vpFREE2 Forums

A Keno Math Problem

#1

I think I am beginning to understand this problem. Without the guarantee you are right Harry this is a complex problem that can't be solved in closed form. Without the guarantee let P(n) stand for the probability that in your last n games you have a 60 game losing streak. It is obvious that P(n) = P(n-1) + ((1-P(n-61))x(0.04324789135)x(0.070463738969)). This involves solving a 61st degree polynomial which can not be solved in closed form. To get you started P(60) = 0.070463738969, P(61) = P(60) + (0.04324789135)x(0.070463738969) = 0.07351114706. Years ago I solved the problem of a baseball team in n games having a 2 game winning (or losing) streak with the probability of a win or a loss a constant with independence of games. This involved solving a cubic equation which can be solved. It still took me a few days to put this in closed form. Good luck on this one Mickey!

···

Sent from my iPhone

#2

After reading sayitsme and vp wiz I think I'm going to let the frequency stand at 23.12 in analyzing the play. I always come up with minimum playable numbers. Leaving the frequency where it is will be a slight error that favors me.

#3

I believe this suggests that we're on a similar wavelength now :wink:

For the skillful, I suspect there's some elegant math that might be applied to simplify the solution. It's beyond me, however. I advise simulation.

My hands are full presently, but I may take a crack at an estimate and post back.

---In vpFREE@yahoogroups.com, <Nordo123@...> wrote :

I think I am beginning to understand this problem. Without the guarantee you are right Harry this is a complex problem that can't be solved in closed form. Without the guarantee let P(n) stand for the probability that in your last n games you have a 60 game losing streak. It is obvious that P(n) = P(n-1) + ((1-P(n-61))x(0.04324789135)x(0.070463738969)). This involves solving a 61st degree polynomial which can not be solved in closed form. To get you started P(60) = 0.070463738969, P(61) = P(60) + (0.04324789135)x(0.070463738969) = 0.07351114706. Years ago I solved the problem of a baseball team in n games having a 2 game winning (or losing) streak with the probability of a win or a loss a constant with independence of games. This involved solving a cubic equation which can be solved. It still took me a few days to put this in closed form. Good luck on this one Mickey!

[Non-text portions of this message have been removed]

···

Sent from my iPhone

#4

There is an adjustment I had to make to the 23.12 frequency. Per 326.4 games (the frequency of hitting the solid 4) you will hit 14.12 3/4's and one solid 4. This reduces the number of games you will play in the green, yellow, blue, orange, purple and pink tabs to 21.59.

I had to make adjustments to the red, yellow and aqua tabs factoring in the extra draws and multipliers. I had to use a lot of empirical evidence on the extra draws and multipliers. This is where I'm at so far:

Red...15.864 games @ 149.99%
Green 7.5 bets plus 21.59 games @ 50%
Yellow...21.59 games @ 122%
Aqua....12.683 games @ 95.47%
Orange...21.59 games @ 50%
Blue...21.59 games @ 50%
Purple....21.59 games @ 50%
Pink....21.59 games @ 50%

So the cycle for hitting all 8 tabs is 158.084 games.The number of bets returned is 123.72.

123.72/158.084 means this phase of the game returns 78.26%.

#5

The next thing I worked on is the true frequency of the solid 4. With 20 draws the frequency is 326.4. But 10% of the time (red tab) I'm getting two extra draws and 8% of the time I'm getting anywhere from 3 to 8 extra draws (aqua tab). I had to use emperical evidence on the aqua tab. So I adjusted the solid 4 frequency down to 290.348. Since the drop is 21.74% I would have to average winning 63 bets for hitting the solid 4 to put the game at 100%. But I would need a number bigger than that because I dont play at 100%.

