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Holding Deuce Four Five in NSU Deuces Wild --- Part I of II

The simplified strategy for the game has been published several places (and indeed in a few months Liam W. Daily and I will be adding the game to our series of 4-level strategy cards published by Huntington Press), but the fine points of the game are elusive. The fine point I want to talk about this week and next deals with a single deuce (indicated by W for wild card) and a suited 45. The suit of the deuce is irrelevant in this game, so I am obviously referring to the 4 and 5 both being spades, both being hearts, both being diamonds or both being clubs. I will use a "bold italic" font to show that the 4 and 5 are suited with each other.

The W45 is a unique 3-card straight flush. Although it doesn't look significantly different from W56, it is, and this uniqueness arises from its proximity to the deuce. Consider the number of straights you can get starting from each combination. On all of the straights you get starting from W56, (whether 9-high, 8-high or 7-high), any deuces you receive may be used to fill in for any "holes" in the straight. On the A2345 straight starting from W45, of the deuces MUST be used to fill in for a 2.

Another way to say this is that from W56, there are seven 2-card combinations to complete a straight: 34, 37, 47, 48, 78, 79 and 89. From W45, there are only six combinations: A3, 36, 37, 67, 68 and 78. This extra straight (and straight flush) potential is worth about 17¢ to the dollar player.

Strategically, this 17¢ difference USUALLY doesn't make a difference. For almost all combinations of cards, usually the player will treat W45 and W56 identically. In fact, on Daily's and my strategy card, on the simplest three levels, i.e. Level 1 (Beginner), Level 2 (Recreational) and Level 3 (Basic), W45 and W56 are treated identically IN EVERY POSSIBLE CASE. You either hold either combination if there is nothing else in the hand, or you discard either combination if there is something better in the hand (such as three of a kind, a 3-card royal flush, or even a better 3-card straight flush such as a suited 9J of a different suit.) Probably 90% of players are satisfied with this level of accuracy.

To get a more accurate strategy, we have to discuss penalty cards. A penalty card is a card in the original five cards that COULD have formed part of a paying hand in combination with cards that might have been held. Let start with a hand such as W 4h 5h 9h Jc. The 9h is a FLUSH penalty card, because it could have been used to form part of a heart flush, along with the W45. Compared to W 4h 5h 9s Jc (where both the 9 and the J are of a different suit than the heart 45, so there is an extra heart still in the deck to complete a flush), the value of W45 was lowered about 15¢ because of the flush penalty. Generally speaking, all flush penalties are equal to each other.

Now compare the value of W45 in the two hands W 4h 5h 8s Jd and W 4h 5h 9s Jd. There is no flush penalty here (i.e. no heart), but the 8 is a STRAIGHT penalty, because it can be used in the same straight as W45. In this particular case, the straight penalty is worth about 9¢. Sometimes a straight penalty is worth more than this --- which we'll discuss further next week.

To put these amounts in context, in a hand such as W 4h 5h 9s Td (i.e. no flush penalty and no straight penalty), the value of holding W45 is about 20¢ higher than holding the deuce by itself. It is easy to see that if we have TWO separate penalties (some worth 15¢ and some worth 9¢ or more), the value of holding W45 would become less than the value of holding the deuce by itself.

The simplest advanced rule is that we hold W45 except when we have two separate penalties, in which case we hold the deuce by itself. Consider these examples:

W 4s 5s Ac 9h	hold W45	The A is a straight penalty and there is no flush penalty
W 4s 5s Ac 9s	hold W	The A is a straight penalty and the 9 is a flush penalty
W 4s 5s Ac 7h	hold W	The A and the 7 are both straight penalties
W 4s 5s Jc 9s	hold W45	The 9 is a flush penalty and there is no straight penalty
W 4s 5s 3c 7d	hold W4537	If both straight penalties can be used in the same five card straight, hold the entire straight.

We now have a rule that is satisfactory for at least 98% of all players. Next week we will cover the special W45 cases so we have the 100%-accurate rule.