[QUOTE I believe Darryl is close to what the actual odds would be.
wil.[/QUOTE]
Darryl was close, but I posted the actual odds earlier in the thread:
Here are the odds of getting ONE blackjack in single-deck BJ:
Ace first: 4/52 * 16/51 = .02413 or 1 out of 41.44 hands.
Ten first: 16/52 * 4/51 = .02413 or 1 out of 41.44 hands.
Total : = .04826 or 1 out of 20.72 hands.
What you experienced has odds of 1/20.72 to the 6th power. This equals:
0.0482625 to the 6th power, which equals 1.2638 -08 in scientific notation. In plain numbers, getting 6 BJs in a row will happen 1.26 times every 100 million trials.
Phaedrus - you are correct that one trial does not affect the outcome of the next, just as with flipping a coin. The odds we are describing are for a series of identical results of such independent trials, and the odds of what you experienced are close to one in 80 mil.
UT
wil.[/QUOTE]
Darryl was close, but I posted the actual odds earlier in the thread:
Here are the odds of getting ONE blackjack in single-deck BJ:
Ace first: 4/52 * 16/51 = .02413 or 1 out of 41.44 hands.
Ten first: 16/52 * 4/51 = .02413 or 1 out of 41.44 hands.
Total : = .04826 or 1 out of 20.72 hands.
What you experienced has odds of 1/20.72 to the 6th power. This equals:
0.0482625 to the 6th power, which equals 1.2638 -08 in scientific notation. In plain numbers, getting 6 BJs in a row will happen 1.26 times every 100 million trials.
Phaedrus - you are correct that one trial does not affect the outcome of the next, just as with flipping a coin. The odds we are describing are for a series of identical results of such independent trials, and the odds of what you experienced are close to one in 80 mil.
UT
Uber Tout,
Sorry for not noticing your post. Yours is indeed the more accurate number so my post was redundant.
Phaedrus,
I think you are missing something, or at least you are missing the fact that there is nothing to miss.
When there is reshuffling, you use what's called "sampling with replacement" which means you just take the probability to the appropriate exponent.
If there is no reshuffling, you use "sampling without replacement" and so at each stage you must consider the number of cards remaining. In a 6-deck shoe it would be:
24*96*2*23*95*2*22*94*2...*19*91*2
----------------------------------
312*311*310*309*...*301
which is even smaller and therefore more astronomically improbable.
Sorry for not noticing your post. Yours is indeed the more accurate number so my post was redundant.
Phaedrus,
I think you are missing something, or at least you are missing the fact that there is nothing to miss.
When there is reshuffling, you use what's called "sampling with replacement" which means you just take the probability to the appropriate exponent.
If there is no reshuffling, you use "sampling without replacement" and so at each stage you must consider the number of cards remaining. In a 6-deck shoe it would be:
24*96*2*23*95*2*22*94*2...*19*91*2
----------------------------------
312*311*310*309*...*301
which is even smaller and therefore more astronomically improbable.
Well, it was certainly a weird experience. To better put the odds in perspective, I have played at this casino for four years, practically seven days a week with little break, no possible estimate on the number of hands per day. Almost any time I am online I have it open in another window, sort of like the Rx.
So, again, while really freakishly rare, I've had lots and lots of opporunities for it to happen. And as I said before I already made back the $100 or so that it cost me, so it's academic at this point.
I really appreciate the keen insights from the math guys, Darryl et al. Probability fascinates me.
Phaedrus
So, again, while really freakishly rare, I've had lots and lots of opporunities for it to happen. And as I said before I already made back the $100 or so that it cost me, so it's academic at this point.
I really appreciate the keen insights from the math guys, Darryl et al. Probability fascinates me.
Phaedrus
Well Phade, there are several possibilities:
1) The casino IS crooked after all ("Well blow me down" - Popeye)
2) The RNG is REALLY REALLY BAD and somehow it deals the 6 BJ's to the house instead of you, leading to
3) Yes, it's a crooked casino because if the RNG is this bad they'd be out of business in a hurry, thus it ain't the RNG.
Then there's
4) Supposedly smart offshore gamblin' guy buys notion that an online casino could be anything other than rigged
But I'm sure that's not it...
I'd stick to betting sports or playing in a real casino with a real deck of cards.
1) The casino IS crooked after all ("Well blow me down" - Popeye)
2) The RNG is REALLY REALLY BAD and somehow it deals the 6 BJ's to the house instead of you, leading to
3) Yes, it's a crooked casino because if the RNG is this bad they'd be out of business in a hurry, thus it ain't the RNG.
Then there's
4) Supposedly smart offshore gamblin' guy buys notion that an online casino could be anything other than rigged
But I'm sure that's not it...
I'd stick to betting sports or playing in a real casino with a real deck of cards.
Nice posts Uber and Darryl...people don't understand that just because the dealer got 3 or 4 blackjacks in a row doesn't mean the odds of him getting another one change on the next hand. It's similar to the way the casinos have put those columns up now next to the roulette wheel showing the previous spin results. People try and read into that "data" to make a bet on the next spin and it has absolutely ZERO relevance.
As to evidence that some online casinos are rigged, how about software in use at one(that I know of) sportsbook/casino that has an external "take" variable that may be changed at the management's discretion? For God's sake Phaedrus you're playing against a computer program that's designed for them to make money! I know it's great entertainment,but it's not a long term money making proposition.
