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Thread: On Average How Many Blackjack Hands Have to be Played to Win 5 in a Row

  1. #14


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    Quote Originally Posted by G Man View Post
    James, I think people are confusing the probability of getting 3 heads in a row (0.125 or 1/8) with the average number or throws required for that probability to happen (3 heads in a row). Maybe you can explain the nuances in more details for the audience!
    It is average number or throws required for that probability to happen (3 heads in a row)

  2. #15


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    Quote Originally Posted by aceside View Post
    Let me focus on the coin flipping case. Based on your formula, what is the probability of getting 3 or more heads in a row? Is this prob close to 0.5^3 ?
    probability of getting 3 head in a row = 0.5^3 = 0.125, but average no of flips to have a 3 head in a row = 14.

  3. #16
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    Quote Originally Posted by James989 View Post
    updated :-

    Just an estimate for your actual case, average rounds required before you get a 5 hand winning streak(pushes don't break the streak) is 84, so your net profit = 250 - 84 * 25 *0.005 = 239.5.
    Although this number 84 sounds good for me, your calculation of EV sounds not correct. If the table minimum is $10, we expect to lose 10x0.005=$0.05 each hand while gaining a free bet amount of 10x$25x2.418% each hand. My above calculation should be good.
    Last edited by aceside; 11-20-2021 at 01:09 PM.

  4. #17


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    Quote Originally Posted by James989 View Post
    Just an estimate for your actual case, average rounds required before you get a 5 hand winning streak(pushes don't break the streak) is 84,
    No, it's 77, if you're using 0.475 as the probability of a resolved win. What number did you use? It's kind of silly arguing about this. I've posted these sites before. All you ever need to know about streak probabilities is here: https://sites.google.com/view/krapstuff/home
    or here: http://williamray.net/statistics/CalculateStreaks.shtml

    Same results, but the first site provides more information, including the result we're discussing.

    Don

  5. #18


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    Quote Originally Posted by DSchles View Post
    No, it's 77, if you're using 0.475 as the probability of a resolved win. What number did you use? It's kind of silly arguing about this. I've posted these sites before. All you ever need to know about streak probabilities is here: https://sites.google.com/view/krapstuff/home
    or here: http://williamray.net/statistics/CalculateStreaks.shtml

    Same results, but the first site provides more information, including the result we're discussing.

    Don
    The estimated rounds of 84(average rounds required before you get a 5 hand winning streak) is based on p = 0.4332, q = 0.4788, r = 0.088, and pushes don't break the streak.


    I guess your 77 rounds(
    average rounds required before you get a 5 hand winning streak) is based on p = 0.475, q = 0.525, r = 0, and pushes don't break the streak.
    Last edited by James989; 11-20-2021 at 03:36 PM.

  6. #19


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    Quote Originally Posted by DSchles View Post
    No one is calculating this correctly. Streak probabilities are very complex to calculate. Just saying 0.475^5 gives you only the probability of playing five hands and winning them all. It has nothing to do with playing x number of hands and wondering if a winning streak of, say, 5 will occur.

    Some examples: 50 hands: 47.6% probability
    100 hands: 74.5%
    200 hands: 95.3%
    300 or more hands: virtual certainty

    So, giving you $250 in free bets seems impossible to me. It's impossible to play more than a couple of hours without winning five in a row--unless, of course, you're cheated. And, since it's online, I'd say the chances of that are extremely high.

    Don
    Thanks Don and everybody else who contributed to this thread. I did get a couple of 5 win streaks in a row in less than 2 hours. The first one was on Spanish 21 which I found out didn't count because the game was not blackjack. I then got another on blackjack. Interesting twist in my 5 hand winning streak. One of the hands in the streak was actually a split and then a double down. I lost one hand of the split but won the double down hand. There is always a message that flashes up on the screen if you have 3 or more wins in a row. Yeah, I got my 250 free credits.

    The other day when I was playing to get my 5 hand winning steak, it was quite difficult. Today when playing on a different promotion I must of got 6 or 7 in a couple of hours with the first one being less than 5 minutes.

    Just a note for Aceside. The 250 free credits is based on on your lowest wager for the day with a max of 250 free credits. If you only play $10 game you will only get $100 free credits. Even if you play $25 min and then drop to $10 min you free credits are based on your lowest wager.

