difference between a gambler and a 2+2er

[tomdemaine]

I'm trying to come up with some probabilistic definitions for the two. My definition of a gambler so far is someone who will bet $1000 on a coin flip for odds of 0.97 (ie a return of $970) just to get action see blackjack or slots gamblers. What odds would a 2+2er need to take this bet? 1.01 is +EV but is it enough? What if you were offered 1000 $1 coinflips?

[Snoogins47]

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I'm trying to come up with some probabilistic definitions for the two. My definition of a gambler so far is someone who will bet $1000 on a coin flip for odds of 0.97 (ie a return of $970) just to get action see blackjack or slots gamblers. What odds would a 2+2er need to take this bet? 1.01 is +EV but is it enough? What if you were offered 1000 $1 coinflips?

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This clearly depends on bankroll considerations.

If it were $1 flips for me, I would take a 1.01:1 pay out.

If it were a single $10 flip, I'd probably take the worst of it, had I been drinking, or if I was bored. Lord knows I've knowingly taken the worst of it for larger amounts of money than that, especially while drunk.

I don't really count though.

[k_squared]

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My definition of a gambler so far is someone who will bet $1000 on a coin flip for odds of 0.97 (ie a return of $970) just to get action see blackjack or slots gamblers.

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First of all, to be nitpicky... this is not really a definition, but more precisely an example of some one you would consider a gambler.

Second, I appreciate that you want to quantify the difference between a '2+2er' and a 'gambler', but I think the distinction you have laid out is not entirely accurate, and in large part misleading. I disagree with your assumption that someone who takes the best of a bet is not a gambler. That person is still a gambler, their is still a chance that they will lose (hence the gamble, the risk involved) they are just a smart gambler. They choose to play when they have the best of it, and in so doing minimize their risk of losing, while maximizing their chances of winning. Poker players ARE GAMBLERS!!!

To prove my point we can use a thought experiment... Is it possible (in a purely theoretical sense) for someone who in hold'em only plays when both his hole cards are aces to lose every hand? Yes, it is possible, it is unlikely and begins to border on the absurd over a huge number of hands, but it is nonetheless possible. What this shows is simply that you are still gambling, you are still wagering money without the assurance that you will win. Now, could a poker player play in such a way that they never gambled? Yes, but those situations would happen so rarely after the flop that they would inevitably be a losing player (even flopping four of a kind cannot guarantee that you will have the nuts after the river [any two suited cards that could make a straight flush with any of the three flop cards have 2 more cards to complete a hand that beats four of a kind]! You can only win at poker if you are willing to gamble.

So what then is the sort of edge that a '2+2er' needs to play, versus the odds that a random player is willing to take? I think that is largely a situational question that relates to your risk aversion. The more risk averse you are the less likely you are to take a bet without a significant advantage. Frankly, good players can fall all over the spectrum in this regards. Some (especially recreational players) would be willing to put half their bankroll on the line if the game was good enough, and others cringe at the thought of that kind of risk. Most 2+2ers probably are willing to push small edges because they want to maximize their long-term winnings and hopefully have enough sense to be playing at a level for which their bankroll is sufficient, and hence it is a relatively low risk to push those small edges. I am not sure how you quantify what edge they would need without more specifics...

-k_squared

[Cheeseweasel]

I can't speak for "2+2'ers" but this is how an advantage player would analyze the situation.

First of all, you should compute the required bankroll for the positive expectation endeavor.

Let f* = the optimal percentage of your bankroll to invest on each event. The formula for f* when you win A times a favorable bet with probability p is

f* = e/A

where e=(A+1)p-1>0

Let's plug in some numbers.

e=(1+1)*.505-1
e=.01
f* = .01/1 = .01

Therefore, your minimum required bankroll is $1/.01 = $100

I think that a reasonable estimate would be fifteen seconds for each coin flip, including flipping the coin, logging the results, and all of the attendant jawjacking. This gives an hourly expectation of $2.40. Your total expectation for the 1000 events is $10.00 and will take approximately four hours. This does not include the time required to mobilize to and demobilize from the coin-flipping site.

Let's say that you are playing a video poker promotion that lasts 24 hours which has an expectation of $2.00/hr. If you leave the machine you will not be able to get back on it for the duration of the promotion. Just as you get on the machine you hear about this wonderful coin-flipping opportunity. You might well decide that it is more beneficial for you to continue to play the promotion and forego the coin-flipping opportunity for a slightly lower hourly rate but a higher overall expectation, namely $48.00. On the other hand, you may be highly risk-averse and/or have a small bankroll. In that case you may opt for the lower EV+ but lower variance coin-flipping opportunity.

Another consideration would be your "walk away" minimum. What is the threshold where it is more beneficial for you to be scouting more EV+ plays rather than playing a substandard one?

I think that most professional gamblers are better off plugging themselves into a narrow specialty such as 10/7 Double Bonus video poker, banking slot machines, or limit holdem. However, to maximize your bankroll growth, you have to learn how to do the above type of analysis and constantly be scouting out new EV+ opportunities wherever they may be.

I hope that the above is not too confusing, but helps you to get an idea of the factors that have to be considered in analyzing an EV+ play.

Best of Luck

[Siegmund]

In economics, they like to say that people act to maximize their utility, which may or may not mean making as much money as they can, depending what tradeoff between money and pleasure exists in the person's mind.

This suggests a two possible definitions of a gambler you might try on for size:

Someone for whom there exist bets with negative (monetary) expectation but positive utility;

Someone who, given a choice two propositions with the same expectation, prefers the one with higher variance.

More generally, you might measure "how much of a gambler someone is" by the size of the deviation between utility and expectation. (There is a LITTLE bit of a gambler in most of us here - if ALL we cared about was money we could've all gone to law or medical school and be gotten a better hourly rate for our effort.)

This is imperfect - ignoring size-of-bankroll considerations - combining this with a previous poster's suggsetion, maybe a refinement is to say a gambler is someone who bets more than the Kelly stake on a given proposition (which includes betting on negative expectation propositions at all)?

[wdbaker]

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(There is a LITTLE bit of a gambler in most of us here - if ALL we cared about was money we could've all gone to law or medical school and, ((be)-edited), have gotten a better hourly rate for our effort.)

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I resent that remark, I care a lot about money and I never endulged my self in higher education(College, finish high school etc...) and i still have a little bit of Gambler in me. Now leave me alone while I count your chips /images/graemlins/grin.gif

One Street at a Time
wdbaker Denver, Co

[scottjack]

a gambler is someone who starts playing with $100, with the goal of trying to win $10,000.

a "2+2er" as you put it, is someone who starts with $10,000, with the goal of winning $100.