Dick,
Before delving into your two examples, let me discuss the rules for
holding an Ace in general.
The basic non-penalty rules will serve most everyone very well.
Taking penalty cards into consideration in determining what cards to
hold when an Ace is present gains you very little over the non-penalty
strategy. If you're not thoroughly familar with the non-penalty
strategy rules, I'd advise you obtain a strategy card or purchase a
product such as VP Strategy Master, Frugal VP, or VP Wizard which will
provide the strategy.
However, the basic situation we're concerned with here is when you
have an Ace and another unsuited high card, where no other cards are
present that would form a hand that is more attractive than just
holding one or both of these cards. The basic rule is to always hold
a lone Ace. However, there are penalty considerations that when you
practice the game using a product such as winpoker will cause the
software to frequently flag an error if you do this.
The basic rules taking into account flush and straight penalty
considerations that will eliminate roughly 95% of the related A hold
errors that you experience follow. (Note, there is an additional
straight consideration that adds only nominal benefit but considerable
conplexity and I feel is best ignored. It acounts for the very
infrequent and very slight occasional error that will still pop up.)
- In absence of another low card suited the same as the Ace, hold
just the Ace.
- If a suited low card is present and a 10 is also present, hold just
the Ace.
- If a suited low card is present and there is no 10 in the hand,
hold both the Ace and the unsuited high card.
The logic of these rules is that the presence of a suited low card
reduces the value of holding just the Ace since fewer flush draws are
possible once you discard the low card. At this point, the value of
holding the A and the unsuited high card becomes more valuable. This
increases the liklihood of drawing a straight or a high pair than if
you just hold the Ace.
However, if you also have a 10 in your hand, then once it's discarded
the probability of drawing a straight is reduced and the A-HC hold
value is likewise reduced ... below that of holding just the A by itself.
You can now understand your examples:
[ex.1] (7d Ad 4c Jc 8s) Ace with non-suited high card. There's a
suited low card (referred to as a flush penalty to the Ace) and no 10
present in the hand. Therefore, hold (Ad Jc)
[ex.2] (Ah 4h 7d 10c Js) Ace with non-suited high card. There's a
suited low card, however a 10 is also present. Therefore, hold the
lone A.
A final comment about my experience in learning DB:
I found in my winpoker practice of the game that when I had achieved a
proficiency accurate enough to reduce the cost of errors to less than
.2% it was worthwhile to learn the penalty rules to accurately handle
the Ace holds. By itself, it wouldn't improve my game return.
However, the basic penalty considerations are fairly straightforward
to master and served to eliminate a large number of the minor errors I
experienced. I found that I derived a beneficial side effect once I
incorporated the penalty consideration into my play: My accuracy on
significant errors had plateued until then. The additional attention
to detail involved in taking the Ace penalties into account served to
increase my overall attention to the game and my total error cost was
quickly reduced significantly.
I hope this extended discussion is useful.
- Harry