Probability Blackjack
2021年4月19日Register here: http://gg.gg/p36jb
*Probability Of Losing 5 In A Row Blackjack
*Odds Of Getting A Blackjack
One of the most interesting aspects of blackjack is theprobability math involved. It’s more complicated than othergames. In fact, it’s easier for computer programs to calculateblackjack probability by running billions of simulated handsthan it is to calculate the massive number of possible outcomes.
Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 5-2014 The Expected Value of an Advantage Blackjack player. According to my blackjack appendix 4, the probability of an overall win in blackjack is 42.22%, a tie is 8.48%, and a loss is 49.10%. I’m going to assume you wish to ignore ties for purposes of the streak. In that case, the probability of a win, given a resolved bet, is 46.36%. The probability of winning n. The bust probability is calculated by dividing the number of Dealer’s busted hands to the total possible blackjack actions. Blackjack actionsis a parameter that counts everything: Busted hands, pat hands (17 to 21), blackjack hands, and draws or hits to the first 2-card hands (incomplete hands). The software does NOT print the incomplete bj hands. Blackjack and Probability Chongwu Ruan Math 190S-Hubert Bray July 24, 2017 1 Introduction Blackjack is an usual game in gambling house and to beat the dealer and make money, people have done lots of research on it. They come up with several basic strategy which is consist of three tables corresponding to the different rules.
This page takes a look at how blackjack probability works. Italso includes sections on the odds in various blackjacksituations you might encounter.An Introduction to Probability
Probability is the branch of mathematics that deals with thelikelihood of events. When a meteorologist estimates a 50%chance of rain on Tuesday, there’s more than meteorology atwork. There’s also math.
Probability is also the branch of math that governs gambling.After all, what is gambling besides placing bets on variousevents? When you can analyze the payoff of the bet in relationto the odds of winning, you can determine whether or not a betis a long term winner or loser.The Probability Formula
The basic formula for probability is simple. You divide thenumber of ways something can happen by the total possible numberof events.
Here are three examples.Example 1:
You want to determine the probability of getting heads whenyou flip a coin. You only have one way of getting heads, butthere are two possible outcomes—heads or tails. So theprobability of getting heads is 1/2.Example 2:
You want to determine the probability of rolling a 6 on astandard die. You have one possible way of rolling a six, butthere are six possible results. Your probability of rolling asix is 1/6.Example 3:
You want to determine the probability of drawing the ace ofspades out of a deck of cards. There’s only one ace of spades ina deck of cards, but there are 52 cards total. Your probabilityof drawing the ace of spades is 1/52.
A probability is always a number between 0 and 1. An eventwith a probability of 0 will never happen. An event with aprobability of 1 will always happen.
Here are three more examples.Example 4:
You want to know the probability of rolling a seven on asingle die. There is no seven, so there are zero ways for thisto happen out of six possible results. 0/6 = 0.Example 5:
You want to know the probability of drawing a joker out of adeck of cards with no joker in it. There are zero jokers and 52possible cards to draw. 0/52 = 0.Example 6:
You have a two headed coin. Your probability of getting headsis 100%. You have two possible outcomes, and both of them areheads, which is 2/2 = 1.
A fraction is just one way of expressing a probability,though. You can also express fractions as a decimal or apercentage. So 1/2 is the same as 0.5 and 50%.
You probably remember how to convert a fraction into adecimal or a percentage from junior high school math, though.Expressing a Probability in Odds Format
The more interesting and useful way to express probability isin odds format. When you’re expressing a probability as odds,you compare the number of ways it can’t happen with the numberof ways it can happen.
Here are a couple of examples of this.Example 1:
You want to express your chances of rolling a six on a sixsided die in odds format. There are five ways to get somethingother than a six, and only one way to get a six, so the odds are5 to 1.Example 2:
You want to express the odds of drawing an ace of spades outa deck of cards. 51 of those cards are something else, but oneof those cards is the ace, so the odds are 51 to 1.
Odds become useful when you compare them with payouts onbets. True odds are when a bet pays off at the same rate as itsprobability.
