Crazy 4 Poker - Optimal Strategy
Raise on K-Q-8-4-3 and above
Raise on K-Q-8-4-2 if you see all four suits in your hand, bet. If K and Q are the same suits in addition to 8 and 4 being the same suits as each other, you should raise.
Raise on K-Q-7-6-5
Raise on K-Q-7-6-4 if you have cards of every suit unless you have three suits with K and Q having the same suit.
Has anyone tried to describe the perfect strategy before? And can anyone find any errors in my supposed optimal strategy?
Let me know if there are any other games you would like to see the optimal strategy for. Thanks for reading and have a nice day!
Quote: harrisHello everyone! I just joined this forum to make a couple posts. I have been getting interested in combinatorial statistics and gambling mathematics recently, and I wanted to find the optimal strategy for the game called Crazy 4 Poker. According to Wizard of Odds' website, the perfect strategy is extremely close to folding anything below K-Q-8-4. However extremely close is not close enough for me. After writing some code I think I have found the optimal strategy which is the following:
Raise on K-Q-8-4-3 and above
Raise on K-Q-8-4-2 if you see all four suits in your hand, bet. If K and Q are the same suits in addition to 8 and 4 being the same suits as each other, you should raise.
Raise on K-Q-7-6-5
Raise on K-Q-7-6-4 if you have cards of every suit unless you have three suits with K and Q having the same suit.
Has anyone tried to describe the perfect strategy before? And can anyone find any errors in my supposed optimal strategy?
Let me know if there are any other games you would like to see the optimal strategy for. Thanks for reading and have a nice day!
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Welcome to the forum. Nice work.
Your strategy statement for K-Q-8-4-2 isn't quite complete. Should you add "Otherwise fold" for those occasions when K-Q-8-4-2 doesn't meet the stated conditions?
Why do you think there is significance for K and Q to both be the same suit?
Thanks for the reply.
Yes, I meant that KQ842 and KQ764 should be folded if they are not raised.
I think the exceptions involving K and Q have to do with the fact that only two types of straights / straight flushes contain either K or Q (AKQJ, KQJT, and QJT9). Most other combinations of two cards cover a lot more types of four-card straights.
Not that anyone asked but after some mathematical research on my optimal strategy website, I found that KQ765 should be folded if there are only two suits and K and Q are different suits.
There might be other extremely minor gaps with my Crazy 4 Poker "optimal strategy" but I really don't have the motivation to find them all just yet.
