It should be possible to set up P2P distributed poker (and other games) around this.
It is pretty simple to do if you don't mind everyone seeing all the cards, but that loses one of the main features of poker, turning into merely a gamble on what cards will come out, nothing much to bluff with except maybe to simply make such a large bet no-one can match it.
The private keys though can probably provide determinism without those who do not have the private key being able to figure out what card it was that that private key deterministically determined the drawn card to be.
I'd have to do some research to find exact methods but someone more familiar with applications of private key + public key cryptography might wlel know off the top of their head exactly the kind of methods that would produce the desired result.
The desired result being that publishing an "I draw X number of cards" order verifiably results in specific cards by application of hashes found in blockchains by a strict methodology and application of various public and private keys. It might even need all the players to sign something in sequence or something, as I said I am not sure of the exact procudure. But various papers about things one can do with such systems lead me to suspect this is far from not-doable thus probably just requires a bit of know-how that I do not yet have.
A card game application could handle many games and also work with a bunch of blockchains designated red chips, blue chips, green chips, white chips, black chips and so on, with the purported relative values of the chips being basically just arbitrary relative values set by the software, possibly even with the players being able to set them as they wish provided all players at the table agree as to what these relative values are to be for that game or that gaming session. Defaults would probably be a good idea to try to help keep disputes about these values from getting too out of control. This arbitrariness would help indicate these are poker chips not money, even though in practice gosh knows what people might or might not sell or trade them for.
Conversions from bitcoins can be done verifiably by specifying an address which will respoond with X number of Y colour poker chips sent to any address that sends it a bitcoin, provided the send of course first checks the appropriate coloured chip blockchain to ensure the address sent to does in fact have enough such chips to respond with.