The biggest bankroll always wins?

I remember reading somewhere, maybe in _Theory of Poker_ that as a general rule, the person with the bigger bankroll wins, even in a game played with fair wagers and payouts (with no house edge at all in the examples). Because given random distribution of results, you will bust before the house busts. It made me think of some questions. Is this "bankroll edge" quantifiable as a % the same way HE is figured? Is the house just 'greedy' by wanting to also have a mathematical edge in the games or the payouts? Or is the bankroll edge too hard to define? Why doesn't the house offer more 'free' bets if they're going to win in the long run anyway. Could you, even in theory, use bankroll edge to player advantage (even if ridiculous like "max bet on every spot on every open table on every game")?

What do you mean by "win"? The guy with the largest bankroll doesn't "win". It just takes longer for him to lose, that's all.

Quote: Beethoven9th

What do you mean by "win"? The guy with the largest bankroll doesn't "win". It just takes longer for him to lose, that's all.

Wrong

Quote: treetopbuddy

Wrong

Did you even read the OP? The guy mentioned the house, the HE, and free bets. He's obviously not talking about poker (even though he mentioned Theory of Poker).

The "bigger bankroll" rule tends to be true if you are playing until one bankroll or the other is empty. In that case, and assuming each player makes the same bet for each game (not true by any means, of course) and has an equal chance of winning, then it can be calculated.

However, in a player vs. house situation, since the player can walk away at any time, the "player's bankroll" is whatever the player bets in the current game, as far as the house is concerned. Every bet needs a house advantage.

Yeah, the specific example I was remembering I think was talking about a coin-matching game. Even with even-money wagers and a fair coin, the person with the bigger bankroll (how much bigger?) is either guaranteed to win or a big favorite to win. What you're saying ThatDonGuy makes sense, that if you're not playing until bust the advantage is nullified by the player being able to leave...

In table games, the casino advantage is because of the built in house advantage. Let's take blackjack, where a typical house edge for a 6 decks, stand17 game will be in the neighborhood of .6%. BUT, there is a secondary advantage because many players play only to a small fixed bankroll, that they are willing to risk. This is because blackjack like most games has huge swings in both directions. So the player that sits down, pulls out $200 and experiences a immediate negative swing, may exit the table after losing his $200 and won't be there when a positive swing occurs which could bring the loss back closer to expectation. The house having unlimited BR, can ride out extreme short term swings.

Another negative result of a player, playing to a limited BR, is that often, when they get down to their last chips, they will not make the 'correct' double own or split play, even if they have additional funds in their pocket. And this non optimal play, even for a round or two, adds to the house advantage.

True. Players who are short stacked are desperate and do not make optimal decisions so anyone close to the felt, be it in poker or anything else, can't really be measured as precisely as a wealthy player with a fistfull of markers if he ever needs them.

House Edge is built into the game by building it into each bet, each payout and the procedural rules such as Dealer Plays Last and Can Bust.

Bankroll advantage: Maybe some of these sheiks could buy the casino but in reality they can't do that inside the casino.

Quote: kewlj

In table games, the casino advantage is because of the built in house advantage. Let's take blackjack, where a typical house edge for a 6 decks, stand17 game will be in the neighborhood of .6%. BUT, there is a secondary advantage because many players play only to a small fixed bankroll, that they are willing to risk. This is because blackjack like most games has huge swings in both directions. So the player that sits down, pulls out $200 and experiences a immediate negative swing, may exit the table after losing his $200 and won't be there when a positive swing occurs which could bring the loss back closer to expectation. The house having unlimited BR, can ride out extreme short term swings.

Another negative result of a player, playing to a limited BR, is that often, when they get down to their last chips, they will not make the 'correct' double own or split play, even if they have additional funds in their pocket. And this non optimal play, even for a round or two, adds to the house advantage.

Exactly, which is also why the hold on a table game is higher than the HE. Most players (all virtually), don't have the bankroll or the stones to ride out any negative swings. That and lots of non-optimal play. Side or Horn bets anyone?

Quote: vendman1

Exactly, which is also why the hold on a table game is higher than the HE. Most players (all virtually), don't have the bankroll or the stones to ride out any negative swings. That and lots of non-optimal play. Side or Horn bets anyone?

Hold is only related to house edge indirectly. Hold will always be different from house edge as people make different sized bets and play for different times.

In a coin-flipping game, the 'bankroll effect' can be calculated easily using the random walk model. If player a has x units and player b has y units, then player a wins all the money with probability:
x / (x+y)

You can use this to estimate the effect for any game with low volatility and house edge.

Quote: AndyGB

Because given random distribution of results, you will bust before the house busts. It made me think of some questions.

This misconception is very prevalent. The feeling is that the house edge is just greed on the part of the casino, because most people will play until they are out of money. While a handful of players will walk away, most players will keep on playing in hopes of winning a return on initial investment that is extremely unlikely. Given games with the edge eliminated, the casino would still make money (albeit at a slower rate).

Note that there is a difference between a hypothetical roulette game with the zero and double zero removed. This is a game of pure luck with no house edge.

Another game without a house edge would be a hypothetical blackjack game where only flatbetting is permitted (to prevent benifitting from card counting). The rules would be 1 deck; dealer stands on soft 17; player may resplit to four hands, except aces; player may not double after split.
This game has an EV for the player of +0.000423, but it assumes optimal play. Some players will not play optimally, but bet with their gut.

It's very common erroneous thinking that the casino would make money even without the house edge. There is no mathematical justification for this argument. In fact, the casino doesn't want you to run out of money. That's why they offer so many ways to get more cash.