Here’s an example of true odds:
You and your buddy are playing a simple gambling game youmade up. He bets a dollar on every roll of a single die, and hegets to guess a number. If he’s right, you pay him $5. If he’swrong, he pays you $1.
Since the odds of him winning are 5 to 1, and the payoff isalso 5 to 1, you’re playing a game with true odds. In the longrun, you’ll both break even. In the short run, of course,anything can happen. Probability and Expected Value
One of the truisms about probability is that the greater thenumber of trials, the closer you’ll get to the expected results.
If you changed the equation slightly, you could play thisgame at a profit. Suppose you only paid him $4 every time hewon. You’d have him at an advantage, wouldn’t you?
*He’d win an average of $4 once every six rolls
*But he’d lose an average of $5 on every six rolls
*This gives him a net loss of $1 for every six rolls.
You can reduce that to how much he expects to lose on everysingle roll by dividing $1 by 6. You’ll get 16.67 cents.
On the other hand, if you paid him $7 every time he won, he’dhave an advantage over you. He’d still lose more often than he’dwin. But his winnings would be large enough to compensate forthose 5 losses and then some.
The difference between the payout odds on a bet and the trueodds is where every casino in the world makes its money. Theonly bet in the casino which offers a true odds payout is theodds bet in craps, and you have to make a bet at a disadvantagebefore you can place that bet.
Here’s an actual example of how odds work in a casino. Aroulette wheel has 38 numbers on it. Your odds of picking thecorrect number are therefore 37 to 1. A bet on a single numberin roulette only pays off at 35 to 1.
You can also look at the odds of multiple events occurring.The operative words in these situations are “and” and “or”.
*If you want to know the probability of A happening ANDof B happening, you multiply the probabilities.
*If you want to know the probability of A happening OR ofB happening, you add the probabilities together.
Here are some examples of how that works.Example 1:
You want to know the probability that you’ll draw an ace ofspades AND then draw the jack of spades. The probability ofdrawing the ace of spades is 1/52. The probability of thendrawing the jack of spades is 1/51. (That’s not a typo—youalready drew the ace of spades, so you only have 51 cards leftin the deck.)
The probability of drawing those 2 cards in that order is1/52 X 1/51, or 1/2652.Example 2:
You want to know the probability that you’ll get a blackjack.That’s easily calculated, but it varies based on how many decksare being used. For this example, we’ll use one deck.
To get a blackjack, you need either an ace-ten combination,or a ten-ace combination. Order doesn’t matter, because eitherwill have the same chance of happening.
Your probability of getting an ace on your first card is4/52. You have four aces in the deck, and you have 52 totalcards. That reduces down to 1/13.Probability Of Losing 5 In A Row Blackjack
Your probability of getting a ten on your second card is16/51. There are 16 cards in the deck with a value of ten; foureach of a jack, queen, king, and ten.
So your probability of being dealt an ace and then a 10 is1/13 X 16/51, or 16/663.
The probability of being dealt a 10 and then an ace is also16/663.
You want to know if one or the other is going to happen, soyou add the two probabilities together.
16/663 + 16/663 = 32/663.
That translates to approximately 0.0483, or 4.83%. That’sabout 5%, which is about 1 in 20.Example 3:
You’re playing in a single deck blackjack game, and you’veseen 4 hands against the dealer. In all 4 of those hands, no aceor 10 has appeared. You’ve seen a total of 24 cards.
What is your probability of getting a blackjack now?
Your probability of getting an ace is now 4/28, or 1/7.(There are only 28 cards left in the deck.)Odds Of Getting A Blackjack
Your probability of getting a 10 is now 16/27.
Your probability of getting an ace and then a 10 is 1/7 X16/27, or 16/189.
Again, you could get a blackjack by getting an ace and a tenor by getting a ten and then an ace, so you add the twoprobabilities together.
16/189 + 16/189 = 32/189
Your chance of getting a blackjack is now 16.9%.
