wining possibility of games

please check my answer and answer the question I cant answer:

1. Lotto
6/49 game, odd is 1 in 14,000,000


2. Caribbean poker
Royal Flush: 1/640,000
Straight Flush: 1/70,000
Four of a Kind: 1/4,000


3. three card poker
Straight flush 1/500
three of kind 1/500


4. blackjack
Perfect pair(same value, same suit), 1/60
Pair 1/17

5. holdem poker
pocket AA 1/221

6 blackjack
777(same suit) ?
777(any suit) ?

8. horse race (let's say there are only 8 horse per race)

First 2 in order = 1/8 x 1/7 = 1/56
First 2 in any order = 2/8 x 1/7=1/28

First 3 in order = 1/8 x 1/7 x 1/6 =1/336
First 3 in any order , 3/8 *2/7*1/6 =1/56


First 4 in order = 1/8 x 1/7 x 1/6 x 1/5 = 1/1680
First 4 in any order 4/8*3/7*2/6*1/5 =1/70

For #6, If there are N decks:
777 (same suit) = (4N x (N-1) x (N-2)) / (52N x (52N - 1) x (52N - 2))
777 (any suit) = (4N x (4N-1) x (4N-2)) / (52N x (52N - 1) x (52N - 2))

Thanks for answer, how about there are 8 decks?

what is the chance to get 777 (same suit) and 777 (any suit) ?

For 8 decks, use the formula I already posted, with N = 8

Quote: razzplayer

please check my answer and answer the question I cant answer...

I'd like to remind everyone that we're not here to do homework.

For #8, not sure if this is the correct way of assigning probabilities for events like that.

For instance if you have a top favorite at 1.5 and second favorite at 2.0 bookmakers odds, then the probability of winning on First two in any order by betting those 2 horses is definitely much higher than 1/28. It's more like 1/4.

My point is for competitions we need to estimate the true odds for a given participant to win and not just use the classical probability ratio of favorable to total outcomes.

Obviously the (early) bookmaker odds are just an educated guess as well, but they are much closer to the true probability than simple permutation of favorable vs total classical interpretation for equally likely outcomes.

Quote: rawtuff

For #8, not sure if this is the correct way of assigning probabilities for events like that.

I'm absolutely sure it's not. There has never in the history of horse racing been a race where eight horses have all had exactly the same probability of winning. Which, by the way, is entirely different than the amount of money in the pool for each horse. The payoff odds are determined by the money in the pool, not any a priori assessment of probability.

Quote: MathExtremist

The payoff odds are determined by the money in the pool, not any a priori assessment of probability.

This may be true in the U.S. but most countries do post odds to win and the bookmakers are actually gambling.

Quote: MathExtremist

I'm absolutely sure it's not.

I was trying to be subtle :).

Quote: MathExtremist

The payoff odds are determined by the money in the pool, not any a priori assessment of probability.

We are talking about two different type of horse race betting here, I guess.

I was referring to the betting sites where there is no pool, but a pre-estimated odds for each and every horse.
To be honest I'm very vaguely familiar with pool betting, but if this was the OP question, then it will be the money flow which defines the odds and not the bookie, but that's not so different either way. The crowd wisdom is heavily used by the bookmakers to fine tune their early odds and exposure..

Quote: DRich

This may be true in the U.S. but most countries do post odds to win and the bookmakers are actually gambling.

True enough, I was assuming pari-mutuel betting, not lines set by the bookmaker like in other sports. I'd hate to have to set lines on horse races manually.

your answer is meaningless.