Gambling Guide
Ask the Wizard #129
"Anonymous" .
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.
Steve A. from Fort Collins, CO
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.
"Anonymous" .
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%.
"Anonymous" .
Combin(6,2)*(1/6)4*(5/6)2 = 0.008037551.
"Anonymous" .
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.
"Anonymous" .
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.]
Hayward D.
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.
"Anonymous" .
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%.
"Anonymous" .
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.
S.R.
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.