This last example demonstrates why counting cards works. Thedeck has a memory of sorts. If you track the ratio of aces andtens to the low cards in the deck, you can tell when you’re morelikely to be dealt a blackjack.
Since that hand pays out at 3 to 2 instead of even money,you’ll raise your bet in these situations.The House Edge
The house edge is a related concept. It’s a calculation ofyour expected value in relation to the amount of your bet.
Here’s an example.If the expected value of a $100 bet is $95, the house edge is5%.
Expected value is just the average amount of money you’ll winor lose on a bet over a huge number of trials.
Using a simple example from earlier, let’s suppose you are a12 year old entrepreneur, and you open a small casino on thestreet corner. You allow your customers to roll a six sided dieand guess which result they’ll get. They have to bet a dollar,and they get a $4 win if they’re right with their guess.
Over every six trials, the probability is that you’ll winfive bets and lose one bet. You win $5 and lose $4 for a net winof $1 for every 6 bets.$1 divided by six bets is 16.67 cents.Your house edge is 16.67% for this game.
The expected value of that $1 bet, for the customer, is about84 cents. The expected value of each of those bets–for you–is$1.16.
That’s how the casino does the math on all its casino games,and the casino makes sure that the house edge is always in theirfavor.
With blackjack, calculating this house edge is harder. Afterall, you have to keep up with the expected value for everysituation and then add those together. Luckily, this is easyenough to do with a computer. We’d hate to have to work it outwith a pencil and paper, though.
What does the house edge for blackjack amount to, then?
It depends on the game and the rules variations in place. Italso depends on the quality of your decisions. If you playperfectly in every situation—making the move with the highestpossible expected value—then the house edge is usually between0.5% and 1%.
If you just guess at what the correct play is in everysituation, you can add between 2% and 4% to that number. Evenfor the gambler who ignores basic strategy, blackjack is one ofthe best games in the casino.Expected Hourly Loss and/or Win
You can use this information to estimate how much moneyyou’re liable to lose or win per hour in the casino. Of course,this expected hourly win or loss rate is an average over a longperiod of time. Over any small number of sessions, your resultswill vary wildly from the expectation.
Here’s an example of how that calculation works.
*You are a perfect basic strategy player in a game with a0.5% house edge.
*You’re playing for $100 per hand, and you’re averaging50 hands per hour.
*You’re putting $5,000 into action each hour ($100 x 50).
*0.5% of $5,000 is $25.
*You’re expected (mathematically) to lose $25 per hour.
Here’s another example that assumes you’re a skilled cardcounter.
*You’re able to count cards well enough to get a 1% edgeover the casino.
*You’re playing the same 50 hands per hour at $100 perhand.
*Again, you’re putting $5,000 into action each hour ($100x $50).
*1% of $5,000 is $50.
*Now, instead of losing $25/hour, you’re winning $50 perhour.Effects of Different Rules on the House Edge
The conditions under which you play blackjack affect thehouse edge. For example, the more decks in play, the higher thehouse edge. If the dealer hits a soft 17 instead of standing,the house edge goes up. Getting paid 6 to 5 instead of 3 to 2for a blackjack also increases the house edge.
Luckily, we know the effect each of these changes has on thehouse edge. Using this information, we can make educateddecisions about which games to play and which games to avoid.
Here’s a table with some of the effects of various ruleconditions.Rules VariationEffect on House Edge6 to 5 payout on a natural instead of the stand 3 to 2 payout+1.3%Not having the option to surrender+0.08%8 decks instead of 1 deck+0.61%Dealer hits a soft 17 instead of standing+0.21%Player is not allowed to double after splitting+0.14%Player is only allowed to double with a total of 10 or 11+0.18%Player isn’t allowed to re-split aces+0.07%Player isn’t allow to hit split aces+0.18%
These are just some examples. There are multiple rulesvariations you can find, some of which are so dramatic that thegame gets a different name entirely. Examples include Spanish 21and Double Exposure.
The composition of the deck affects the house edge, too. Wetouched on this earlier when discussing how card counting works.But we can go into more detail here.
