Ask them to define "skill". If a skill game is one where there are right and wrong decisions, and if a skilled player is one who makes the correct decisions, then ask them how Poker can possibly not be a game of skill. Ask them if calling with the nut low is as correct as folding.

Depends on the stack sizes.

Here's how I explained it to someone who said it just seems like cards are dealt until someone is the winner so it's all random.

It's all in the betting.

Sometimes your cards win, sometimes mine. But if I bet when I'm going to win and fold bad hands, I come out ahead.

Exactly this is the best argument, in casino games you alwayls play against the casino and in poker you play against other players, the casino is not interrested in you winning or loosing, they just want to see you play.

one could also argue that almost every sport has some element of variance/luck for example weather - wind in golf or ski-jumping, poker certanly has much more variance than any other "sport" i can think of but still, luck will average over time and then there is only skill left.

I sent the person my initial hand example in post #9. They totally saw the light, and realized just how complex poker is compared to lucky games of chance. Looks like I didn't need to improve or expand upon it one bit. Feel free to use post #9 if you ever want to explain to someone poker has skill and decision making.

Ok, I think that's more or less what TDA and others have said but there's an easy demonstration:

1- Poker is a zero sum game (minus the rake)
2- Therefore, if there is a losing strategy x, then there are strategies which are at least profitable against said strategy x.
3- Open folding 100% is a trivially -EV strategy.
4- Therefore there are strategies which are profitable against the correct opponents.
=> You can make money with poker.

Each of these steps would deserve more accuracy if we had to write a math paper, but it is not too hard to understand the reasoning for someone who doesn't know anything about game theory or poker.

Alternatively, it's also rather easy to demonstrate that 100% x/c has many counter strats that dominate it.

So your folks are cool now? GG.

fwiw I think a counter-strat can't dominate a strategy by definition; it has to be a strategy of the same player. There also aren't 'many' dominant strats; in fact, I think we can only prove that x/c everything except when you have the nut low OTR, completely blocking chops, dominates it.

You are right, I used the word "dominate" in an ambiguous way and not in the game theory sense. I simply meant that if player A plays 100% x/c, then player B can easily construct a +EV counter-strat. This would prove that poker can be profitable.

About game theory dominance, x/c 100% is also dominated by x/c 100% except otr with the nuts where you x/r OOP or r IP. I actually don't see any situations where you completely block chops with the nut low...

I have a question for you?

Why do you WANT to convince people it's a skill game?

If it's someone in your family, a gf/bf, wife/husband or a close friend I can understand why.

If it's anyone else you probably don't want to convince them of that.

Weakly dominated at least. I think it requires constructing situations with dead cards.

I wanted to explain to a super genius friend of mine who is a master chess player and master piano player...that poker actually is an interesting mental exercise, and not like rolling craps.

No worries, this entire thread was a waste of time with not a single post actually asking what I requested, which was to clean up the one hand example I posted. Whatever.

If he's a super genius, why couldn't he figure out your point any single way you would explain it? I still think it's your folks. I have a person in my family who can figure out sick math problems in her head and she despises what I do, but she knows the diff between rolling dice and poker she just doesn't agree with doing any of it.

On the other hand kid, you learned a useful life lesson, which is that a bunch of strangers who owe you nothing do not feel obligated to read your lengthy, messy posts and then fix them up for you. Not even if you whine about it.