Out of those 100 times, the dealer had a blackjack 8 times. I did have a blackjack twice. The two times that I got a blackjack, the dealer also got a blackjack. Out of the 100 plays, the dealer got a 10 in his visible card 53 times. Out of those 53 times, 35 the dealer had another 10 in his hand. In 11 situations the dealer had a 19 on his hand. Ignoring ties the probability of a new loss for a hand of blackjack is 52.51%. So the probability of losing 8 in a row is.5251 8 = 1 in 173. I play 50 cent slots and higher.
From my video poker appendix 3 we can see the standard deviation for 1-play jacks or better is 4.417542. The standard deviation for 4-play jacks or better is 5.041215. Keep in mind these figures are per hand and relative to the betting unit. Adjusting for bet size and number of hands the standard deviation of $5 bet in 1-play jacks or better is 11/2*5*4.417542 = 22.08771. The standard deviation of 4 bets of $2.50 in 4-play jacks or better is 41/2*$2.50*5.041215 = 25.20608. So you are better off betting the smaller total amount in 1-play. Interestingly you can double the total amount bet in 4-play and the standard deviation only goes up by 14.12%.
Actually I get a player return of 101.62%. Buried within their rules is this statement, 'Please note that all games share the same mechanism which determines the jackpot win. Thus, with card games, the probability of hitting the jackpot combination is not natural but controlled by this shared random mechanism in the same way as slot machines' wins.' It is my understanding that they offered this game for quite a while before posting this warning. I just don't trust any casino that would rig a card game, even if they admit it in the fine print.
For the sake of simplicity let's stay with your example and say the probability of winning is 70% and losing is 30% if you hit. The expected value of hitting would be 0.3*1 + 0.7*-1 = -0.4. This is greater than the expected value of -0.5 by surrendering.
No, these exceptions should not be used for 4-8 decks. There are a few exceptions in 4-8 deck games but they are so border line that it isn't worth the bother to learn them. An interesting rule of thumb for all numbers of decks is that with 16 vs. 10, where the 16 is composed of 3 or more cards, in general the odds favor standing.
The name for this system is the Martingale. Ignoring ties the probability of a new loss for a hand of blackjack is 52.51%. So the probability of losing 8 in a row is .52518 = 1 in 173.
No. If your goal is a small win then you should be playing low volatility, high hit frequency games. I can't suggest any particular games but look for ones with comparatively small jackpots. These will also help you to play longer.
The Martingale is dangerous on every game and in the long run will never win. However it is better to use in baccarat than roulette, just because of the lower house edge. The probability of the player winning 8 times in a row is 0.493163^8 = 1 in 286. Also keep in mind you could win a hand late in the series and still come out behind because of the commission. For example if you started with a bet of $1 and you won on the 7th hand you would win $60.80 ($64*95%), which would not cover the $63 in previous loses.
I've been asked about these North Carolina slot machines so many times I'm tempted to fly there just to see them for myself. Yes, if they did give the probability of each symbol for each reel then an optimal strategy and a return could be fairly easily calculated. However I have never actually seen such a table and have never worked out the odds.
The probability of any hand less than a pair is the product of the number of ways to pick 3 different ranks out of 13, less 12 for the consecutive ranks that result in a straight, and the number of ways to pick a suit 3 different times, less 4 for picking the same suit each time. So the total combinations for ace-high or less is (combin(13,3)-12)*(43-4) = 16,440.
Chances Of Losing 10 Blackjack Hands In A Rowing
Actually I get a player return of 101.62%. Buried within their rules is this statement, 'Please note that all games share the same mechanism which determines the jackpot win. Thus, with card games, the probability of hitting the jackpot combination is not natural but controlled by this shared random mechanism in the same way as slot machines' wins.' It is my understanding that they offered this game for quite a while before posting this warning. I just don't trust any casino that would rig a card game, even if they admit it in the fine print.
For the sake of simplicity let's stay with your example and say the probability of winning is 70% and losing is 30% if you hit. The expected value of hitting would be 0.3*1 + 0.7*-1 = -0.4. This is greater than the expected value of -0.5 by surrendering.
No, these exceptions should not be used for 4-8 decks. There are a few exceptions in 4-8 deck games but they are so border line that it isn't worth the bother to learn them. An interesting rule of thumb for all numbers of decks is that with 16 vs. 10, where the 16 is composed of 3 or more cards, in general the odds favor standing.
The name for this system is the Martingale. Ignoring ties the probability of a new loss for a hand of blackjack is 52.51%. So the probability of losing 8 in a row is .52518 = 1 in 173.
No. If your goal is a small win then you should be playing low volatility, high hit frequency games. I can't suggest any particular games but look for ones with comparatively small jackpots. These will also help you to play longer.
The Martingale is dangerous on every game and in the long run will never win. However it is better to use in baccarat than roulette, just because of the lower house edge. The probability of the player winning 8 times in a row is 0.493163^8 = 1 in 286. Also keep in mind you could win a hand late in the series and still come out behind because of the commission. For example if you started with a bet of $1 and you won on the 7th hand you would win $60.80 ($64*95%), which would not cover the $63 in previous loses.
I've been asked about these North Carolina slot machines so many times I'm tempted to fly there just to see them for myself. Yes, if they did give the probability of each symbol for each reel then an optimal strategy and a return could be fairly easily calculated. However I have never actually seen such a table and have never worked out the odds.
The probability of any hand less than a pair is the product of the number of ways to pick 3 different ranks out of 13, less 12 for the consecutive ranks that result in a straight, and the number of ways to pick a suit 3 different times, less 4 for picking the same suit each time. So the total combinations for ace-high or less is (combin(13,3)-12)*(43-4) = 16,440.
Chances Of Losing 10 Blackjack Hands In A Rowing
Chances Of Losing 8 Blackjack Hands In A Row
Now let's look at the combinations for a jack high or less. We have omitted 3 ranks so there are 3 ranks to choose from among 10. However 8 of these combinations result in a straight (2/3/4 to 9/10/J). Again there are 43-4 ways to pick the suits. So the total combinations is (combin(10,3)-8)*( 43-4) = 6,720. The total combinations for Q-A high is simply 16,440-6,720=9,720. For an explanation of the combin function please see my probabilities in poker section.