Edge Conditions in Razz Showdowns

[shipitfish]

A good friend of mine and lurker here at my journal is a software developer for a startup online poker site. I have served from time to time as their “poker world expert”, which I've enjoyed immensely. These days, they are all accomplished low limit players themselves and don't need my expertise often, but my friend sent me this question that I think I have an answer for, but am curious what others think.

They are implementing Razz, and like all good programmers, they are making sure that every edge condition is handled. My friend has discovered a case where the otherwise excellent Poker Source hand evaluation library (which folks in the poker world who don't also live in the Software Freedom world know as “twodimes”, a web repackager of that library) does something suspicious. We are trying to decide what the right solution is.

Suspend your disbelief for the moment, and consider two Razz hands that have gotten to showdown heads-up. One hand is the 5 5 6 6 7 7 7. The other hand is the 4 4 8 8 9 9 9. Obviously, there wouldn't be a huge pot between these two unless they were total maniacs, but there's at least the antes, the bring-in, and a limp. Who should be awarded that pot?

Poker Source says that the winner is the latter hand. I disagree, I think the former wins. In Razz, we have all learned the rule “best five low cards, aces play low, straights and flushes do not count against you“. We've also learned that if all players at showdown must make at least one pair (because they paired twice, for example), the lowest pair wins. I would argue that this continues on up through the rankings of poker hands, skipping the straights and flushes. So, if all players in the hand must make at least two pair, they should make the lowest two pair they can. By this logic, sixes-up is a worse hand than eights-up, and therefore sixes-up should win.

I am not sure what case could be made for declaring the latter hand the winner. It can make four different five card poker hands: eights-up, nines-up, nines-full-of-eights and nines-full-of-fours. The other hand can also make four: sixes-up, sevens-up, sevens-full-of-sixes and sevens-full-of-fives. Can anyone therefore speculate why Poker Source would think the latter hand is a winner in Razz? Is it just a bug, or are we missing something?

Comments

[bobby-the-worm.livejournal.com]

My only speculation is that it's considering two-pair hands differently than in normal, high-hand poker. I would assume it's looking at what you call "eights-up" more like "fours-down." Which, in this topsy-turvy world, would be a better (lower) hand than the "fives-down" ("sixes-up") in the former hand.

I'm not saying this means of evaluation is right, but that was my thinking on...uh...its thinking. :)

Why the first hand wins in razz

[(Anonymous)]

consider the case:

5555666 vs. 4444888

In razz to determine the winner, it is an easy two-step process. The fist step is to make the lowest 5 card hand possible with the 7 cards you have available. After step 1 we have:

55566 vs 44488

Next we see which of these hands would win under normal poker rules after removing straights and flushes. This gives us: 5s full vs 4s full. In normal poker rules the 5s full wins.

Finally, we take the lowest of the two hands for razz which is 4s full. Therefore in razz 4s full beats 5s full.

The same logic must be applied to the two-pair case. Under normal poker rules you consider both pair together as a single ranking. 6s up vs 8s up. In razz you do the opposite, so 6s up wins over 8s up in razz.

I like the concept of a "4s down vs 5s" down, but this logic does not work. If you applied that logic to the full house case, you could argue that KKK22 beats 33344 because the 2s are lower than the 3s. This obviously is incorrect.

I hope I've made this clear.

[swolfe.livejournal.com]

i vote bug

[(Anonymous)]

Thanks for the answer that closes a 4 years old TODO comment in the sources

/* TODO -- review and fix code for hands with >5 cards, in particular
21: hands like KK77442, KKK7733, 777KK33, 333KK77, 4444KKK. */

http://cvs.gna.org/cvsweb/poker-eval/include/inlines/eval_low.h?rev=1.7;cvsroot=pokersource

I'll fix this.

Loic.

[jellymillion.livejournal.com]

I'm pretty sure that the code as provided doesn't cater properly for hands that don't have five distinct ranks. I suggest your friend take a look at mktab_lowball.c, which seems to support this from a quick look. From a site development point-of-view, this is a problem - it's quite conceivable that something like the case outlined could occur with an all-in on 3rd or 4th street. The table generation stuff in poker-source/poker-eval is tricky. Clever and fast, but tricky.

[saali2010.livejournal.com]

5-card draw poker continues purity even today and often found as component of mixed cash games, tournament adjuncts & tournaments devoted to 5-card draw poker alone. Even though many still see it as jumping off place for more complex varieties of poker, it does have own structure, strategy & tactics.

5 card stud (http://poker.winner.com/5_card_stud.html)