Every card that is removed from the deck moves the house edgeup or down on the subsequent hands. This might not make senseinitially, but think about it. If you removed all the aces fromthe deck, it would be impossible to get a 3 to 2 payout on ablackjack. That would increase the house edge significantly,wouldn’t it?
Here’s the effect on the house edge when you remove a card ofa certain rank from the deck.Card RankEffect on House Edge When Removed2-0.40%3-0.43%4-0.52%5-0.67%6-0.45%7-0.30%8-0.01%9+0.15%10+0.51%A+0.59%
These percentages are based on a single deck. If you’replaying in a game with multiple decks, the effect of the removalof each card is diluted by the number of decks in play.
Looking at these numbers is telling, especially when youcompare these percentages with the values given to the cardswhen counting. The low cards (2-6) have the most dramatic effecton the house edge. That’s why almost all counting systems assigna value to each of them. The middle cards (7-9) have a muchsmaller effect. Then the high cards, aces and tens, also have alarge effect.
The most important cards are the aces and the fives. Each ofthose cards is worth over 0.5% to the house edge. That’s why thesimplest card counting system, the ace-five count, only tracksthose two ranks. They’re that powerful.
You can also look at the probability that a dealer will bustbased on her up card. This provides some insight into how basicstrategy decisions work.Dealer’s Up CardPercentage Chance Dealer Will Bust235.30%337.56%440.28%542.89%642.08%725.99%823.86%923.34%1021.43%A11.65%
Perceptive readers will notice a big jump in the probabilityof a dealer busting between the numbers six and seven. They’llalso notice a similar division on most basic strategy charts.Players generally stand more often when the dealer has a six orlower showing. That’s because the dealer has a significantlygreater chance of going bust.Summary and Further Reading
Odds and probability in blackjack is a subject with endlessramifications. The most important concepts to understand are howto calculate probability, how to understand expected value, andhow to quantify the house edge. Understanding the underlyingprobabilities in the game makes learning basic strategy and cardcounting techniques easier.
Register here: http://gg.gg/p36jb
https://diarynote-jp.indered.space
*Probability Of Losing 5 In A Row Blackjack
*Odds Of Getting A Blackjack
One of the most interesting aspects of blackjack is theprobability math involved. It’s more complicated than othergames. In fact, it’s easier for computer programs to calculateblackjack probability by running billions of simulated handsthan it is to calculate the massive number of possible outcomes.
Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 5-2014 The Expected Value of an Advantage Blackjack player. According to my blackjack appendix 4, the probability of an overall win in blackjack is 42.22%, a tie is 8.48%, and a loss is 49.10%. I’m going to assume you wish to ignore ties for purposes of the streak. In that case, the probability of a win, given a resolved bet, is 46.36%. The probability of winning n. The bust probability is calculated by dividing the number of Dealer’s busted hands to the total possible blackjack actions. Blackjack actionsis a parameter that counts everything: Busted hands, pat hands (17 to 21), blackjack hands, and draws or hits to the first 2-card hands (incomplete hands). The software does NOT print the incomplete bj hands. Blackjack and Probability Chongwu Ruan Math 190S-Hubert Bray July 24, 2017 1 Introduction Blackjack is an usual game in gambling house and to beat the dealer and make money, people have done lots of research on it. They come up with several basic strategy which is consist of three tables corresponding to the different rules.
This page takes a look at how blackjack probability works. Italso includes sections on the odds in various blackjacksituations you might encounter.An Introduction to Probability
Probability is the branch of mathematics that deals with thelikelihood of events. When a meteorologist estimates a 50%chance of rain on Tuesday, there’s more than meteorology atwork. There’s also math.
Probability is also the branch of math that governs gambling.After all, what is gambling besides placing bets on variousevents? When you can analyze the payoff of the bet in relationto the odds of winning, you can determine whether or not a betis a long term winner or loser.The Probability Formula
The basic formula for probability is simple. You divide thenumber of ways something can happen by the total possible numberof events.
