10-04-2021

Blackjack Probability Questions



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familyguy96
Yes, doing the simulation for just 1 player would be easiest.

Connect probability and odds with different games from around the world. 2.1 Finding the Probability of Being Dealt a Blackjack. The class creates a graph showing the trends found. Here is one simple question that opens the doors to a nice. Blackjack Basic Strategy Quiz. Think you know your basic blackjack strategy like the back of your hand? We’ve created a simple quiz here so you can put your knowledge to the test and determine whether you truly know perfect basic strategy. For the purpose of this test, we are going to use common rules which are: 6 Decks; Dealer stands on soft 17. First we have to find the probability of a win for any given hand, which will depend on the rules, which weren't stated in your original question. In my page on variance in blackjack, I give the probability of a net win, push, and loss under 'liberal Strip rules,' which are: six decks, blackjack pays 3 to 2, dealer stands on soft 17, double. To decide whether it is worth opening another card, calls into question what will be the probability to win if player decides to take another card. Insight 2 – If your sum is more than 17 and dealer gets a card 2-6, odds of winning is in your favor. This is even without including Ties.

We can then ask some basic probability questions, such as: 1.What is the probability of the player being dealt blackjack? 2.If the dealer has a hand total of 16, what is the probability of the dealer busting? 3.Should the player take the insurance bet if o ered? Pragel Blackjack November 20, 2015 3 / 11.

gordonm888
I would divide this 'last card analysis' into 4 scenarios:
1. The facedown card of the dealer is the last card because all players had initial hands of 17-21 and dealer has a 17 -20.
2. Dealer is last to draw a card because 1 or more players have not busted and the dealers original 2 card hand was 16 or less.
3. A player is the last to draw a card because player had a hand that required a Hit and:
a) dealer's first two cards are 17 -20
b) OR, dealers first two cards were <17 but all players HIT and busted.
4. Dealer gets a blackjack, peeks, and turns his cards over ending the hand. (Last card is Ace or Ten with equal probability.)Blackjack Probability Questions
Under scenario 1, there is a bias: the last card must be a 7, 8, 9, T or A.
In scenarios 2 and 3 there is also a bias towards high cards because of the possibility of multicard draws. When the dealer or player is hitting a hand that 7-11, than a high card may possibly end the drawing process immediately, while a low card will require the dealer/player to hit again. Even if say, dealer or player has a hard 15 and hits, then a 2-T will end the hand ,whereas an Ace will require a re-draw - so in that scenario a 2-T has a higher probability of being the last card than an ace would.
Blackjack Probability QuestionsI will note that the probability of scenarios 1 - 3 are strongly dependent upon the number of players at the table.
Edited: inserted scenario 4, Dealer blackjack.
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
gordonm888
I imagine someone will just simulate this problem and get the bottom-line answer, but I find that working through this kind of problem is educational.
Let's assume 1 player, infinite deck and H17, DOA2
For scenario 1: The facedown card of the dealer is the last card because all players (the only player) stood on initial hands of 17-21 and dealer has a H17-20.
This scenario will occur with a probability of 0.067295.
The last card drawn in this scenario is
Ace: 0.005042_____7.4922%
Ten: 0.037289____ 55.411%
9: 0.011834_____17.5858%
8: 0.009839_____14.6202%
7: 0.003291______4.8907%
This was tricky to calculate, because of the need to factor in that the following hands are not in the scenario: 99 vs 8,9 (Split) and A8 vs 9,T,A (HIT)
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
familyguy96
Is this for Stand 17 or Hit 17 game, b/c you said if dealer had hard 17 through 20, but the last card could also be 6 with Ace showing. Also, I agree that the scenarios are likely player # dependent for the first hand in a shoe, but may eventually equalize in infinite deck and nearly equilibrate in a shoe game. I would be interested in these 4 scenario results for 6D, S17, DAS, peek, late surrender game, but this looks like a good start.
gordonm888
First, the result was for Hit 17.

