taternuggets wrote:Typically, the house can outlast a player to where the mathematics will ultimately fall in their favor.
In my experience, my bankroll will not allow me to see how things would ultimately shake out in the end.
I chose to not employ my weblinks.
You win. Split those tens.
I'm by no means saying "split those tens", but I am saying that the math justifies at least one situation where it's more EV for the player to split than not to split. Therefore, in a very few limited situations, you should split tens, but most players will never even know how to properly utilize that math (including me). Your initial reaction to my saying that I was pretty sure there were a few situations where you are supposed to split tens just wasn't mathematically correct, and since we were starting to enter a discussion where math is crucial, it was just worth noting.
A few more thoughts, there isn't a requirement for duration of time required for the house to outlast a player for the math to fall in the houses favor. It's almost always in the houses favor. The only real exceptions that I can think of is card counting situations in blackjack/cheating.
I realize that a savvy gambler can pick up on +EV situations for him/her in other areas, but this doesn't mean the favor still wasn't to the house. One such situation would be progressive jackpots. This only happens though when the progressive jackpot reaches a point where the odds vs payout rewards get to be in the current players favor. However, for this to happen, many other players have had to lose more money to allow the jackpots to build to this point. An easy example of this is the powerball. I calculated it one day and I don't remember the exact number, but it was something like, when the jackpot reached $180,000,000ish+, you could "expect" a return on your $1 investment that would be larger than $1. But for the jackpot to have gotten that large, so many other people have lost more money in it, so the favor hasn't shifted to the player from the house, it's just a situation that now yields a positive expected value from other people's lost money.
With the above example though, you can't realistically expect to put in enough volume to see an expected value and results value be close to each other, and after cash option deductions/taxes etc, it's pretty hard for it to actually remain a +EV situation.
Sorry this is so long, but I'm going to add a few more things to try to fully articulate what I'm trying to say about the "house outlasting for the odds to go in their favor".
Take the martingale system for example. This is the system players will try to use to "beat the house". In this system, a player playing a game like roulette will start with a minimum bet, then if he loses, he will double the bet. He continues this thinking something along the lines of "the odds of the ball landing on not my choice 8 (or any large arbitrary number) times in a row are really small, so I can beat the house". This isn't what the math says though.
The payout is even, so a $1 bet that wins receives $2 (for a net win of $1). A loss obviously loses the $1. If there were no non black/red parts on the table, it would be even money all the time. However, the 0 and 00 places also lose for the player betting on red or black. So now the odds of wining are 18 in 38, or roughly 47.37%. If you were to place a single $1 bet 10,000 times, you can expect a return of $9473.68. Or you are essentially losing $0.0526/play. Now with the martingale system, you only speed up the rate of losing money. This is because with a $2 bet, you can expect to lose $0.105/play. Then with a $4 bet you can expect to lose $0.211/play. Then with your $8 bet, you'll lose $0.421/play and so on. This is because the edge is always in favor of the house. It doesn't matter what you bet, the house doesn't need any time for the "math to be in their favor". It always is. With blackjack, sure, the decks go through the hot streaks and cold streaks, but the same principles apply (with the exception of card counting). It's always going to be in favor of the house, or the house would not offer the game (at least for very long at all if for some reason something was miscalculated).
There is no need for the statement "ultimately fall in their favor." The math just is in the house's favor. Sure the house's profit will see ups and downs, but the results don't matter here. The math either is or is not in the house's favor, and I believe I've showed enough now for it to be reasonable to understand that the math favors the house.
All right, I'm finished. All of the above is why I can only justifiably play poker. The house always has the rake there, but other players enjoy giving away money, and it is possible to put yourself in more +EV situations than the rest of the field, allowing a positive long-term expected return on your investments.