Here are three examples.Example 1:
You want to determine the probability of getting heads whenyou flip a coin. You only have one way of getting heads, butthere are two possible outcomes—heads or tails. So theprobability of getting heads is 1/2.Example 2:
You want to determine the probability of rolling a 6 on astandard die. You have one possible way of rolling a six, butthere are six possible results. Your probability of rolling asix is 1/6.Example 3:
You want to determine the probability of drawing the ace ofspades out of a deck of cards. There’s only one ace of spades ina deck of cards, but there are 52 cards total. Your probabilityof drawing the ace of spades is 1/52.
A probability is always a number between 0 and 1. An eventwith a probability of 0 will never happen. An event with aprobability of 1 will always happen.
Here are three more examples.Example 4:
You want to know the probability of rolling a seven on asingle die. There is no seven, so there are zero ways for thisto happen out of six possible results. 0/6 = 0.Example 5:
You want to know the probability of drawing a joker out of adeck of cards with no joker in it. There are zero jokers and 52possible cards to draw. 0/52 = 0.Example 6:
You have a two headed coin. Your probability of getting headsis 100%. You have two possible outcomes, and both of them areheads, which is 2/2 = 1.
A fraction is just one way of expressing a probability,though. You can also express fractions as a decimal or apercentage. So 1/2 is the same as 0.5 and 50%.
You probably remember how to convert a fraction into adecimal or a percentage from junior high school math, though.Expressing a Probability in Odds Format
The more interesting and useful way to express probability isin odds format. When you’re expressing a probability as odds,you compare the number of ways it can’t happen with the numberof ways it can happen.
Here are a couple of examples of this.Example 1:
You want to express your chances of rolling a six on a sixsided die in odds format. There are five ways to get somethingother than a six, and only one way to get a six, so the odds are5 to 1.Example 2:
You want to express the odds of drawing an ace of spades outa deck of cards. 51 of those cards are something else, but oneof those cards is the ace, so the odds are 51 to 1.
Odds become useful when you compare them with payouts onbets. True odds are when a bet pays off at the same rate as itsprobability.
Here’s an example of true odds:
You and your buddy are playing a simple gambling game youmade up. He bets a dollar on every roll of a single die, and hegets to guess a number. If he’s right, you pay him $5. If he’swrong, he pays you $1.
Since the odds of him winning are 5 to 1, and the payoff isalso 5 to 1, you’re playing a game with true odds. In the longrun, you’ll both break even. In the short run, of course,anything can happen. Probability and Expected Value
One of the truisms about probability is that the greater thenumber of trials, the closer you’ll get to the expected results.
If you changed the equation slightly, you could play thisgame at a profit. Suppose you only paid him $4 every time hewon. You’d have him at an advantage, wouldn’t you?
*He’d win an average of $4 once every six rolls
*But he’d lose an average of $5 on every six rolls
*This gives him a net loss of $1 for every six rolls.
You can reduce that to how much he expects to lose on everysingle roll by dividing $1 by 6. You’ll get 16.67 cents.
On the other hand, if you paid him $7 every time he won, he’dhave an advantage over you. He’d still lose more often than he’dwin. But his winnings would be large enough to compensate forthose 5 losses and then some.
The difference between the payout odds on a bet and the trueodds is where every casino in the world makes its money. Theonly bet in the casino which offers a true odds payout is theodds bet in craps, and you have to make a bet at a disadvantagebefore you can place that bet.
Here’s an actual example of how odds work in a casino. Aroulette wheel has 38 numbers on it. Your odds of picking thecorrect number are therefore 37 to 1. A bet on a single numberin roulette only pays off at 35 to 1.
You can also look at the odds of multiple events occurring.The operative words in these situations are “and” and “or”.
*If you want to know the probability of A happening ANDof B happening, you multiply the probabilities.
*If you want to know the probability of A happening OR ofB happening, you add the probabilities together.
Here are some examples of how that works.Example 1:
You want to know the probability that you’ll draw an ace ofspades AND then draw the jack of spades. The probability ofdrawing the ace of spades is 1/52. The probability of thendrawing the jack of spades is 1/51. (That’s not a typo—youalready drew the ace of spades, so you only have 51 cards leftin the deck.)
