what are the true payout odds of a blackjack?

i am curious as to what the true payout odds should be for getting a blackjack. 1.5 to 1 doesn't seem right. if the % of getting a blackjack is 4.8%* or something like that, and from what ive heard "a blackjack comes once every 20 hands" wouldnt the "true and FAIR" edgeless payout for a blackjack be 21 to 1??

also how do you figure out the odds for a curtain "outcome" of a deck of cards that is constantly shuffled?

if i may ask the one who knows the answer to my question, may i ask if you will please show your work and how you came to that conclusion?

Thanks

Quote: ponyboy

i am curious as to what the true payout odds should be for getting a blackjack.

True odds for a player getting a blackjack or for a blackjack being dealt? According to "a blackjack comes once every 20 hands" that portion of the 1 in 20 which turns out to be the Dealer getting the blackjack would have to be subtracted from the payout odds.
Does this mean a different theoretically-neutral payout for each player position? How many players are to be assumed, a full table?

>also how do you figure out the odds for a certain "outcome" of a deck of cards that is constantly shuffled?
I think the "constantly shuffled" means that it is not a finite deck and is simply considered to be an infinite deck since all cards that have previously been dealt have in actuality been replaced into the deck. The only cards that are removed are the ones removed for a particular hand. So I guess its best to calculate for a finite shoe consisting of "x" numbers of decks from which previously dealt cards are not replaced.

>may i ask if you will please show your work?
Sorry, but for me any mathematics beyond the number 10 would be a video of me taking my shoes off.

Quote: ponyboy

i am curious as to what the true payout odds should be for getting a blackjack. 1.5 to 1 doesn't seem right. if the % of getting a blackjack is 4.8%* or something like that, and from what ive heard "a blackjack comes once every 20 hands" wouldnt the "true and FAIR" edgeless payout for a blackjack be 21 to 1??

Yes but only if you got paid ONLY if you have blackjack, effectively a bj sidebet. If you don't have blackjack you're still getting paid - a push or a win is still a a payout. The concept of 'fair' payout for blackjack is meaningless, they could make it 1:1 or 2:3 or anything, it depends on the other rules of the game as to how distant the payout is from 100%.

Quote:

also how do you figure out the odds for a curtain "outcome" of a deck of cards that is constantly shuffled?

depends how many decks.

one deck.

ok so a blackjack is effectivley truly worth a payout of 21 to 1?

like if you where to consider it a side bet that your next hand is going to be a blackjack, it would pay 21 to 1 in a total honest and fair payout and game?

21 for 1, technically: i.e. 20 to 1.

The continuous shuffling machine doesn't change things much, all it means is that the cards left in the deck are always those not on the table. The odds of a certain outcome, say a 16 are quite complicated due to the myriad ways you can make that and cannot be calculated using simple arithmetic. Of course the odds of a given two card hand, such as blackjack, are straightforward.

got ya! i understand the difference between to for's and the to's. thanks!

so what is the dealers edge on paying you 3 to 2 for a blackjack if it is worth 20 to 1?

20-1.5=18.5 (the difference in what they pay)

100%-18.5=81.5% (does that mean that the dealer has a 81.5% edge on the payout of a blackjack?)

lol i have no idea if this is how to figure it or not, but it was the best i could do, and it sounds fairly accurate to me.**

Quote: drw

Yes but only if you got paid ONLY if you have blackjack, effectively a bj sidebet.

Interesting that you should view it as if it were a side bet. Although it has several aspects contrary to the viewpoint of a side bet, it is an interesting viewpoint.

It is not an optional bet. It is not for a nominal amount.
However, if we do view it as if it were a side bet then the 'fair payout' odds would have to reflect that the wager was a risk that would payoff for a bj and would also have paid off if there simply a player win by beating the dealer by attaining a hand other than blackjack.

So a fair payout would be what was fair for the actual chances of the Win-by-Blackjack event taking place minus the fair payout of the non-blackjack but winning hand taking place.

This is key:

Quote: FleaStiff

So a fair payout would be what was fair for the actual chances of the Win-by-Blackjack event taking place minus the fair payout of the non-blackjack but winning hand taking place.

In other words, paying 20 to 1 is only fair if all other hands lost.

Since you're not doing that, 3:2 is very close to fair. How close? The difference is commonly called the "house edge".

Quote: DJTeddyBear

This is key:In other words, paying 20 to 1 is only fair if all other hands lost.

Since you're not doing that, 3:2 is very close to fair. How close? The difference is commonly called the "house edge".

i had created an entire "side bet layout' for my blackjack table. "calling a blackjack was one of them, and yes, that bet loses on all other hands besides of course a blackjack. i opted for a payout that looks neat and that i thought was "generally fair" yet had what i thought was an edge and also looked neat when painted of 17 to 1.

it makes sence that 3 to 2 is close to fair if playing a normal game now, Thank you

17 to 1 also gives that "lucky number impression'! lol

it was just a way to make the game of blackjack for my game nights to be a little more interesting and a way of offering some fun bets that are found no where else.

i have a thread here titled interesting fantasy sidebets if your curious and would like to comment. =]

Quote: DJTeddyBear

This is key:In other words, paying 20 to 1 is only fair if all other hands lost.

Since you're not doing that, 3:2 is very close to fair. How close? The difference is commonly called the "house edge".

Again, the 3:2 number is irrelevant by itself. With sufficiently generous other rules you could make it 1:1 for blackjack. You cannot say 'that video poker machine pays 10 for a flush, it must be +EV', without considering other pays. It is meaningless to say 3:2 is 'fair'.

please explain the rules that are in place to force the house to pay 3 to 2, and what is missing for them to pay 1 to 1 or vice versa

Quote: ponyboy

please explain the rules that are in place to force the house to pay 3 to 2, and what is missing for them to pay 1 to 1 or vice versa

The rules are printed on the table and are known by custom to players, if they deviate from that then players may shun the game - or then again maybe not. The casinos has a degree of lattitude to experiment with game rules. Obviously if it's a 3:2 game they can't simply pay out 1:1 on winning bjs, but they could make a game that is openly advertised as 1:1.