We play some interesting dealer’s choice games, but the one that’s getting the most action lately is five-card stud low. It’s a high action game because it’s so often to correct by pot odds to call when you’re behind. This can produce some dramatic results in a table stakes game. As plain as the game sounds, and as closely related to regular razz as it is, you’d not expect it to be quite so volatile. What makes it volatile is that it’s almost impossible to feel comfortable going into the river with an opponent who isn’t holding a pair. The reason for this should be obvious. Holding four cards it’s quite easy to make a pair yourself while your opponent does not. Of course played with more than two players it’s foolish to make big calls unless you really do have a premium hand, but head’s up you’re never more than 81.5% loser when you haven’t paired. That’s the equivalent of about eight outs in Holdem. Sure the pot has to offer you pretty good odds to call with worse than a four to one shot, but that’s the worst possible case scenario. By the way, the scenario in question, and it’s at least the worst I can think of, is A23K vs. A234. Of course the individual ranks don’t matter as much as how they relate to each other. Matched perfectly for three ranks, and then the king. In this scenario your opponent must draw an Ace, Deuce, Trey, or Four to pair while you must not catch a larger pair than he catches. Perhaps there are worse scenarios, but taking the general concept of having different cards to an extreme, I did the math for four overs (A234 vs. TJQK) and actually came out a little better, at over 19.6%. Of course we’re talking about hands that do not hold a pair. It’s possible to be much farther behind, but probably not with any kind of brain. Obviously AAAA is a 100% lock vs. 2222. The only way you’re taking worse than 18% is if you’re bluffing, and then you’re laying odds, not taking them. Of course, most bluffing is done early with a high card in the hole or after the last draw, so this article doesn’t really address that part of it.

Discovering the odds of a particular play with two cards to remain is much more difficult, at least for me since the only way I know to calculate odds is to find all possible outcomes and add the good ones together. But I can find the odds for being ahead after the fourth card is dealt. In a recent hand against a friend of mine in which he found my call to be foolish, I was about thirty percent to be ahead after the fourth card was dealt. Depending on how far ahead I was at that point, I was about seventy-five percent to stay ahead after the last card, about fifteen percent (allowing that I could have paired) to get ahead if I was still behind. So with approximations we can see that I was the victor about (30% X 75%) + (70% X 15%) of the time, which comes out to about 33%. Of course that leaves a large margin of error, since I don’t have the patience to figure it out exactly. At the time in question there was a pot of about $15 into which my opponent bet his last $22. The pot was seven dollars short of offering me the odds to call. Since he was all-in there were no implied odds, so mathematically it was an incorrect call.

So why did I call? Was it just a foolish mistake? There were a couple intangibles that I valued that caused me to call. Before I am shouted down and certain folks say I made this up after the fact, I want to say that these factors were the main things I was thinking about before I made the call, and I had no idea that the pot odds were even as close as they were. First of all, I was up, and not just up, but had been pushing my opponents mercilessly since the beginning of the game. I could tell that this particular opponent was starting to get a little uncomfortable with my constant aggression and that he was one or two bad beats away from full tilt. To put a bad beat on him that would felt him was likely to do the job. Because of my stack size the loss of the twenty-two dollars wasn’t such a big deal, but getting him into a place from which he couldn’t fight back was a big deal. I was right, got a little bit lucky, and he did go on tilt from that moment forward.