Now I know some more astute posters here have found some pigeon casinos who are giving away the house in bonuses. What happens in the long run to businesses that are run in that fashion? The many sportsbooks that had stupid bonus programs either have cut them out entirely or worse...went out of businesss stiffing many of the RX posters.
I truly believe we are doing a disservice to the RX poster base by encouraging online casino play for profit.
As to evidence that some online casinos are rigged, how about software in use at one(that I know of) sportsbook/casino that has an external "take" variable that may be changed at the management's discretion? For God's sake Phaedrus you're playing against a computer program that's designed for them to make money! I know it's great entertainment,but it's not a long term money making proposition.
Now I know some more astute posters here have found some pigeon casinos who are giving away the house in bonuses. What happens in the long run to businesses that are run in that fashion? The many sportsbooks that had stupid bonus programs either have cut them out entirely or worse...went out of businesss stiffing many of the RX posters.
I truly believe we are doing a disservice to the RX poster base by encouraging online casino play for profit.
The dealer getting 6 blackjacks in a row would be enough for me. The odds are as stated above... about 1 in 100 million.
I've played more blackjack than just about anyone here, thousands of hours. I have never seen anything like that. 3 blackjacks in a row I've seen a handful of times. I have lost 19 hands in a row, but that's another story.
Either the casino cheats intentionally, or there is a problem with the RNG which is unintentional. Maybe you'll get dealt 6 blackjacks in a row if that's the case.
I've played more blackjack than just about anyone here, thousands of hours. I have never seen anything like that. 3 blackjacks in a row I've seen a handful of times. I have lost 19 hands in a row, but that's another story.
Either the casino cheats intentionally, or there is a problem with the RNG which is unintentional. Maybe you'll get dealt 6 blackjacks in a row if that's the case.
<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>
As to evidence that some online casinos are rigged, how about software in use at one(that I know of) sportsbook/casino that has an external "take" variable that may be changed at the management's discretion?
Now I know some more astute posters here have found some pigeon casinos who are giving away the house in bonuses. What happens in the long run to businesses that are run in that fashion? The many sportsbooks that had stupid bonus programs either have cut them out entirely or worse...went out of businesss stiffing many of the RX posters.
<HR></BLOCKQUOTE>
OK, as an indsider I can share something with you. ALL casino back-end systems that I have experience with have an algorythm to adjust the hold %. Some couch it in terms of changing rules, some don't. Some are at the discretion of the operator, the company that sets up and manages the back end. Some are at the discretion of the software provider.
Bonuses are the great equalizer. Bonuses are the comp drink of the internet. If it weren't for the fact that the majority of online BJ players were undisciplined and do not play perfect strategy, online casinos could not afford to offer bonuses.
Same concept at the brick-and-mortar. If everyone played perfect strategy, the 1.5% hold would not pay for all that silicone and spandex for cocktail waitresses and the delicious drinks they bring you.
If you play perfect strategy and avail yourself of bonuses while adhering to all bonus requirements, you can approach a 50/50 game over time.
Something to consider, for those (like me) who have put in serious time playing online BJ and are observant. Does your 'luck' at the BJ table seem to fluctuate slightly with the day of the week, or the season?
Before no-pay situations, there are slow-pay situations, and before slow-pay, there is often a tightening of casino rules and algorythms to increase the hold.
UT
As to evidence that some online casinos are rigged, how about software in use at one(that I know of) sportsbook/casino that has an external "take" variable that may be changed at the management's discretion?
Now I know some more astute posters here have found some pigeon casinos who are giving away the house in bonuses. What happens in the long run to businesses that are run in that fashion? The many sportsbooks that had stupid bonus programs either have cut them out entirely or worse...went out of businesss stiffing many of the RX posters.
<HR></BLOCKQUOTE>
OK, as an indsider I can share something with you. ALL casino back-end systems that I have experience with have an algorythm to adjust the hold %. Some couch it in terms of changing rules, some don't. Some are at the discretion of the operator, the company that sets up and manages the back end. Some are at the discretion of the software provider.
Bonuses are the great equalizer. Bonuses are the comp drink of the internet. If it weren't for the fact that the majority of online BJ players were undisciplined and do not play perfect strategy, online casinos could not afford to offer bonuses.
Same concept at the brick-and-mortar. If everyone played perfect strategy, the 1.5% hold would not pay for all that silicone and spandex for cocktail waitresses and the delicious drinks they bring you.
If you play perfect strategy and avail yourself of bonuses while adhering to all bonus requirements, you can approach a 50/50 game over time.
Something to consider, for those (like me) who have put in serious time playing online BJ and are observant. Does your 'luck' at the BJ table seem to fluctuate slightly with the day of the week, or the season?
Before no-pay situations, there are slow-pay situations, and before slow-pay, there is often a tightening of casino rules and algorythms to increase the hold.
UT
BTW, I quoted SENDITIN above. And SENDITIN, I think it's amusing also to see folks writing down roulette numbers to see which number is 'overdue'..
Darryl Parsons is on the money with sampling and replacement.
That's why when my lottery numbers come up (1,2,3,4,5,6) I won't be sharing my prize with anyone except some other smartass mathematician...or maybe Darryl P and SENDITIN
UT
Darryl Parsons is on the money with sampling and replacement.
That's why when my lottery numbers come up (1,2,3,4,5,6) I won't be sharing my prize with anyone except some other smartass mathematician...or maybe Darryl P and SENDITIN
UT