The probability of drawing those 2 cards in that order is1/52 X 1/51, or 1/2652.Example 2:
You want to know the probability that you’ll get a blackjack.That’s easily calculated, but it varies based on how many decksare being used. For this example, we’ll use one deck.
To get a blackjack, you need either an ace-ten combination,or a ten-ace combination. Order doesn’t matter, because eitherwill have the same chance of happening.
Your probability of getting an ace on your first card is4/52. You have four aces in the deck, and you have 52 totalcards. That reduces down to 1/13.Probability Of Losing 5 In A Row Blackjack
Your probability of getting a ten on your second card is16/51. There are 16 cards in the deck with a value of ten; foureach of a jack, queen, king, and ten.
So your probability of being dealt an ace and then a 10 is1/13 X 16/51, or 16/663.
The probability of being dealt a 10 and then an ace is also16/663.
You want to know if one or the other is going to happen, soyou add the two probabilities together.
16/663 + 16/663 = 32/663.
That translates to approximately 0.0483, or 4.83%. That’sabout 5%, which is about 1 in 20.Example 3:
You’re playing in a single deck blackjack game, and you’veseen 4 hands against the dealer. In all 4 of those hands, no aceor 10 has appeared. You’ve seen a total of 24 cards.
What is your probability of getting a blackjack now?
Your probability of getting an ace is now 4/28, or 1/7.(There are only 28 cards left in the deck.)Odds Of Getting A Blackjack
Your probability of getting a 10 is now 16/27.
Your probability of getting an ace and then a 10 is 1/7 X16/27, or 16/189.
Again, you could get a blackjack by getting an ace and a tenor by getting a ten and then an ace, so you add the twoprobabilities together.
16/189 + 16/189 = 32/189
Your chance of getting a blackjack is now 16.9%.
This last example demonstrates why counting cards works. Thedeck has a memory of sorts. If you track the ratio of aces andtens to the low cards in the deck, you can tell when you’re morelikely to be dealt a blackjack.
Since that hand pays out at 3 to 2 instead of even money,you’ll raise your bet in these situations.The House Edge
The house edge is a related concept. It’s a calculation ofyour expected value in relation to the amount of your bet.
Here’s an example.If the expected value of a $100 bet is $95, the house edge is5%.
Expected value is just the average amount of money you’ll winor lose on a bet over a huge number of trials.
Using a simple example from earlier, let’s suppose you are a12 year old entrepreneur, and you open a small casino on thestreet corner. You allow your customers to roll a six sided dieand guess which result they’ll get. They have to bet a dollar,and they get a $4 win if they’re right with their guess.
Over every six trials, the probability is that you’ll winfive bets and lose one bet. You win $5 and lose $4 for a net winof $1 for every 6 bets.$1 divided by six bets is 16.67 cents.Your house edge is 16.67% for this game.
The expected value of that $1 bet, for the customer, is about84 cents. The expected value of each of those bets–for you–is$1.16.
That’s how the casino does the math on all its casino games,and the casino makes sure that the house edge is always in theirfavor.
With blackjack, calculating this house edge is harder. Afterall, you have to keep up with the expected value for everysituation and then add those together. Luckily, this is easyenough to do with a computer. We’d hate to have to work it outwith a pencil and paper, though.
What does the house edge for blackjack amount to, then?
It depends on the game and the rules variations in place. Italso depends on the quality of your decisions. If you playperfectly in every situation—making the move with the highestpossible expected value—then the house edge is usually between0.5% and 1%.
If you just guess at what the correct play is in everysituation, you can add between 2% and 4% to that number. Evenfor the gambler who ignores basic strategy, blackjack is one ofthe best games in the casino.Expected Hourly Loss and/or Win
You can use this information to estimate how much moneyyou’re liable to lose or win per hour in the casino. Of course,this expected hourly win or loss rate is an average over a longperiod of time. Over any small number of sessions, your resultswill vary wildly from the expectation.
