Gambling Probabilities

Gambling is of course a game of chance where luck has a lot to do with how well you pay!  However the odds of winning and losing can be seen by a Probability Analysis which is a statistical study conducted by mathematician.  The scientific study of probability has been going on for the ages.  Gambling has always peaked the interest in the study of probability.  The doctrine of probabilities dates to the correspondence between a couple of mathematicians over 300 years ago!  Pierre-Simon was a French mathematician and astronomer.  He made the first attempts to deduce a rule for his observations from the principles of probabilities.  You can read his bio here.   Now I'm not a mathematician, I've always hated math, partly because I was never any good at it :-(  But I do find the work of modern day mathematicians who provide probability analysis on gambling fascinating.  These are they people the casinos hire to come up with the gambling games different combinations and odds of winning and losing.   So take a deep breath it's math but in the end gambling is but a numbers game anyway.

Bingo Probability Analysis

Your online playing bingo over at Bingo Tide, you're playing 8 bingo cards, you're having a great time playing bingo and chatting with your roomies when you hear BINGO!  Someone else won the big jackpot coverall in 50 balls!  This was the big jackpot and you wonder man what were the odds!  The probability is 0.00000472!  But don't take my word for it, two different mathematicians have studied this and they came to the same conclusion! 

1) A single board has a 0.00488136 probability of producing a Bingo when the 20th number is called.
2) A single board has a 0.0228745 probability of producing a Bingo on or before the 20th number called.
3) In a 50 board game there is a 0.088966 probability someone will get a Bingo when the 20th number is called.
4) In a 50 board game there is a 0.685574 probability someone will get a Bingo on or before the 20th number called.

Putting math to work for you

In Bingo the variables that determine whether you win or lose are made up of several key factors including how many players are in the game, how many bingo cards you and the other player have purchased, and what type of pattern is trying to be covered.  You can calculate your odds if you apply the probability analysis.  If you purchase 10 bingo cards out of 1,000 cards purchased for that game your chance to win the jackpot is 1 in 100.  So your chance of winning does increase if you purchase more bingo cards but remember those odds only increase minimally while your paying a lot more to play more cards!  It can be a vicious cycle to get into.  That is why I suggest you play for fun not because you want to strike it rich.  The odds my friend are against you.  You can review the entire bingo probability statistics by visiting Durango Bill's Bingo Probabilities Statistical page.

That's as in-depth as I want to get when it comes to math and bingo!  But if you want to learn more I suggest checking out the probabilities done by two different math geeks who came to the same probability.  Check out Durango Bill's analysis and The Wizard of Odds.  They dig deep into this subject and provide very detailed charts and graphs about their analysis.

Casino Probabilities

Slots

Check out the Wizard of Odds explanation of how slots work.  He also conducted a study in which he played and recorded 3,976 plays at a land-based casino.  His explanation on how slots work can be found by clicking here.  His study can be found here.

BlackJack

BlackJack is the game that has been written about most but forget what you see in the movies about counting cards.  In order to improve your odds winning at blackjack you need to master basic strategy.  Don't even thing about trying to count cards if you don't have basic strategy memorized.

You can read more about basic strategy by reading my article but I'll provide a detail basic strategy table you can use.  Memorize it if you're serious about playing BlackJack and if you're thinking about learning how to count cards.  If you want a pocket size BlackJack Basic Strategy Card join my newsletter and I'll mail you one for free.  Read about my free offer and privacy policy/no-spam promise here.

Basic strategy tables

Your Hand	Dealer's face-up card
	2	3	4	5	6	7	8	9	10	A
Hard totals
18-21	S	S	S	S	S	S	S	S	S	S
17	S	S	S	S	S	S	S	S	S	Rs
16	S	S	S	S	S	H	H	Rh	Rh	Rh
15	S	S	S	S	S	H	H	H	Rh	Rh
13-14	S	S	S	S	S	H	H	H	H	H
12	H	H	S	S	S	H	H	H	H	H
11	D	D	D	D	D	D	D	D	D	H
10	D	D	D	D	D	D	D	D	H	H
9	H	D	D	D	D	H	H	H	H	H
5-8	H	H	H	H	H	H	H	H	H	H
Soft totals
A,9	S	S	S	S	S	S	S	S	S	S
A,8	S	S	S	S	D	S	S	S	S	S
A,7	D	D	D	D	D	S	S	H	H	H
A,6	H	D	D	D	D	H	H	H	H	H
A,4-5	H	H	D	D	D	H	H	H	H	H
A,2-3	H	H	H	D	D	H	H	H	H	H
Pairs
A,A	SP	SP	SP	SP	SP	SP	SP	SP	SP	SP
10,10	S	S	S	S	S	S	S	S	S	S
9,9	SP	SP	SP	SP	SP	S	SP	SP	S	S
8,8	SP	SP	SP	SP	SP	SP	SP	SP	SP	Rsp
7,7	SP	SP	SP	SP	SP	SP	H	H	H	H
6,6	SP	SP	SP	SP	SP	H	H	H	H	H
5,5	D	D	D	D	D	D	D	D	H	H
4,4	H	H	H	SP	SP	H	H	H	H	H
2,2 3,3	SP	SP	SP	SP	SP	SP	H	H	H	H

The above is a basic strategy table for the most common 6- to 8-deck, Las Vegas Strip rules. Specifically: dealer hits on soft 17, double after split allowed, multiple split aces, one card to split aces, blackjack pays 3:2, and (optionally) late surrender.

Key:

S = Stand

H = Hit

D = Double

SP = SPlit

Rh = suRrender if allowed, otherwise Hit

Rs = suRrender if allowed, otherwise Stand

Rsp = suRrender if allowed, otherwise SPlit

Poker

 

Pete