Seems fairly simple to me. Tightening up the odds and the trip-to-trip 20% discount means he would be seeing a nearly 10% return on every visit. Those odds don't sound like good business.
Re: the card counting thing, is it really that clear cut? He sounds like a sharp guy. Couldn't he just be pattern matching and getting a small advantage without actively trying to do card counting? I'm kind of talking out of my ass here, but it seems like you could get some mileage out of simply tracking whether you've seen a lot of high cards or not: https://en.wikipedia.org/wiki/Card_counting#Basics
A couple other related thoughts: I'm taking a course on Markov chains this summer, and it's nice to be able to relate it to a real world example (i.e. "Gambler's ruin"). In short, this guy would be guaranteed to lose his money if he played indefinitely EVEN if the odds were 50-50 https://en.wikipedia.org/wiki/Gambler's_ruin
>Another common meaning is that a gambler with finite wealth, playing a fair game (that is, each bet has expected value zero to both sides) will eventually go broke against an opponent with infinite wealth. Such a situation can be modeled by a random walk on the real number line. In that context it is provable that the agent will return to his point of origin or go broke and is ruined an infinite number of times if the random walk continues forever.
And if you like these sort of pieces on gambling, maybe you'd like this article I wrote recently about winning money in an indie gambling game: http://www.jere.in/13
Re Re card counting: The vast, vast majority of advantage when counting is the choice to change your bet size depending on the count. When a deck starts you are at some initial count and then it goes up or down as the deck goes along. While the count is at or below a certain point (low counts are considered bad and high counts are considered good), you usually just bet the table minimum as you do not have an advantage over the house. Once the count reaches a certain level you start betting more aggresively. There is usually a spread to counts where for example if the count is 1 you bet 2x table minimum if it is 3 you bet 4x table minimum etc. This is how you take advantage of the fact that the odds are in your favor - if you just bet the same amount all the time you are not really doing anything different (assuming you are following Basic Strategy at all times).
The rub here is that this type of betting can be seen by the house. If you are of enough interest to the casino (something you can get playing $100 hands let along $100K hands) they will watch you bet and try and look for this pattern. Most casinos employ former counters or have people on staff you can, after a little bit of time, determine if you are counting or not and politely ask you to leave. In fact most counters will specifically give away some of their advantage by going against the recommended bet at a given count to try and make it look less like they are counting. One such practice would be to never go from a minimum bet to a max bet, as it is most likely not something a regular counter would do (aka bet $100 one hand then bet $1K the next hand).
You are correct however that some advantage can be gained by just "tracking whether you've seen a lot of high cards". Players use indexes which will change their play depending on the count, and use this skill to augment their changes in betting amounts to better take advantage of their current position. You can see the effect of using indexes vs. no indexes here: https://www.qfit.com/cardcountingindexes.htm
Re: the card counting thing, is it really that clear cut? He sounds like a sharp guy. Couldn't he just be pattern matching and getting a small advantage without actively trying to do card counting? I'm kind of talking out of my ass here, but it seems like you could get some mileage out of simply tracking whether you've seen a lot of high cards or not: https://en.wikipedia.org/wiki/Card_counting#Basics
A couple other related thoughts: I'm taking a course on Markov chains this summer, and it's nice to be able to relate it to a real world example (i.e. "Gambler's ruin"). In short, this guy would be guaranteed to lose his money if he played indefinitely EVEN if the odds were 50-50 https://en.wikipedia.org/wiki/Gambler's_ruin
>Another common meaning is that a gambler with finite wealth, playing a fair game (that is, each bet has expected value zero to both sides) will eventually go broke against an opponent with infinite wealth. Such a situation can be modeled by a random walk on the real number line. In that context it is provable that the agent will return to his point of origin or go broke and is ruined an infinite number of times if the random walk continues forever.
And if you like these sort of pieces on gambling, maybe you'd like this article I wrote recently about winning money in an indie gambling game: http://www.jere.in/13