Blackjack Probability Questions

Nanumula, welcome to the forums. You posted an interesting question and some of us have spent a little time looking at aspects of it. But also realize that we are thinking about the question you posted out of:Probabilities
1. Good willProbability
2. Curiosity.
It is a bit unreasonable to suppose that forum members are going to do complex calculations/simulations as a function of number of decks and rule variations, etc. simply because a new member has posted and asked.
It would help if you would tell us why you are asking. Maybe tell us a little background info about yourself.
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
unJon

First, the result was for Hit 17.
Nanumula, welcome to the forums. You posted an interesting question and some of us have spent a little time looking at aspects of it. But also realize that we are thinking about the question you posted out of:
1. Good will
2. Curiosity.
It is a bit unreasonable to suppose that forum members are going to do complex calculations/simulations as a function of number of decks and rule variations, etc. simply because a new member has posted and asked.
It would help if you would tell us why you are asking. Maybe tell us a little background info about yourself.


If I were a betting man I would wager the OP has an idea for a BJ bonus bet.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
familyguy96
Thank you for the warm welcome, gordonm888.
Okay, I thought you had said the dealer would stand on Hard 17 to 20, in which 6 could be the last card, or maybe it is hard 18-20. I usually only play Stand 17 b/c of the better odds, so I am not as familiar with Hit 17.
I agree discussing it with other ppl is helpful. I thought I may be able to use this information to help guide strategy to play in a mid-shoe game, as I often don't want to wait sometimes 1 hour for a shoe, or if i don't want to play no-mid-shoe.
I can try to run my own simulation, but I figure there are longer members with more experience who can offer some greater insight. I greatly appreciate all of the posts thus far and they already provided some of the answer to my opening question. If will try to search the forums as well, to see if there is anything else on this.
Best regards.
familyguy96

If I were a betting man I would wager the OP has an idea for a BJ bonus bet.


Lol, that could also be a good idea for the future. Although, I can't implement it since I don't work for the casino. It would be fun though to design new sidebets with huge house advantages and just rake in the dough from the casino side haha.
charliepatrick

...interesting question...we are thinking about the question you posted out of:
1. Good will
2. Curiosity. ...

I agree it is an interesting puzzle in terms of working out how one might attack the calculation for a single player. However I think it gets too complicated with multiple players. So thanks for exercising the brain cells!
If I was continuing past that, I would write code to work out all the reasonable permutations (initially ignoring the effect of re-splits) and list the last card used assuming there was only one player (having more players is too much work at this stage).
QuestionsIf it was a phD then I should run simulations to confirm the calculations of one player and then add more players to see whether that affects anything (in practice it would mean the dealer plays out their cards more often).

Blackjack Probability Calculator


Given the last part there might be a thought that one works out, given a number of players, how often the dealer does or doesn't play out their hand given any of their possible upcards (and not having BJ). For instance if the dealer has a 4, 5 or 6 faceup (except 6A s17) then the only thing to consider is all players get a BJ, otherwise whatever happens they don't bust and the dealer will act last.
Using UK rules (no peek, DDAS, s17, 6 decks) I got the following (you can see from the different counts for Kings, Queens etc how much of an estimate this gives).

Blackjack Probability Theory

Note I merely added code to set lastcarddrawn in the getacard routine and when the hand was over tallying the values of lastcarddrawn before moving onto the next hand; so I haven't checked the results in any detail.

Craps Probability Questions


charliepatrick

...new sidebet...[on the last card drawn]

Blackjack Probability Math

You could design a sidebet based on the last card the dealer drew (that is easy to work out assuming you always play the dealer's hand to a finish, similar to the '22' bet in freebet). The problem if you includes the player's cards is it might affect their decisions, for instance the last player to act has a clear advantage as they could stand on their 2-card hand or deliberately take another card.

Probability Blackjack Questions

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