Note: Though I dont have this game fully analyzed yet I'm already throwing down plays. I have a general idea of what is an advantage though I haven't gotten it down to the 7th decimal yet. For the small plays, if I find the game in red tab mode, either 2X or 3X pay with 2 extra draws, I'm at either 137.4% or 206% until the tab changes so I go ahead and play it off. If the yellow tab is up and it 3X,4X,5X, I'm at 150%,200%,or 250%, so I play it until the tab changes. If the aqua tab is up and its either 6 or 8 extra draws, either 122% or 169% I play it off.

If I punch the game up and I'm eligible for all three meters, Free Games, Multiplier, Extra Draws, and they are in the high single digits, I'll play it until it changes modes or I hit the solid 4. If all three meters are in double digits I'm on a straight through ticket until I hit the solid 4.

#6

When the 4 machine picks hit there are 4 different things that can happen. If the game is in Free Games, Multiplier, Extra Draws mode (FME), which is the ultimate objective of this play, then you will be awarded however many games the meter is on, whatever multiplier the meter is on, and however many extra draws the meter is on. Once you play it off the meters will reset to 5-2-3. The game is in this mode for an average of 138 games.

The next mode it will move to is Free Games, Extra Draws (FE). If you hit the solid 4 here then you are awarded however many free games are in the meter plus however many extra draws are in the meter. Plus a 2X multiplier. Once you play it off the Free Games and Extra Draws meters will reset to 5 and 3. But the Multiplier meter will stay where it is. The game is in this mode for an average of 138 games.

Not hitting the solid 4 in FE mode the game will move to Free Games, Multiplier mode (FM). If you hit the solid 4 here you are awarded however many free games are in the meter plus whatever multiplier is in the meter plus 2 extra draws. Once you play it off the Free Games and Multiplier meters will reset to 5 and 2 but the Extra Draws meter will stay where it is. The game is in FM mode for an average of 158 games.

Not hitting the solid 4 in FM mode the game will move to Progressive mode. The PRG starts at 20 bets and per the average 4 bets will be added every time you catch the pink tab or once every 158 games. This equates to 2.5% meter movement. When you hit the solid 4 here you are awarded the money in the meter. And the great thing about hitting it is it doesn't reset the Free Games, Multiplier and Extra Draws meters. I'm always getting built up money from past players in this meter and it cuts the drop from 21.74% to 17.5%. The game is in this mode for an average of 118 games.

Then the cycle starts all over again with FME.

So now its time to develope a strategy for the game, i.e., minimum playable numbers. Later posts.

#7

I'm on the tail end of a 3 week road trip. I'll be back home next Tuesday. I've been getting up early and working on this keno play for a couple of hours before getting out and hitting the casinos. I just about have the 7 spot solved. I chose to do the 7 spot first because, while I might find a play on anywhere from a 2 spot to a 10 spot, I'm getting the most plays on the 7 spot, hence that is where the ploppies are giving the most action. This is followed by the 10 spot, then the 9 spot, then the 6 spot. The 2, 3, 4, 5 and 8 spots get very little action.

The key to the play is knowing what the extra draws are worth per the payscale. So far I've done the math for up to 17 extra draws. And I'm going to have to take it higher than that. I got a play a couple of days ago where I got 21 extra draws.

#8

The frequency of the solid 4 is 290. Per empirical evidence there is a disparity in the number of games I'm in each mode (FME;FE;FM;PRG) as it cycles through FME and FE mode is 138 games each; FM mode is 158 games; and PRG mode is 118 games. Percentagewise that would be:

FME....25%
FE.......25%
FM......28.4%
PRG...21.4%

Per 100 cycles (29,000 games) I'm expected to hit 21.4 solid 4's in PRG mode. This doesn't kill the play as it doesn't reset the meters. That means I will hit 78.6 solid 4's in FME/FE/FM modes which, after playing off the free games, will reset the meters and I will have ti take a walk as the game is back in negative expectation.

29,000/78.6 means I will average playing 369 games to hit in one of those modes.

369 times the 17.5% drop means the cost to play it off is 65 bets. So I need an average win bigger than that number. I'll go through some scenario's in the next post.

