Initial odds of ... (not considering dealer or player starting hands).

Hi,

I work in a small online casino and amazing as it may seem, software providers do not always have calculated the odds of every feature they offer (I won't name the Casino and the provider).

We plan to offer some "Missions" that provide rewards based in gameplay triggers. I would like to calculate the odds for the next events to occur, but not considering any dealer or player initial cards, and all the BJ probability tables I've found are "what to do when...".

Could someone point me out a site where to check probabilities for the next, or to assist me with formulas I can use to calculate it myself? My target is to set accurate rewards for these missions.

Rules are: 8 decks, dealer stands on soft 17.

Missions I need probabilities for are (assuming there's only one player at the table):
- Having a Blackjack.
- To place an insurance bet (odds of dealer having an ace on initial hand)
- Split (odds to have a pair on initial hand)
- Winning with 5 cards.
- Split and win with 21 (odds for splitting and having 21 in one of the hands)
- Playing 3 hands simultaneously (Multi hand tables): odds to win the three, odds to lose the three, odds to split the three, odds of obtaining BJ in the three hands.
- Playing 5 hands simultaneously (Multi hand tables): odds to win the five, odds to lose the five, odds to split the five, odds of obtaining BJ in the five hands.

Thanks!

"- Double Down (odds to have a pair on initial hand)"

Not sure I understand this question. Did you mean Split instead of Double Down?

Basic strategy would have you split some pairs and double down on others.

Odds to have a pair on initial hand would be one number,

odds to split as best strategy a second,

odds to double down instead would be a third,

odds to hit rather than either another,

and stand yet another.

Thanks for replying.

"- Double Down (odds to have a pair on initial hand)" - Not sure I understand this question. Did you mean Split instead of Double Down?"

- Yes, I meant Split, my bad when copy pasting.

What I am looking for are not figures related to "best" strategies, but plain base odds of the events to occur.

In this particular case, what are the odds for the player to have a pair in the initial hand, considering a 8 decks game. This way if the mission is to Split, and I know that odds for a pair are XX, I can set an accurate reward if a player splits (if splitting was a wrong choice, is something I don't need to know, that goes for the players).

E.g. for Insurance, I don't need what the best strategy to use it is, or the odds to win when using insurance if the player or the dealer has this or that, but the odds for the dealer to have an ace on initial so the player can do it.

Hope this clarifies, and thanks in advance for assistance, I'm learning a lot through this site.

Quote: Ultramein

Thanks for replying.

"- Double Down (odds to have a pair on initial hand)" - Not sure I understand this question. Did you mean Split instead of Double Down?"

- Yes, I meant Split, my bad when copy pasting.

What I am looking for are not figures related to "best" strategies, but plain base odds of the events to occur.

In this particular case, what are the odds for the player to have a pair in the initial hand, considering a 8 decks game. This way if the mission is to Split, and I know that odds for a pair are XX, I can set an accurate reward if a player splits (if splitting was a wrong choice, is something I don't need to know, that goes for the players).

E.g. for Insurance, I don't need what the best strategy to use it is, or the odds to win when using insurance if the player or the dealer has this or that, but the odds for the dealer to have an ace on initial so the player can do it.

Hope this clarifies, and thanks in advance for assistance, I'm learning a lot through this site.

Welcome to the forum. It seems you do not have a basic knowledge of statistics? I'll take on one question for you and walk you through it. The odds of being dealt a pair (assuming you do NOT consider any face or ten a pair) is pretty easy to calculate. In an 8 deck game there are 416 cards. Whatever first card you are dealt there are 31 remaining cards that can make a pair, with 415 cards remaining. So the odds of making a pair is 31/415, or 0.0747, or 7.47%.

If you are really asking the odds for the first card for the dealer being an ace and don't immediately know that is 1/13, then you are really starting from the beginning.

Quote: Ultramein

<snip>Rules are: 8 decks, dealer stands on soft 17.

Missions I need probabilities for are (assuming there's only one player at the table):
- Having a Blackjack.
- To place an insurance bet (odds of dealer having an ace on initial hand)
- Split (odds to have a pair on initial hand)
- Winning with 5 cards.
- Split and win with 21 (odds for splitting and having 21 in one of the hands)
- Playing 3 hands simultaneously (Multi hand tables): odds to win the three, odds to lose the three, odds to split the three, odds of obtaining BJ in the three hands.
- Playing 5 hands simultaneously (Multi hand tables): odds to win the five, odds to lose the five, odds to split the five, odds of obtaining BJ in the five hands.

Thanks!

Ultramein,

Some of these are easy to calculate.

BJ probability: 2*32*128/(416*415), or once every 21.07... hands.

Dealer Ace-up probability: 1/13

Pair probability: 31/415. However, this is not the same as the probability that the player could split, as it does not account for hands like J Q which, while not a "pair", can (almost always) be split. Thus, the Split probability is instead this: (9/13)*(31/415) + (4/13)*(127/415).

5-card win: this depends on the player's strategy. For example, if I hold 5 3 6 6 (so a 4-card hard 20) and I choose to hit, I'll probably bust: in fact, my bust probability would be about 92.2%. However, if you're offering a bonus of 100 times my bet for a 5-card win, I'll still be hitting.

Split and draw to 21: again, this depends on the player's strategy.

Multi-hands: again, this depends on the player's strategy.

Hope this helps!

Dog Hand

Hi,

Thanks for welcoming me and for the help. Indeed I start from the beginning, I work with statistics about player's behavior, bonuses usage, rounds per player, etc. but never calculated the probabilities of BJ outcomes as I work as marketeer.

With yours and the other responses I have some material to start with.

You are right, some of the asked are quite simple calculations, apologies for that (as the dealer having an ace), but the provider did not help and since I've never done this I felt unsure to calculate on my own in case I missed to consider anything.

Thanks! Is very helpful.

I was may be too naive to think that all of the requested can be calculated without considering any strategy, specially for the multi hands "missions".

Very enlightening.

Regards.