[Solved] Formula for Paroli/Parlay betting system

[withnail]

Hi all,

My question relates to the so-called Paroli/Parlay progressive staking system used in gambling.
The system works as follows:

To keep it simple we'll assume the gambling odds are always evens (1/1 fractional, 2 decimal), and the base stake is always 1. So for a winning bet, a stake of 1 would win 1 + stake.
The Paroli/Parlay works by adding all profit from winning bets to the next stake, but reverting to the base stake after a losing bet.
So when on a winning streak you are compounding your profit by raising the stakes for a pre-determined number of bets.
In this case, the base stake is 1 so if the first bet wins the profit is also 1, so this is added to the next stake which will then be 2. If this bet also wins the profit is 2. The total profit is now 3, so the next stake is 4 (3 + base stake) and so on.
You have to decide how long to let the winning streak ride (because it can't last forever unfortunately), so in this example I want the system to attempt to ride maximum 3 winning bets in a row, then revert back to base stake.
You can see in the figures below quite clearly how it works.

W=winning bet
L=losing bet

W = +1
W = +2
L = -4
L = -1
L = -1
W = +1
L = -2
W = +1
W = +2
W = +4
W = +1
L = -2
L = -1
W = +1
W = +2
W = +4
L = -1
L = -1

Total = +6

I want to make a spreadsheet where I can paste in results from sports events in the form of W or L (or 1 or 0, doesn't really matter) and have the sheet calculate the total at the end of the run.
Also, I would need a column to paste in the odds (decimal odds) as these would be slightly different for every bet.
The part I really have no clue how to acheive is how to get it to revert back to the base stake once the system reaches it's target of 3 winning bets.
There would also need to be an option to adjust the amount of bets you want to win in a row. In the example I've used 3, but this could be 2, 5, 8, or whatever.

I already have some spreadsheets for the Martingale betting system, this is a negative progressive system which is essentially the reverse of what I want to do.
I've been able to modify this sheet somewhat for other purposes but it's beyond me to convert this to a Parlay system.
The attached sheet calculates for a Martingale system using back AND lay bets, it would be awesome to have a sheet like this but with the Parlay system instead of Martingale

[MrProgrammer]

The Paroli/Parlay works by adding all profit from winning bets to the next stake, but reverting to the base stake after a losing bet. So when on a winning streak you are compounding your profit by raising the stakes for a pre-determined number of bets. In this case, the base stake is 1 so if the first bet wins the profit is also 1, so this is added to the next stake which will then be 2. If this bet also wins the profit is 2. The total profit is now 3, so the next stake is 4 (3 + base stake) and so on. You have to decide how long to let the winning streak ride …, so in this example I want the system to attempt to ride maximum 3 winning bets in a row, then revert back to base stake.

W = +1
W = +2
L = -4
L = -1
L = -1
W = +1
L = -2

After the third win, the profit is +1+2-4-1-1+1 = -2. After a single win (the third W), you've said the system bets the profit plus the base stake so -2+1. However one cannot bet a negative amount. Explain in detail why this system bets a stake of 2 (L = -2) when the profit is negative. If the stake of 2 was an error, please repost the corrected series of all 18 values.

[withnail]

Hi MrProgrammer,

Thanks for your reply.
The stake of 2 isn't dependent on whether the profit at that moment is negative or not.
It's because the previous bet was a win, so the next stake is automatically doubled.
The rule is whenever a bet wins, the next stake is double the previous winning bet.
This carries on 3 times (1,2,4) and then reverts back to base stake of 1.
If previous bet was a loss, then next bet is always base stake

[MrProgrammer]

The stake of 2 isn't dependent on whether the profit at that moment is negative or not. It's because the previous bet was a win, so the next stake is automatically doubled. The rule is whenever a bet wins, the next stake is double the previous winning bet. This carries on 3 times (1,2,4) and then reverts back to base stake of 1. If previous bet was a loss, then next bet is always base stake

That is simpler than what I'd understood at first.

201906161226.ods

(13.01 KiB) Downloaded 144 times

Based on this topic, I suggest that you read [Tutorial] Ten concepts that every Calc user should know especially sections 8. Using formulas and cell references and 9. Using functions and cell ranges. Material there may help you with this project.

If this solved your problem please go to your first post use the Edit button and add [Solved] to the start of the title. You can select the green checkmark icon at the same time.

[withnail]

Thanks for your sheet!

I have a sheet where I can input different prices (odds) and that also calculates running profit/loss and commission etc.
I've modified this but only gotten as far as getting the staking right (and I can also input different odds and base stakes) but I can't think of a way to make it return to base stake after a run of 3 wins.
If there happens to be a winning streak of say 7 or 8, it does the first 3 stakes correctly but then just continues with base stakes.
I've attached the sheet, ignore the LAY columns, I'll modify those later once I've got the back (from D8 onwards) columns sorted out.
I can't use your formula to do this because your formula works on the assumption that the stakes/profit are always fixed, but I can use your formula for testing winning/losing streaks in general without the other calcs.
I realise this is slightly different from what I originally asked but only saw this was a requirement once I'd started modifying the sheet myself...

I'll do some more learning later when I've more time

[MrProgrammer]

I can't think of a way to make it return to base stake after a run of 3 wins. If there happens to be a winning streak of say 7 or 8, it does the first 3 stakes correctly but then just continues with base stakes.

An auxillary column to determine the streak count makes it easy to calculate when to return to the base stake and begin a new set of doublings.

201906181009.ods

(11.9 KiB) Downloaded 151 times

If this solved your problem please go to your first post use the Edit button and add [Solved] to the start of the title. You can select the green checkmark icon at the same time.

[withnail]

Voila, that's the difference between a tradesman and an amateur
I already have another sheet which counts negative/positive streaks, it never occured to me to use that formula to assist with this sheet.
Of course it's simple now, thanks!

[RoryOF]

OT: We are asked frequently to help with prediction/analysis spreadsheets. It would be interesting to learn if any of them yield a result (and then we may look for a cut!).

[withnail]

No problem, when I get this sheet finalized and paste some data into it (next week), I'll let you know how it turns out