    I sure hope there is no cheating. The game is regulated by the State of MI and is not some off shore casino. If there is any doubt, they always seem to give the player the best deal. However, things have not been going well for me at this casino for the last couple of months. I actually lost around $12,000 from my high a couple of months ago. However, on the other hand I'm still having my best year ever. I'm presently Diamond status and only need less than 20,000 points out of 1,000,000 to reach the top tier of Onyx by the end of the year. Maybe I will even get better promotions then.

    Well back to play my latest promotion. I'm only half way thru. I get $1 free credit for every $100 bet up to $1,000 in free credits. I think last time they gave $2., but I'm also chalking up points for the leaderboard at the same time. No free sports bets this week.
    Last edited by Midwest Player; 11-21-2021 at 12:17 PM.

  7. #20


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    Quote Originally Posted by Midwest Player View Post
    Thanks Don and everybody else who contributed to this thread. I did get a couple of 5 win streaks in a row in less than 2 hours. The first one was on Spanish 21 which I found out didn't count because the game was not blackjack. I then got another on blackjack. Interesting twist in my 5 hand winning streak. One of the hands in the streak was actually a split and then a double down. I lost one hand of the split but won the double down hand. There is always a message that flashes up on the screen if you have 3 or more wins in a row. Yeah, I got my 250 free credits.

    The other day when I was playing to get my 5 hand winning steak, it was quite difficult. Today when playing on a different promotion I must of got 6 or 7 in a couple of hours with the first one being less than 5 minutes.

    Just a note for Aceside. The 250 free credits is based on on your lowest wager for the day with a max of 250 free credits. If you only play $10 game you will only get $100 free credits. Even if you play $25 min and the drop to $10 min you free credits are based on your lowest wager.

    I sure hope there is no cheating. The game is regulated by the State of MI and is not some off shore casino. If there is any doubt, they always seem to give the player the best deal. However, things have not been going well for me at this casino for the last couple of months. I actually lost around $12,000 from my high a couple of months ago. However, on the other hand I'm still having my best year ever. I'm presently Diamond status and only need less than 20,000 points out of 1,000,000 to reach the top tier of Onyx by the end of the year. Maybe I will even get better promotions then.

    Well back to play my latest promotion. I'm only half way thru. I get $1 free credit for every $100 bet up to $1,000 in free credits. I think last time they gave $2., but I'm also chalking points for the leaderboard at the same time. No free sports bets this week.

    I think you may play the game with strategy deviate from BS, you may get higher win rate(p value), then you can get a 5 hand streak much faster. But such strategy will cause you to lose more on the basic bet.

  8. #21
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    Quote Originally Posted by James989 View Post
    The estimated rounds of 84(average rounds required before you get a 5 hand winning streak) is based on p = 0.4332, q = 0.4788, r = 0.088, and pushes don't break the streak.


    I guess your 77 rounds(
    average rounds required before you get a 5 hand winning streak) is based on p = 0.475, q = 0.525, r = 0, and pushes don't break the streak.
    I looked into the two online streak calculators. Neither can calculate the numbers in your first case because there is a tie probability here. You can just make a more advanced online calculator to benefit the people.

  9. #22
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    Quote Originally Posted by James989 View Post
    probability of getting 3 head in a row = 0.5^3 = 0.125, but average no of flips to have a 3 head in a row = 14.
    I used the two online calculators to find the number 14, but the exact wording there is the average number of flips to have a 3 or more head in a row.

  10. #23


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  11. #24


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    Quote Originally Posted by aceside View Post
    I used the two online calculators to find the number 14, but the exact wording there is the average number of flips to have a 3 or more head in a row.
    It should be exactly 3 head. Is it possible to have 20 head streak( more than 3 head) in 14 rounds ?

  12. #25
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    Quote Originally Posted by James989 View Post
    It should be exactly 3 head. Is it possible to have 20 head streak( more than 3 head) in 14 rounds ?
    That is impossible in only 14 rounds. However, let me give you an example of having both 5 head and 3 head in a 24-round flip.
    Let us define x=head, o=tail.

    xox,xoo,oxx,oxo,xxx,xxo,oox,ooo

    This represents a set of 8 3-round flips, and there is one 3-head flip, xxx; however, there is also one 5-head flip, xxxxx.
    It all depends on how many flips we are going to do, there will be 3-head, 4-head, 5-head ... and so on.

  13. #26


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    Quote Originally Posted by Midwest Player View Post
    The beating bonuses results don't correspond to the two that I sent you, so I didn't include it.

    Don

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