# Coin flips and Dice rolls in a stored procedure

I saw a post in chat a few days ago, of what I thought was an interesting (albeit fairly simple) statistical challenge:

By @skiwi:

If I shoot once with 50% chance of target A and 50% of target B, and if I hit target A I have 95% chance to shoot again, then how many of target A will I hit on average?

So I broke out the SQL machine and decided to write something like this, but more generic. So for the 50/50 chance I used a coin-flip-like logic, then for the subsequent rolls, I used the analogy of a dice roll, as I feel these two are clear and should be familiar to anyone.

I wrapped this into a stored procedure usp_CoinFlipAndDiceRolls.sql (the usp_ or sp_ prefix is very commonly used in databases when naming procedures).

I did as much as I could to make it set-based, but some parts, especially the repeated dice rolls, I couldn't think of a good way to do it without a loop.

Execution is still quite fast, 1-2 seconds for 10000 rows and about 5 seconds for 10000 rows. What can I improve on? Do my statistics make sense?

use PhrancisLocal;
go
if object_id('dbo.usp_CoinFlipAndDiceRolls') is not null
drop procedure dbo.usp_CoinFlipAndDiceRolls;
go
set ansi_nulls on;
go
set quoted_identifier on;
go

create procedure dbo.usp_CoinFlipAndDiceRolls
@numberOfRuns int = 1000,
@chanceToWinDiceRoll float = null,
@includeStatistics bit = 0
as
begin
set nocount on;

/* Default dice roll to 1 chance in 6 if not passed in to the procedure as a parameter: */
if @chanceToWinDiceRoll is null
set @chanceToWinDiceRoll = (1.0/6);

/* CONSTANTS */
declare
@CHANCE_TO_WIN_COIN_FLIP float = 0.5,
@WIN bit = 1,
@LOSS bit = 0;

/* Temporary table which will be used to hold the results of the operations
and aggregate statistics from the results to return to the caller. */
if object_id('tempdb..#CoinFlipAndDiceRolls') is not null
drop table #CoinFlipAndDiceRolls;
create table #CoinFlipAndDiceRolls (
row_id int identity(1,1) primary key,
CoinFlipSeed float,
CoinFlipWon bit,
NumberOfDiceRolls int
);
/* Seed the coin flip according to the number of runs desired,
and populate the coingFlipWon value accordingly based on a 50% random chance */
declare
@row_num int = 1,
@CoinFlipSeed float = null;
while (@row_num <= @numberOfRuns)
begin
set @CoinFlipSeed = rand();
insert into #CoinFlipAndDiceRolls (
CoinFlipSeed,
CoinFlipWon,
NumberOfDiceRolls
)
select
@CoinFlipSeed,
case
when @CoinFlipSeed >= @CHANCE_TO_WIN_COIN_FLIP then @WIN
else @LOSS
end,
case
when @CoinFlipSeed >= @CHANCE_TO_WIN_COIN_FLIP then 0
else null
end;
set @row_num = @row_num + 1;
end;

/* Begin logic for dice rolls:
* A dice is rolled once for each run (i.e. row) where the coin flip was a Win.
* Each dice roll Win triggers another dice roll, and so on until a dice roll is Lost.
* The criteria for a dice roll to be a Win is determined by the @chanceToWinDiceRoll number
* where a 0.25 value will result in a 25% chance to Win.
* @diceRollSeed represents each individual dice roll.
*/
declare @diceRollSeed float = null;
declare @currentRow int = (
select min(row_id)
from #CoinFlipAndDiceRolls
where NumberOfDiceRolls = 0
and CoinFlipWon = @WIN
);
while exists (
select 1
from #CoinFlipAndDiceRolls
where NumberOfDiceRolls = 0
and CoinFlipWon = @WIN
)
begin
set @diceRollSeed = rand();
while @diceRollSeed <= @chanceToWinDiceRoll
begin
update #CoinFlipAndDiceRolls
set NumberOfDiceRolls = NumberOfDiceRolls + 1
where row_id = @currentRow;
/* Roll a new dice value: */
set @diceRollSeed = rand();
end
set @currentRow = (
select min(row_id)
from #CoinFlipAndDiceRolls
where NumberOfDiceRolls = 0
and CoinFlipWon = @WIN
);
end;

/* Return the result finished result set: */
select * from #CoinFlipAndDiceRolls order by row_id asc;

