Digging into the Math of Gambling

It's pretty basic, and kind of flawed. For example, it says you can easily calculate the house advantage for craps...that might be the hardest game to calculate the HA for.

If this kind of stuff interests you and you want someone else to do the math, I recommend visiting the wizard of odds. Much more in depth than this article, but still easy enough to understand for non math people.

 

Hardest? Nah. Most single bet rolls in Craps are nearly as easy as Roulette.
Now Passline bets or Hardways are beyond the author's ability I am sure, but still easier than the remainder of most table games.

http://wizardofodds.com/games/craps/appendix/1/

Games way harder than craps:
All Poker based games
All Blackjack based games

Games easier than craps:
Roulette
Big Six Wheel
Sic Bo?

 

Craps HA is very easy to calculate. It gets a little more involved if you try to calculate the HA including the action you place on the odds bet, but since the odds bet has a 0 edge, you don't include it. People try to make themselves feel better about playing craps by including the odds bet in their total action, which lowers the HA as a percentage of their total action, but that's just self delusion.

 

Not really, unless your odds bets are making you bet more than you normally would. If you're a $100/hand bettor, then betting $20 pass line and full odds will give you a lower house edge than simply betting $100 pass line.

Of course, it will also mean you get rated much lower, since odds bets are not rated.

The reason HA for craps is hard to specify is that many bets do not resolve on a per-roll basis.

 

Thanks for sharing. I'm not much of a math guy but I do try to read up on and understand the HA on games I like to play.

I gamble for entertainment so knowledge of games enhances the value and prolongs my gaming experience.

Even though roulette has a relatively high HA I still play because it's fun. I just play sensibly.

Even at craps I'll play the prop bets once in a while cause its fun when it hits!

 

No kidding.

The fact that the author used the term "Digging Into The Math" to describe that article shows why we're so far behind in math.

 

Blackjack, Video Poker, Live Poker, and the Sports/Race book (for an handful of elite group of sports / race handicappers) are the only casino offerings which offer the possibility of a long term positive win expectation. Most gamblers attempting these four offerings are also net losers over the long term, due to lack of knowledge, ability, money management and/or discipline. More than 99% of gamblers play games with negative win expectations or lack in one or more areas to win at games of skill.

Gamblers playing all other games will do well to stay within their budget, not chase comps and pick the better offering when offered (such as 3/2 BJ) to extend your playing time, enjoyment and possibility of winning a session or trip.

People tend to place great importance on marginal factors (nibbling at the interest rate, earning comp/cc points) while ignoring the big picture (principal payments, not playing for comps, acquiring debt for perks). Casinos (and other large corporations) spend billions to market the marginal with a focus on maximizing their net revenue.

 

Single roll bets are easy. Multiple roll bets are not. Figuring out your overall house advantage when you've got a pass line bet and two place bets, not so easy.

I'm not saying you can't do it, but it's not nearly as easy as figuring out what your odds of hitting quads are if you hold a pair and throw away 3 cards.

 

Funny...

"Games way harder than craps:
All Poker based games
All Blackjack based games"

Craps is the one game that I struggle to understand! I have played a bit & have found it fun if I am with others to guide me...

And NL Texas Hold 'em is my game of choice--and I often am mentally figuring odds (others as well as my own). LOVE this game.

Funny, my games of choice are poker & vp and DH's are the same plus the sportsbook...we do pretty well, especially me. (tho I had an 18 month poker dry spell...hit 3 royal flushes-my only royals EVER--and a $1K jackpot on stupid slots during that time--and these are on .25VP, and had tossed $10-20 in! Slot was $20...a fav of a friend I thought I play cuz she likes it!)

 

Well, I am too when I bother to play live poker. But I was referring to "casino poker games" such as Ultimate Texas Hold 'Em which requires a computer and a smart programmer to calculate the house edge (2.185% of an ante with optimal strategy). Because there are C(52,5)*C(47,2)*C(45,2) = 2598960*1081*990 = 2,781,381,002,400 possibilities to account for between the board, the player's cards, and the dealer's cards. I don't even believe that the complete optimal strategy has ever been fully summarized. There are decent approximate strategies available though (house edge of ~2.3%).

 

The house edge at Pai Gow Poker is quite easy to deduce, (5% commission on wins, an even game except for the ties won by the house), but the optimal strategy isn't. You'd think with computer analysis that they'd have come up with the 'exact' strategy for the game, but I think since you don't know what strategy you are playing against, ('house ways' are always different), it's impossible to know the exact best play every time.

It also seems there could be a somewhat different best strategy as a single player vs. being the banker and playing against many hands.

 

Very, very well said.