Gambling

Okay, figured some of you may like to know how exactly the gambling on 2F really works. So looked into a bit, and here's what I found. (By the way, for the duration of this post, I will be assuming that the RNG is completely perfect with no flaws and every roll being completely independent. This obviously isn't true for any PRNG you can think of, but it's good enough to showcase the numbers behind it all.)

The goal of the game is for your two dice to beat your opponent's two dice. If your result is equal to or lower than the opponent, then you lose.

However, you don't throw two dice. No. You throw *three*. And here's where the Gambling skill comes into play. If you do not have Gambling, then you take the first two results of the three, no matter what they are — just as if you'd only thrown two dice. But if you *DO* have Gambling, then you take the *highest* two results of the three. That is, you get to ignore the lowest of the three rolls.

Now, your opponent, thief that he is, already has Gambling. So trying to play this without the Gambling skill is very very difficult. As a comparison, here's the chances you have of getting each roll with and without the Gambling skill:

Without Gambling
2: 2.78% (1/36)
3: 5.56% (2/36)
4: 8.33% (3/36)
5: 11.11% (4/36)
6: 13.89% (5/36)
7: 16.67% (6/36)
8: 13.89% (5/36)
9: 11.11% (4/36)
10: 8.33% (3/36)
11: 5.56% (2/36)
12: 2.78% (1/36)

With Gambling
2: 0.46% (1/216)
3: 1.39% (3/216)
4: 3.24% (7/216)
5: 5.56% (12/216)
6: 8.80% (19/216)
7: 12.50% (27/216)
8: 15.74% (34/216)
9: 16.67% (36/216)
10: 15.74% (34/216)
11: 12.50% (27/216)
12: 7.41% (16/216)

A marked difference, yes? Oh, and in spite of what has been said elsewhere, it *does* matter who you pick to throw the dice: only that character's Gambling skill counts.

So, what are the chances of winning? Well, without Gambling, it's a rather low 27.58% per throw. The chances of winning five times in a row with that is 0.16%, or 1 in 627. Not good.

*With* Gambling, the chances jump up to 43.69% per throw, with a 5-win streak happening 1.59% of the time, or 1 in 63. Much *much* better. You'll still lose a good amount of the time, but at least it'll take you roughly 1/10th of the time.

In any case, knowing all this won't actually help your chances any (other than making sure you're using the correct person to throw the dice and not even bothering without the Gambling skill), but at least you'll know what you're getting yourself into.

Oh, and for the sake of curiousity, I tested the PRNG itself and ran the numbers through some programs I quickly typed up. The game uses the RNG well enough that the final chances match the predicted figures.

Of course, being a PRNG, there are some limitations. For instance, it doesn't matter how insanely lucky you are: you won't get more than a 15-win streak without Gambling, and Gambling only increases that possible streak to 27. And out of the 4,294,967,296 states the RNG can be in, only 8 will allow the 15-streak win without Gambling.

Oh, and actually getting a 24+ streak? The game… doesn't like it very much, since it'll try to tell you that you'll be winning 3,355,443,200 gold on your next win. And instead crash most wonderfully. 26 of the 2^32 states will allow for a 23+ streak win, and 12 of those will allow the 24th and cause a crash.

Of course, while hilarious, this is extremely unlikely to happen. So I wouldn't worry about it, especially when almost all of you are going to have cashed out long before you get to these limits.

Credits to Terence from the GameFAQs message boards.

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