3 balls or 5 for points?

[mikehg]

Haven't decided yet...

The main scoring isn't that different - just ups the pop bumper to 1000 from 100.

But the 2x and 3x bonus are available on your second and third ball respectively - averages out to 2x per ball.

On a 5 ball game you're only getting 1.6x per ball on average.

Since I seem to play this table well in fits and spurts - I'll have a few useless balls, then one when I'm on a roll and get a couple of extra balls, playing with 3 balls increases the chance that that ball lands on one with a higher bonus.

Thoughts?

 

[vikingerik]

It's not the average bonus x that matters for a game, it's the total. 1x-1x-1x-2x-3x will always be more than 1x-2x-3x.

The thought of spotting your good ball into a 3x bonus slot is a gambler's fallacy. Each particular ball doesn't know how many other bad balls you had around it. Ball #5 is no less likely to be good than Ball #3. It's not a question of "where do you have your good ball" because your good ball isn't guaranteed to ever happen.

I didn't know that the 3 balls setting increased the bumper score, though, thanks for that info. Probably not worthwhile, even at 1000 the bumper is probably no more than 20% of the total score. It would need to be at least 33% to make up for the loss of the additional balls (accounting for the fact that only 1x bonuses are missed out on; if all the balls were equal, this would be 40%.)

 

[mikehg]

It's not the average bonus x that matters for a game, it's the total. 1x-1x-1x-2x-3x will always be more than 1x-2x-3x.

That would be true if each ball had the same length. But I have many bad balls and a few good runs every so often.

The thought of spotting your good ball into a 3x bonus slot is a gambler's fallacy. Each particular ball doesn't know how many other bad balls you had around it. Ball #5 is no less likely to be good than Ball #3. It's not a question of "where do you have your good ball" because your good ball isn't guaranteed to ever happen.

I don't follow you. Let's say you play twenty balls either way (ignoring extra balls), you'll get the following multipliers:

3 ball: 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2
5 ball: 1 1 1 2 3 1 1 1 2 3 1 1 1 2 3 1 1 1 2 3

So for 3 ball games you've had 7 at 1x, 7 at 2x, 6 at 3x.
For 5 ball games you've had 12 at 1x, 4 at 2x and 4 at 3x.

Assuming the scoring is concentrated into a few good balls (which for the way I'm playing at the moment, I think it is...), that could be an advantage - not necessarily in any given game or the average, but in the maximum score attained over a spread of games.

I didn't know that the 3 balls setting increased the bumper score, though, thanks for that info. Probably not worthwhile, even at 1000 the bumper is probably no more than 20% of the total score. It would need to be at least 33% to make up for the loss of the additional balls (accounting for the fact that only 1x bonuses are missed out on; if all the balls were equal, this would be 40%.)

That's the problem - weighing that possible advantage against the extra length of the 5 ball games. I'm still on the fence...

 

[mikehg]

As an ETA, and perhaps more importantly...

Let's say the odds of having a good ball are 1 / 10 (and for the sake of simplicity, let's count extra balls gained as part of the same ball).

The way for an inconsistent player to get a good score is to have two good balls on higher multipliers in the same game.

Now the chance of that happening per game is 1 / 100 either way - you've got two balls with higher multipliers whichever you choose.

But the chance of it happening over, say 30 balls is 1 - (99/100)^10 = about 9.5% in the 3 ball game, vs 1 - (99/100)^6 = about 6% in the 5 ball (unless my maths is wrong, and I'm very out of practise at maths...)

Obviously this effect is only important if you're a shaky player, with only occasional good balls. A consistent player should definitely go for the 5 ball game, as you say. And I'm still not sure this effect outweighs the extra points from the 'normal' balls. But it's worth thinking about...

 

[vikingerik]

Let's say you play twenty balls either way

This is still a disguised way of thinking in terms of average. Yes, the average per ball is higher in the 3-ball game. But why would the population size be measured in balls? I'd measure it in games. Per game, the additional two 1x balls can't ever hurt.

But the chance of it happening over, say 30 balls is 1 - (99/100)^10 = about 9.5% in the 3 ball game, vs 1 - (99/100)^6 = about 6% in the 5 ball (unless my maths is wrong, and I'm very out of practise at maths...)

This is correct, if you're measuring the population in balls. But not if you're measuring in games. The good 3-ball game requires the 2x ball and the 3x ball to both be good. The 5-ball game has the same chance of seeing a good 2x ball and good 3x ball -- but also has an additional way to do it by seeing multiple good 1x balls then the 3x ball. In other words, it's possible for the 5-ball game to afford a bad 2x ball, a luxury the 3-ball game doesn't have.

But yes, this is good stuff to think about.

 

[mikehg]

Yup, having posted that and had a think, I got my head around your gamblers' fallacy point - in terms of games you're quite correct.

I think it can make sense either way. If you've got X amount of time to play (as opposed to X amount of games), and want to maximise your score, there are conditions (specifically being rubbish ) in which having fewer balls / game is better. Sounds perverse, but I suppose you can think of it as exactly the same as draining the first two balls deliberately to save time for the high scoring ones...