Probability

[bjarg]

Just wondering if anybody could help me figure this out.
Game is 6D, das, rs4, 3:2, doa, 75-80%
for a basic strategy player, what are the odds that in in one point or another to be 1 unit ahead.
boy my english sucks.
for example, if my unit is 400, what is the probability of at a given time of 1 session to be winning 400.
just basic strategy, not counting.
bankroll is 40 units and max time per session is 12 hours.
and risk of going broke withiut ever being up 1 unit?
Anybody who might know how to put numbers to this?
thanks!

[dharmaprija]

	Expected outcome in units -7.56
	Expected outcome in dollars -3024
	The standard deviation from desired outcome .217
	Probability percentage of winning at least the desired amount 41.41%

your expected outcome is NEGATIVE as you are at about a -.36 disadvantage playing Basic Strategy with that set of rules. Youre expected to lose about $3000 in that length of time. With standard deviation it is possible that you can be ahead and
this is the formula for standard deviation

standard-deviation-sample.gif

[Nyne]

I think the only way to answer the OP's question will be to sim it. CVData can handle this with session statistics. You would set it to a target of 1 unit, a session bank of 40 units, and a max of 1200 hands. That's assuming you are stopping once you are up at least 1 unit. You'll still be losing money with this approach.

[bjarg]

Sory! I forgot about a very important rule: ES10!
this game has an advantage for the player off the top... Wouldnt that mean that a bs player should have a positive ev?

[Tom]

what are the odds that in in one point or another to be 1 unit ahead.

1-(probability of losing all rounds)^number of rounds = probability of being ahead at the end of all rounds.

If game has +EV then yes player will have +EV, but don't forget about variance.

[zengrifter]

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[bjarg]

1-(probability of losing all rounds)^number of rounds = probability of being ahead at the end of all rounds.

If game has +EV then yes player will have +EV, but don't forget about variance.

Thanks Tom.
I understand that if the game has +EV a BS player should come ahead.
What Im trying to do is put numbers on those 2 things, specially at being up at least 1 unit at any point in a 12 hrs session.

[Tom]

Thanks Tom.
I understand that if the game has +EV a BS player should come ahead.
What Im trying to do is put numbers on those 2 things, specially at being up at least 1 unit at any point in a 12 hrs session.

It depends on your edge. With edge of 0.50% you can expect to profit 0.50% per bet over time. In random walk the probability of returning to 0 (original level) from 1 (or -1) is 1. Probability of going 0 to 1 or -1 is equal. With a positive EV the higher the % and the more rounds played, the higher the probability of you being ahead. Again, variance plays into this. You should look into N0, which is # rounds where accumulated expectation equals accumulated standard deviation.

[Nyne]

I thought Dharmaprija nailed it.
Not everything, not even indices, require sims.

Dharmaprija did not nail it. It was a good attempt, but it didn't answer the question that was asked at all. The question specifically deals with the probability of being ahead by 1 unit at some point during the session. What Dharmaprija attempted to calculate is the probability of being ahead 1 unit or more at the end of 12 hours of play. He also made some assumptions that were not specified in his response, such as apparently playing 175 hands per hour (based on the expected loss and house edge that he quoted). This is obviously going to depend on how many players are at the table on average. The average number of players and/or rate of play were not specified by the OP. It's fine to make an assumption, but it should be clearly stated. Also, he appears to have miscalculated the standard deviation for the session. The numbers used would imply a standard deviation of 0.86 units for a single hand played (based on Dharmaprija's apparent assumption of 2100 hands per session, and 8.56 units being 0.217 standard deviations), rather than a more typical value of 1.14 or so. My intent wasn't to tear into the specifics of Dharmaprija's post, but rather to point out that it did not apply at all to the question that was asked, and I still believe that the correct answer to OP's question will require a sim. That said, I don't really understand the point of the question either. Unless there is some sort of loss rebate or other factor that will adjust the results of the game, I don't see why it's relevant how often you will be ahead at some point.

[zengrifter]

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[Nyne]

Dharmaprija redo your algebra and show these guys that sims are not always necessary.

Did you even read what I wrote?

It was a good attempt, but it didn't answer the question that was asked at all. The question specifically deals with the probability of being ahead by 1 unit at some point during the session. What Dharmaprija attempted to calculate is the probability of being ahead 1 unit or more at the end of 12 hours of play.

[zengrifter]

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[ZenMaster_Flash]

Yes, simulating is silly here.

I would amend the O.P.'s question by adding:

and what is the probability of being behind $400