#9

This is what happens when you hit a solid 4 in FME/FE/FM modes when the meters are showing:

Free Games....8
Multiplier..........8
Extra Draws....8

The key is knowing what the extra draws are worth. At 20 draws the payscale is worth 50% or half a bet. But with 28 draws the payscale is worth 1.6 bets. Then there is the adjustment for the number of games you are in each mode. Per 78.6 cycles you are in FME mode 31.8% of the time; in FE mode 31.8% of the time; and FM mode 36.4% of the time. So getting the average values looks like this:

fFree Games-Multiplier-Extra Draws
1.6X8X8x31.8 = 3256.32

If you hit in Free Games-Extra Draws mode you get a 2X multiplier.

1.6X2X8X31.8 = 814.08

If you hit in Free Games-Multiplier mode you get 2 extra draws which puts the base payscale at 68.7%.

.687X8X8X36.4 = 1600.44

3256.32 plus 814.08 plus 1600.44 totals to 5670.84.

5670.84/100 means the average return is 56.7 bets. Since the cost to play the game off is 65 bets this would be an 8.29 bet deficit.

8.29/369 = 2.25% which would put the game at 97.75%.But can I play an 8-8-8 anyway? I'll get to that in the next post.

#10

So can I play the 8-8-8 even though it shows a return of just 97.75%. You bet your bippy I can. Because 8-8-8 is not what I'm expected to solid 4 out on. Per the tabs I'm expected to increase each meter by 1 per 158 games. So I'm expected to go out on a 10-10-10. Ten extra draws has a value of 2.07 bets and using the same math formulas I used on the 8-8-8 the expected return is 101.3 bets.

Since the cost is 65 bets thats an expected earn of 36.3 bets.

36.3/369 means an advantage of 9.8%. The progression in value from an 8-8-8 (56.7 bets)to a 10-10-10 i(101.3 bets) is equivalent to a 12% progressive meter. And the bigger the numbers you find the greater the value of adding free games, multipliers and extra draws while you are playing. In the next post I'll tell you about my most succesful play so far.

#11

A couple of weeks ago I sit down on a machine, go through all the spots and betting levels looking for a play or plays. Sometimes I get multiple plays on a machine. So I find the 9- spot at the $2 bet level showing this:

Free Ganes......17
Multiplier...........18
Extra Draws. 16

I had a brain orgasm! Even though I hadn't done much math on the game at that point I knew it was huge. So I stick a hundred in the machine. Right off the bat I catch the aqua tab and was awarded 8 extra draws. Then I promptly hit 8 out of 9 for $800. This was outhouse lucky. I'm on a short term play and the frequency for 8/9 with 8 extra draws is around 1450 I think.

I sure wanted to hit all three meters at once but it did't work out. I 4'rd out on FE and was awarded 18 free games with 18 extra draws and a 2X multiplier.

I play all my keno plays on turbo speed as time is money. I just want to get the play over with and move on to the next play. But in this case, before playing off the free games, I sat the speed back to the slowest so I could have a little fun watching the numbers pop in.

Through the free games I racked it up to $2018 in credits. I let the $18 go as a tip. So it was a $1900 earn. Not bad for 15 minutes work.

I haven't found anything close to those numbers since. But I have made a couple of $1000 scores. Thegame is still new. The public has over 20 keno games to choose from on these machines, about a dozen poker games, and a half dozen line games. I've seen it before with other new games. It will take several months of the game being there before I start getting lots of plays on a regular basis.

#12

So now that I've solved the 7 spot I have nothing to do but look forward to solving the 10 spot. The base payscale is just 45% compared to the 7 spot at 50%. So the minimum playable numbers are going to be different. Then its the 9 spot, then the 6 spot. And eventually I'll get around to doing the rest.

So ya wanna be a hardcore AP, huh? Well, this is some of the misery you have to put yourself through. Doing the math on these games is tedius, repititious, boring, time consuming and tiresome. But its what you have to do if you want the money.