Sousem Still Wows 'em: Conclusion

In the previous article we obtained the following numbers of types of hands: There are 40 five-card straight flushes, 624 four-of-a-kind hands, 3,744 full houses, 316 five-card flushes containing 4-card straight flushes, 4,792 five-card flushes not containing a four-card straight flush, 240 five-card straights containing four-card straight flushes, 9,960 five-card straights not containing a four-card straight flush, 54,912 three-of-a-kind hands, 123,552 hands with two-pair, 528 four-card straight flushes with a pair, 948 four-card straight flushes without a pair, 3,792 double sousem hands (a hand containing both a four-card flush and a four-card straight but not a four-card straight flush), 33,792 four-card flushes containing a pair, 71,880 four-card flushes without a pair, 16,368 four-card straights which also have a pair, 75,840 four-card straights without a pair, 1,047,552 hands with one pair, and 1,150,080 hands with no pair or better.

``Alright, Bib, let's rank sousem hands in three different scenarios. First, let's assume that we recognize only four-card straights and four-card flushes as separate hands. This means we have to decide whether to count a four-card straight flush as a straight or a flush, and similarly for a double sousem. Since there are so many pairs compared to four-card straights and four-card flushes, it is clear the hands containing both a four-card straight and a pair, or a four-card flush and a pair will be ranked higher as four-card straights and flushes. Now if we add the 528 four-card straight flushes with a pair, the 948 four-card straight flushes without a pair, the 3,792 double sousems, the 16,368 four-card straights with a pair, and the 75,840 four-card straights without a pair, we obtain 97,476 hands which could qualify as four-card straights. Note that there are 33,792 + 71,880 = 105,672 four-card flushes meaning we are correct in calling the previous hands four-card straights because they will rank higher and this is what a player holding such a hand would want. This gives us the following table.''

``That's not the way we played those hands in my old game.''

``You have to admit, Bib, it's not the first time your old home game had hand rankings confused. Next, let's admit a four-card straight flush as a recognized hand. Since their number is so small, five-card straights and flushes containing four-card straight flushes will be ranked higher as four-card straight flushes. In addition, the other hands having a four-card straight flush will rank higher as four-card straight flushes. We obtain the following table.''

``Of course, Bib, some people will be surprised by the preceding rankings, but that is what they deserve if they introduce weird hands. And if the preceding rankings surprise them, how do you suppose they will react upon seeing the rankings when double sousems are recognized as a hand as they should be if you are going to allow four-card straights and flushes. Their rarity makes them most valuable when interpreted as a double sousem. So this yields the following table. This would be the most interesting way to play the game in my opinion.''

``Don't you think some players would get confused, professor?''

``Not after they got used to the rankings. Poker players by and large are smart although there is a certain conservative streak running through them making them complain about changes.''

This completes the series on sousem hands and the correct rankings for the various hands.