We have a game in our area called Crazy 4 Poker. The casino who has it is running a promotion on it. The promotion is, they took out the ace of spades and inserted a joker. The joker is played as the ace of spades if you recieve it. You also get a $25 bonus if you have it in your hand. With the pay table they use on this game, the house has a 3.42% edge. The minium bet is $2 a spot. They also charge a 50 cent ante at that level. You have to bet $6 dollars to see your five cards. This is a single deck game. Assuming that you are familiar with this game, does this actually create an advantage to the player if you are betting table miminums?
There are a couple of details missing that would affect the answer:
1) Does the joker only act like the Ace of Spades for the dealer too? (If so, it seems strange to even use a joker if it only ever takes the place of the Ace of Spades.)
2) Is the $25 bonus awarded when the joker is dealt to you but not used? For example, if your hand is 22-33-Joker, the joker is the dead card. Is the $25 bonus still awarded in this case?
Assuming the best case scenario (where the joker acts like the Ace of Spades for everyone including the dealer, and the prize is awarded even if it isn't used in the best 4-card hand), then:
The average bonus prize for every hand is $25 * combin(51,4) / combin(52,5) = $2.40, and with a $6 bet the expected loss is 20.52 cents, so the net advantage would be about $2.19 per hand when betting the minimum of $6.
If the joker acts as a true wild card for the dealer, then the house advantage of the base game would increase. If the bonus is only awarded when it is dealt to the 5-card hand AND used in the best 4-card hand, then the average bonus per hand would decrease.