/* Statistics about the finished result set, if the call includes this parameter: */
if @includeStatistics = 1
begin
select
[NumberOfRuns] = @numberOfRuns,
[ChanceToWinDiceRoll] = @chanceToWinDiceRoll,
[TotalCoinFlipWins] = sum(convert(int, CoinFlipWon)),
[TotalDiceRolls] = sum(coalesce(NumberOfDiceRolls, 0)),
[AverageDiceRollsPerCoinFlipWon] = (select avg(NumberOfDiceRolls) from #CoinFlipAndDiceRolls where NumberOfDiceRolls is not null)
from #CoinFlipAndDiceRolls;
end;

/* Cleanup */
if object_id('tempdb..#CoinFlipAndDiceRolls') is not null
drop table #CoinFlipAndDiceRolls;
end;
go


Test runs

-- No params
execute dbo.usp_CoinFlipAndDiceRolls;
-- With params
execute dbo.usp_CoinFlipAndDiceRolls
@numberOfRuns = 1000,
@chanceToWinDiceRoll = 0.95;
-- With params & statistics
execute dbo.usp_CoinFlipAndDiceRolls
@numberOfRuns = 1000,
@chanceToWinDiceRoll = 0.75,
@includeStatistics = 1;


The results look something like this (when ran with @includeStatistics on):

Overall, I think your procedure is very good. It's consistent in layout, capitalisation and style, and well commented. I had no problems reading through it and understanding what it was doing (and how) without actually running it.

I really like the way you distinguish global constants with @ALL_CAPS, from regular "true" @variables. I'd not seen this before in T-SQL, but know it as a general programming style, and will be copying in my own SQL code from now on.

Performance-related improvements

It obviously depends on the spec of the SQL box, but 5 seconds for 10,000 runs seems entirely reasonable to me, and I don't see a need to improve on this for the sake of it.

In the context of this problem, iterative looping is a perfectly reasonable approach; this doesn't lend itself to set-based processing and after a brief think, I can't see how I'd do it without loops. I'm sure it's possible but does it merit the thought-effort required? Not for me.

One way you might get better performance is by replacing the temporary table with a table variable. This is highly debateable and would depend on a lot of factors (which version of SQL Server, how many rows are a realistic load, amount of memory, etc etc). Rather than debate it academically, in this situation I'd create a copy of the proc using an @table and compare their performance side-by-side.

Temporary table scope

Another minor performance improvement (not necessarily measurable) could be to remove the statements dropping #CoinFlipAndDiceRolls before creating it, and at the end. Temporary tables are scoped to the instance of the stored procedure anyway, so it can't already exist at the start of the proc (unless a parent callee stored procedure has created it - which you'd know about). Similarly, you don't have to clean it up at the end, SQL will do that for you.

Syntactic short-cuts / improvements

• I quite like the += operator (official documentation here), allowing set @row_num += 1 instead of set @row_num = @row_num + 1.

• When you insert into #CoinFlipAndDiceRolls, in your particular case I would normally use values (val1,val2,val3) syntax rather than selecting the values, because these are a single row of values with no from clause.

• Where you declare @currentRow - personally if I'm setting to a value dynamically (rather than just hardcoded) I don't like to do this in the declare. Rather, I declare it then assign in a subsequent statement.

• For that and some other variable assignments from a select query, having declared the variable you can do this:

select @currentRow = min(row_id)
from #CoinFlipAndDiceRolls
where NumberOfDiceRolls = 0
and CoinFlipWon = @WIN


which is a little terser than your subquery-style approach.

Clarity of loop control

In your dice-roll block, I think it'd be clearer to maintain @currentRow at the start of the loop not the end.

begin
set @diceRollSeed = rand();

select @currentRow=min(row_id)
from #CoinFlipAndDiceRolls
where NumberOfDiceRolls = 0
and CoinFlipWon = @WIN;

while @diceRollSeed <= @chanceToWinDiceRoll
begin
update #CoinFlipAndDiceRolls
set NumberOfDiceRolls = NumberOfDiceRolls + 1
where row_id = @currentRow;
/* Roll a new dice value: */
set @diceRollSeed = rand();
end

);
end;


This way, you wouldn't need to initially assign it at all outside the loop.

• Nice answer, but one point is that SQL Server does not support += syntax (otherwise I would have used it). Try running this select 1 += 1 you will get Incorrect syntax near '+=' Feb 23, 2016 at 18:06
• I agree with you that select 1 += 1 would be incorrect, because += is a compound addition/assignment operator and one cannot assign a value to the integer literal 1 - it's not a variable! However, if you try the usage I give in my answer (set @row_num += 1) you will find it works perfectly well provided @row_num has been initialised to a non-null value. :) I've updated my answer to provide a link to the official documentation of the += operator. Feb 23, 2016 at 19:12
• Dang, you are right, I had no idea! I'll be using this going forward. Feb 23, 2016 at 19:31