A Free Bet When You Have A Pair Of 8. Whats the advantage after this rule ?

Hi,

I recently find out a casino offering if you have any pair of 8 , they will give you a free bet chip of 8 pounds no matter the hand win or lost or how much you bet.

Can someone do some help me to do a calculation of the house advantage of this ?
I would like to know how low the advantage will go down to.
I am not too sure will they take away that free bet chip after you use it.


4 decks
no hole card
split 4 hands
double after split
resplit aces
soft 17

The free bet chip cannot be use on the hand you playing for splitting the eights.

Thanks !

Well, you don’t say what the table minimum is.

The probability to be dealt a pair of 8s in 4-deck game is 0.5574% or once in every 179.4 hands.

The game has a house edge of about 0.4%.

If your average bet is 8 pounds, then you are supposed to lose 5.7408 pounds to get a free bet of 8 pounds. Further, 8 pounds exposed on the house edge will become 7.968 pounds. If you are allowed to keep the free chip after using, your expected value for 179.4 hands will be 2.2272 (7.968-5.7408) pounds. Thus, you’ll have an advantage of about 0.155%. If they take the free chip after using, its value will be about 3.664 pound (an approximation supposing 8% of all hands are pushes). Now your expectation after 179.4 hands will be negative (-2.0768=3.664-5.7408). Or you’ll have a disadvantage of about 0.145%.

Of course, you could better your position if you are eligible for the bonus by betting less than 8 pounds a hand.

Would you care to share if this is an online casino?

Hi

Thanks for the calculation. Unfortunately that's a local casino in England. The table minimum is 5 pounds.

If I flat bet 5 pounds , I am expected to lost 3.508 pounds to get the free bet chip.
So I will have a thin advantage if they take it away after i use it. Am I correct ? (3.664-3.508=0.156).

Thanks again !

Quote: blackjackhaha

Hi

Thanks for the calculation. Unfortunately that's a local casino in England. The table minimum is 5 pounds.

If I flat bet 5 pounds , I am expected to lost 3.508 pounds to get the free bet chip.
So I will have a thin advantage if they take it away after i use it. Am I correct ? (3.664-3.508=0.156).

Thanks again !

At that point (a basic strategy advantage off the top) I don't get why one wouldn't count using a very light spread that should go under the radar but really maximize the advantage. Most people fight for a 1%, upwards of 2% advantage... You can basically add half a percent to that off the top for your average. If you're that interested in the house edge, and how to get the odds on your side with just BS, then why wouldn't you be interested in really getting the odds in your favor?