Mickey,
I imagine the frequencies can be expressed as a "continued fraction" that would give rise to an elegant solution. However, the determination of the frequency with which you successfully are allowed to pick "n" doors in the bonus round yields nicely to brute force.
Set up a spreadsheet with the following columns:
A: "Cumulative Pick"
B: "Stop Doors"
C: "Other Doors"
D: "Total Remaining Doors"
E: "P(Stop)
F: "Conditional P(Stop)"
G: "P(Cum)",
where:
"Cumulative Pick" identifies the pick for which you're calculating the probability of stopping at (1,2,3 ... 16)
"Stop Doors" is the number of stops remaining when initiating that pick (a constant of 5)
"Other Doors" are the non-stops, starting at 15 and declining to 0.
"Total" is the sum of "Stop Doors" and "Other"
"P(Stop)" = "Stop Doors"/"Total Rem Doors" is the probability of hitting a Stop on this pick, = 5/20 to start with, increasing to 1
"Conditional P(Stop)" represents the cumulative probability of hitting a Stop on the "nth" Pick, and is the product "P(Stop) for this pick * "Conditional P(Stop) for the prior pick.
"P(Cum)" is a check sum on the Conditional P(Stop) column, which, if accurately entered, should total 1 at the bottom.
-------
Multiplying (A) by (F) and summing the results will give the Exp(Picks). I get exactly 3.5.
I imagine you slapped your head 2 sec into this explanation, Mickey.
- H.
--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:
>
> I spend a considerable amount of time analyzing games. I'm always looking to add a play to my repertoire. Most of the work goes for naught but I do come up with a gem every once and awhile.
>
> It's these type of video keno games that I think are the wave of the future in advantage play. I see more and more of them these days. They can't be fully analyzed by existing commercial software. Here's what this 8-SPOT video keno play looks like:
>
> PAYSCALE
>
> 8 of 8.............800
> 7 of 8.............160 + 2% METER
> 6 of 8.............19
> 5 of 8.............11
> 4 of 8.............4
> 3 of 8.............1
>
> I know how to do the math for the payscale with a calculator, pen and pad, but Bob pointed out to me about a month ago that the Wizard of Odds has a keno analyzer on his website. That saves me a lot of time.
>
> So the payscale came up 81.6246%. The first thing I did was cull out the payback for hitting a solid 8, putting the number at 81.277%. I don't like the extreme longshots figuring into these types of plays.
>
> But there is another segment to the game. A game within the game. The player picks his/her numbers. When you hit the start button STARS jump out onto 7 randomly picked numbers. The machine picks change every game while the player can just keep playing the same numbers.
>
> When you hit a pay with your numbers and at least 4 of the 7 machine picks hit you go into a bonus round. To come up with the frequency of going into the bonus round I looked at it like it was a 15-Spot with 1 way of 8 and 1 way of 7.
>
> I first calculated the frequency for 7 of 15 and how many permutations would be 3 of 8 and 4 of 7. Then 8 of 15 and how many permutations would be 3 of 8 and 5 of 7, and 4 of 8 and 4 of 7. I went on up the line with this but culled out the extreme longshots and put the frequency at 70.26 games for getting into the bonus round.
>
> When you make such a catch the game goes to an alternate screen. There are 20 doors with money prizes behind each. You get to pick the doors. The prizes are multiples of the bet, 1X, 2X, 3X, and 4X. Seven of the doors have 1X, 8 have 2X, 3 have 3X and 2 have 4X. Average pick is 2X.
>
> 15 of the doors allow you to pick again. 5 of the doors, while still awarding a money prize, have a stop sign behind them. When you pick one of them the bonus round is over and you return to the main game.
>
> At first glance I figured to average 4 picks. But this may not be true. On the first pick you are 15 to 5 to keep picking. But if you are succesful there the next pick is only 14 to 5 to keep picking, 13 to 5, etc.
>
> I've never done this kind of math before so I'm looking for any and all opinions on what the exact frequency of picks would be.
>
> Thanks in advance.
>