Here’s an example of how that calculation works.
*You are a perfect basic strategy player in a game with a0.5% house edge.
*You’re playing for $100 per hand, and you’re averaging50 hands per hour.
*You’re putting $5,000 into action each hour ($100 x 50).
*0.5% of $5,000 is $25.
*You’re expected (mathematically) to lose $25 per hour.
Here’s another example that assumes you’re a skilled cardcounter.
*You’re able to count cards well enough to get a 1% edgeover the casino.
*You’re playing the same 50 hands per hour at $100 perhand.
*Again, you’re putting $5,000 into action each hour ($100x $50).
*1% of $5,000 is $50.
*Now, instead of losing $25/hour, you’re winning $50 perhour.Effects of Different Rules on the House Edge
The conditions under which you play blackjack affect thehouse edge. For example, the more decks in play, the higher thehouse edge. If the dealer hits a soft 17 instead of standing,the house edge goes up. Getting paid 6 to 5 instead of 3 to 2for a blackjack also increases the house edge.
Luckily, we know the effect each of these changes has on thehouse edge. Using this information, we can make educateddecisions about which games to play and which games to avoid.
Here’s a table with some of the effects of various ruleconditions.Rules VariationEffect on House Edge6 to 5 payout on a natural instead of the stand 3 to 2 payout+1.3%Not having the option to surrender+0.08%8 decks instead of 1 deck+0.61%Dealer hits a soft 17 instead of standing+0.21%Player is not allowed to double after splitting+0.14%Player is only allowed to double with a total of 10 or 11+0.18%Player isn’t allowed to re-split aces+0.07%Player isn’t allow to hit split aces+0.18%
These are just some examples. There are multiple rulesvariations you can find, some of which are so dramatic that thegame gets a different name entirely. Examples include Spanish 21and Double Exposure.
The composition of the deck affects the house edge, too. Wetouched on this earlier when discussing how card counting works.But we can go into more detail here.
Every card that is removed from the deck moves the house edgeup or down on the subsequent hands. This might not make senseinitially, but think about it. If you removed all the aces fromthe deck, it would be impossible to get a 3 to 2 payout on ablackjack. That would increase the house edge significantly,wouldn’t it?
Here’s the effect on the house edge when you remove a card ofa certain rank from the deck.Card RankEffect on House Edge When Removed2-0.40%3-0.43%4-0.52%5-0.67%6-0.45%7-0.30%8-0.01%9+0.15%10+0.51%A+0.59%
These percentages are based on a single deck. If you’replaying in a game with multiple decks, the effect of the removalof each card is diluted by the number of decks in play.
Looking at these numbers is telling, especially when youcompare these percentages with the values given to the cardswhen counting. The low cards (2-6) have the most dramatic effecton the house edge. That’s why almost all counting systems assigna value to each of them. The middle cards (7-9) have a muchsmaller effect. Then the high cards, aces and tens, also have alarge effect.
The most important cards are the aces and the fives. Each ofthose cards is worth over 0.5% to the house edge. That’s why thesimplest card counting system, the ace-five count, only tracksthose two ranks. They’re that powerful.
You can also look at the probability that a dealer will bustbased on her up card. This provides some insight into how basicstrategy decisions work.Dealer’s Up CardPercentage Chance Dealer Will Bust235.30%337.56%440.28%542.89%642.08%725.99%823.86%923.34%1021.43%A11.65%
Perceptive readers will notice a big jump in the probabilityof a dealer busting between the numbers six and seven. They’llalso notice a similar division on most basic strategy charts.Players generally stand more often when the dealer has a six orlower showing. That’s because the dealer has a significantlygreater chance of going bust.Summary and Further Reading
Odds and probability in blackjack is a subject with endlessramifications. The most important concepts to understand are howto calculate probability, how to understand expected value, andhow to quantify the house edge. Understanding the underlyingprobabilities in the game makes learning basic strategy and cardcounting techniques easier.
Register here: http://gg.gg/p36jb
https://diarynote-jp.indered.space
コメント