Ask The Wizard #129
How likely is it to play 17.76 royal cycles of video poker and hit only three royals?
This is a good question for the Poisson distribution. If an event is equally likely any given moment and independent of other events, and the mean number you can expect is m, then the probability of n events is e-m*mn/n!. So in this situation the probability is e-17.76*17.763/3! = 0.00001808, or 1 in 55321.
I saw in the paper last week that the latest earthquake that ravaged Indonesia hit on December 26th. It also showed that of the eight deadliest earthquakes to hit over the last 100 years, three of them have been on December 26th. I was wondering what the odds are of having three massive quakes hit on the same day knowing these facts: Earthquakes of this magnitude (8.0 or larger) happen only once per year. The last big quake was exactly one year ago, 12/26/03 in Iran (back to back probabilities?) I look forward to hearing from you.
After discovering the claim that the Florida hurricanes only hit Bush voting counties was a hoax (see the October 17, 2004 column) I am going to be more skeptical about such alleged coincidences. According to the National Earthquake Information Center of the top 11 earthquakes since 1990 only the recent one of 2004 hit on a December 26. The Iranian earthquake you mention was only 6.7 in magnitude, which is far from making the top eight.
You are the greatest! I just stumbled across your site a few days ago. My question is in regard to Boston 5 Stud Poker. I saw this game tonight at Mohegan Sun in Connecticut. Their "Ante Bonus" for a Straight is listed at 8 x Ante Bet instead of the 10 x Ante Bet on your pay table. How will this affect the overall odds for this game? Thanks again, keep up the great work!
Thank you for all the kind words. If you lower the bonus on the straight from 10 to 8 the house edge increases from 3.32% to 3.48%.
If I roll a single die 6 times, what is the probability of getting a "2" exactly 4 times?
Combin(6,2)*(1/6)4*(5/6)2 = 0.008037551.
If someone follows such a Martingale system in blackjack, what is the probability of being able to win $200 per day or lose the entire $5,000? Also, does increasing the amount available for total wagering increase the likelihood of winning the $200.
If you had a game with no house edge the probability of winning $200 with $5000 to risk, using any system, would be 5000/(5000+200) = 96.15%. The general formula for winning w with a bankroll of b is b/(b+w). So the larger the bankroll the better your chances. The house edge will lower the probability of success by an amount that is hard to quantify. For a low house edge game like blackjack, the reduction in the probability of success will be small. It would take a random simulation to know for sure. Forgive me if I don't bother with that. VegasClick did a small simulation about the probability of success with the Martingale.
Was reading through your site and browsing the section on tipping and had a few comments to share. I’ve always found it best to place the tip on top of my bet and have the dealer’s "playing with me" until I lose. Usually you are tipping when you are winning and if you get on a long winning streak a $1 tip can turn into much more for the dealers. Just make sure the dealer knows that the extra chip on top of your own bet is for them! Thanks for all the great information on all the games!
I’ve seen this happen before and I agree that some dealers like it. However in my opinion most don’t care because tips are pooled and shared among all the dealers. In 18 years of playing blackjack I have only once seen a dealer ask a player to do this.
[Bluejay adds: I always ask dealers which method they prefer, because some have a distinct preference. Some like the chip riding on top while others hate it. I like giving dealers the option, because just by asking I establish a small bond with them by showing that I’m considering their feelings.]
Thank you for the wonderful site. I check it at least weekly. I also have patronized your sponsors. I am a dealer at an Indiana casino. If I make a mistake in the player’s favor, the last thing I want is a tip because of the mistake. It makes it look like the error was deliberate in an attempt to receive a tip. Advise people that tips should be given for service not for an error that gives them money. Thanks again.
Thanks for the kind words and patronizing the advertisers. I’m happy to post what you said. For the benefit of those new to this column this refers to a question in the December 27, 2004 column.
Dear wonderful Wizard, firstly THANK YOU VERY MUCH for your wonderful site! I have spent hours upon hours exploring all that your superbly done site has to offer, and I am grateful for your truly invaluable advice, so THANK YOU! I have a question regarding a side bet of Keno here in Australia called "Heads and Tails". The board is divided in half, numbers 1 to 40 are heads and 41 to 80 are tails. If the majority of numbers drawn are low (1 to 40) then heads wins, if the majority are high (41-80) then tails wins. Both bets pay 1 to 1. There is also a bet called Evens, which pays 3 to 1 if 10 numbers are low and 10 are high. My question is, what is the house edge of each bet?
Compliments will get you everywhere. The number of combinations for n heads is combin(40,n)*combin(40,20-n). This is the number of ways to choose n numbers out of the top 40 and 20-n out of the bottom 40. The following table shows the probability of 0 to 20 heads.
Probability of 0 to 20 Heads
| Heads | Combinations | Probability |
|---|---|---|
0 |
137846528820 |
0.000000039 |
| 1 | 5251296336000 |
0.0000014854 |
2 |
88436604204000 |
0.0000250152 |
3 |
876675902544001 |
0.0002479767 |
4 |
5744053569793500 |
0.0016247638 |
5 |
26468598849608400 |
0.0074869114 |
6 |
89077015359259200 |
0.0251963366 |
7 |
224342112756653000 |
0.0634574402 |
8 |
429655207020554000 |
0.1215323297 |
9 |
632136396535987000 |
0.1788061862 |
10 |
718528370729238000 |
0.2032430317 |
11 |
632136396535987000 |
0.1788061862 |
12 |
429655207020554000 |
0.1215323297 |
13 |
224342112756653000 |
0.0634574402 |
14 |
89077015359259200 |
0.0251963366 |
15 |
26468598849608400 |
0.0074869114 |
16 |
5744053569793500 |
0.0016247638 |
17 |
876675902544001 |
0.0002479767 |
18 |
88436604204000 |
0.0000250152 |
19 |
5251296336000 |
0.0000014854 |
| 20 | 137846528820 |
0.000000039 |
Total |
3535316142212170000 |
1 |
This shows the probability of 11 to 20 heads is 39.84%, for a house edge of 20.32%. The probability of exactly 10 is 20.32%, for a house edge of 18.70%.
What is the best betting system for a player to use when playing the online casino blackjack games that give the PLAYER the slight edge? Are there any systems when there is a positive player edge that can be used to most effectively gain maximum winnings with minimum chance of losses over the long run? Or would the best system be to bet the same amount consistently and follow the optimum basic strategy (and its exceptions for single deck) for all the hands played?
I would recommend flat betting. The expected return is the same regardless of how you bet, but flat betting is best for minimizing volatility and ensuring bankroll preservation.
I’ve noticed a small disturbing pattern at the craps table that I thought might be worth mentioning on your site. Players will bet the don’t come bar, but if a 6 or 8 is rolled as the point they say "no action" and they keep their money on the don’t come bar. The Luxor even had a boxman ENCOURAGE me to do it saying it’s what "smart people who know the odds are better on the don’t tend to do" or something to that effect. Not sure how you could incorporate this into your site but I’ve seen players doing it and casinos encouraging it and it’s really stooopid.
I agree that this is a very bad decision and poor advice from the dealers. Once a point of 6 or 8 has been rolled the player edge on a don’t pass or don’t come bet is (6/11)*1 + (5/11)*-1 = 1/11 = 9.09%. Taking "no action" is the same as trading it for a bet with a 1.36% house edge. So this decision costs the player 10.45%. To any dealers encouraging this I say shame on you.