it will decrease by the same amount when we decrease the return on full houses from 9 to 8. Therefore, the return on KT will be 2.0650. Since the return on the solitary K decreased by 0.81˘ (2.1039 -- 2.0958 = 0.0081), then we can predict the value of the K in 8/5 is 2.0818 and remains the best play.

The lesson in today's column is a new one for most readers. And it is, if you know the change in the expected value for a given combination for a 1-unit change in the pay table, another 1-unit change in the pay table will generate an equal change in the expected value. Learning this lesson is especially valuable should you ever decide you want to tackle progressives.