I love psychology (poker or not) and this is an interesting situation which is obviously player dependent. I'd interpret it differently if online or live poker and also the specific player.
Here is the core of it:
"I'll show you" sounds like they will show you their hand if you fold and obviously you will see it if you call. Why would they want to show you their hand if they don't have to do so? Possible reasons:
a) They have the nuts/super nuts and just have to share their luck. They just hit a Royal Flush or something and it is so unlikely they just want to show off that it happened.
b) The opposite of the first one; they have completely nothing and are eager to show you a bluff they got away with. Something like Ten-high and they are just showing you they were capable of a bluff like that
c) What Phil Hellmuth calls a "pity show" which is when someone loses a hand but had a good hand themselves. Something like someone having pocket Aces and loses to someone who hit a Flush. The pocket Aces might "pity show" their Aces and convey, 'look! I had a solid hand!'
These are the most common reasons I can think of for someone to willingly want to show their hand under "legitimate" circumstances, but this is not necessarily what we have here! It is different when your opponent shows their hand after showdown versus them offering to show while it is still ongoing
It is generally known that talking during a hand (especially fluid conversation) is a sign a strength. It is no surprise that many pro players and regs have learned how to hold a conversation with good and bad hands alike to induce results they want. This is where this case gets interesting...
A tricky reg or pro telling you this probably knows all of what I said above and will possibly try this line if they think you know it too. Their intention is to trick you with a "reverse tell" and get you to fold under the belief that their hand was strong. Note that I say a "tricky" reg or pro because most are not too great at successfully using "reverse tells" and multi-levels of thinking what this guy is thinking to what this one thinks I'm thinking, you know what I'm thinking?
In the absence of knowing I'm up against this type of sneaky player, then I think the "answer" is much more simple. They either:
- have a really good hand and just want something (more likely if they are a fish who doesn't know talking might come across as strength)
or
- (the most likely case I think) this player holds a marginal hand and is trying to get you to fold okay-ish hands that beat them.
I predict a marginal holding for a few reasons. Let us imagine your opponent is in this exact spot and they are holding the best preflop hand possible, pocket Aces. Are most players going to engage in conversation mid-hand like this? Probably not. A tricky player might use reverse tells here, but most players are going to keep their mouth shut because they don't want to do the slightest thing to make you second guess and fold. AA usually wants a call and opening their mouth might just make you suspicious and fold.
Some players might say "I'll show you" with complete air (bluff) as I mentioned, but I think most reasonable players are more straight-forward and have at least something. The super nutty hands (ignoring tricky players capable of reverse tells) probably aren't held by them since players with them will generally stay quiet. On a board of:
Kc Js 8d 6h 2s
If someone says "I'll show you" then I'm typically expecting marginal hands based on how the action went. Maybe a pair of eights or a pair of Kings with a lousy kicker like Ks 3h.
A trickier player on this same board might have Ace-high that completely missed. It has a little showdown value, but they are worried you might call with some decent pair like a pair of Jacks, so they say this line to you out of desperation as they think you have something and might call. They probably figure you are calling regardless with Top Pair (Kings) or some Two Pair or better, but this statement is probably targeting you to fold a weaker One Pair type of hand.
Live poker gives you a slightly different insight because you can physically see them and try to determine their level of thinking (layers on layers thing) or their intentions. However, online has the absence of these physical tells and everything "said" is typed and no accident. This means it is more deliberate online and more likely to be an act, but it is up to you to still determine what kind of opponent they are and what holding they would say this line with
