Wizard
Joined: Oct 14, 2009
• Posts: 18536
June 13th, 2018 at 7:34:31 PM permalink
Quote: mustangsally

I played this bet about the time I did the math, so I guess I understood the rules better than those who may have just read them a few times
My transition matrix shows this for Point-0=
3/36*15/36+
4/36*16/36+
5/36*17/36+
5/36*17/36+
4/36*16/36+
3/36*15/36 = 388/1296

Maybe we are just disagreeing on how to label losing events. I would file a sequence of 4 and then 7 as a "point and loss." I don't think there is a disagreement on the rules.

Still I think I have a minor error somewhere.
Last edited by: Wizard on Jun 13, 2018
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
Joined: Oct 14, 2009
• Posts: 18536
Thanks for this post from:
June 13th, 2018 at 8:38:32 PM permalink
I found a minor error. Sally and I at least agree on the probability of the highest win. However, I still think we are not interpreting the rules the same way, and the error is probably mine.

Let me think.

It's not whether you win or lose; it's whether or not you had a good bet.
mustangsally
Joined: Mar 29, 2011
• Posts: 2392
June 13th, 2018 at 9:44:49 PM permalink
I was happy someone else came up with the same answer I did a few years back, using a different method.

There is an easier way to populate the transition matrix that I used in Excel. I may re-do it later.

Here is my Excel in Google for those that want to see how I did it
https://goo.gl/b8HCGJ

come to think of it, I do not even see a simulation I ran
Hmmm

Sally

btw, the bet IS addictive, imo. I tried not to make it but it kept winning (the Point2 version)
I Heart Vi Hart
Wizard
Joined: Oct 14, 2009
• Posts: 18536
Thanks for this post from:
June 13th, 2018 at 10:12:39 PM permalink
Okay, I now agree with Sally. Here are my tables.

Chuckleberry Pay Table

Event Pays Probability Return
Five hits plus point 1000 0.000132 0.132305
Five hits 150 0.001058 0.158766
Four hits 15 0.010002 0.150034
Three hits 5 0.040947 0.204737
Two hits 0 0.108353 0.000000
One hit 0 0.206790 0.000000
Zero hits 0 0.299383 0.000000
Come out roll 7 or 11 1 0.222222 0.222222
Come out roll 2, 3, or 12 0 0.111111 0.000000
Total 1.000000 0.868066

darkoz Pay Table

Event Pays Probability Return
Five hits plus point 500 0.000132 0.066153
Five hits 100 0.001058 0.105844
Four hits 10 0.010002 0.100023
Three hits 4 0.040947 0.163790
Two hits 2 0.108353 0.216707
One hit 0 0.206790 0.000000
Zero hits 0 0.299383 0.000000
Come out roll 7 or 11 1 0.222222 0.222222
Come out roll 2, 3, or 12 0 0.111111 0.000000
Total 1.000000 0.874739

Thanks, Sally, for keeping me on my toes.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
Joined: Oct 14, 2009
• Posts: 18536
Thanks for this post from:
June 14th, 2018 at 8:32:54 AM permalink
Here is my new page on Lucky Shooter. As usual, I welcome all questions, comments, and especially corrections.
It's not whether you win or lose; it's whether or not you had a good bet.
darkoz
Joined: Dec 22, 2009
• Posts: 3424
June 14th, 2018 at 8:42:40 AM permalink
Interesting math analysis

One would assume the \$1000 paytable had the better return

Apparently the higher payouts are balanced by the first payout being one extra combination being made before reaching a winning resolution
mustangsally
Joined: Mar 29, 2011
• Posts: 2392
June 14th, 2018 at 10:05:26 AM permalink
Quote: Wizard

Thanks, Sally, for keeping me on my toes.

I do not understand, but ok to you.
standing flat-footed is ok too.
(not saying you are flat-footed, I doubt you are)

as combinations (nCk) are my weakest link in most cases, care to show (and share) how you did your math?
Chuckleberry looks to have done it the same way too in the first link I provided.

As I already mentioned, I was in a Markov chain mode a few years ago and did it that way
to be different

Sally
I Heart Vi Hart
Wizard
Joined: Oct 14, 2009
• Posts: 18536
June 14th, 2018 at 3:19:02 PM permalink
Quote: mustangsally

care to show (and share) how you did your math?

I did it in Excel. I modified my Fire Bet spreadsheet, which is also a Markov Chain. Plus, when we didn't agree, I wrote a simulation in C++, which confirmed you were right. I can share the spreadsheet, if you like, on Google Docs.
It's not whether you win or lose; it's whether or not you had a good bet.
mustangsally
Joined: Mar 29, 2011
• Posts: 2392
June 14th, 2018 at 3:33:01 PM permalink
Quote: Wizard

sure, that would be nice.
thank you
I have yet to simulate this one...
since the Astros just won, I will do just that (I won too)

Sally
I Heart Vi Hart
Wizard
Joined: Oct 14, 2009
• Posts: 18536
June 14th, 2018 at 8:06:06 PM permalink
Quote: mustangsally

sure, that would be nice.

Here is a link to the spreadsheet. Sorry it isn't documented well. https://www.dropbox.com/s/whrxq399i4fa83n/lucky%20shooter.xls?dl=0.

Here is some code for my simulation.

`void LuckyShooterSimulation(void){	int i,end,total,total_array[13],point,nummin,wins;	unsigned int die1,die2;	time_t curtime,endtime;	__int64 count,wins_array[13],tot_no_point,tot_point_loss;	cerr << "Enter number of minutes in simulation: ";	cin >> nummin;	curtime=time(NULL);	endtime=curtime+(60*nummin);	for (i=0; i<=12; i++)		wins_array=0;	count=0;	tot_no_point=0;	tot_point_loss=0;	__int64 tot_jackpot=0;	do	{		count++;		end=0;		wins=0;		for (i=4; i<=10; i++)			total_array=0;		die1=genrand_int32()%6+1;		die2=genrand_int32()%6+1;		point=die1+die2;		if ((point<=3)||(point==7)||(point>=11)) // bet over via repeat, 2, 3, 7, 11, or 12		{			point=0;			end=1;		}		while (end==0)		{			die1=genrand_int32()%6+1;			die2=genrand_int32()%6+1;			total=die1+die2;			if ((total_array[total]==1)||(total<=3)||(total==7)||(total>=11)||(total==point)) // bet over via repeat, point, 2, 3, 7, 11, or 12				end=1;			else			{				wins++;				total_array[total]=1;			}		};		if (point==0)			tot_no_point++;		else if ((wins==5)&&(total==point))			tot_jackpot++;		else			wins_array[wins]++;		if (count%5000000==0)		{			curtime=time(NULL);			cerr << "Minutes remaining: " << (double)(endtime-curtime)/60.0 << "\n";		}	}	while (curtime<endtime);	printf("No point\t%I64i\t%f\n",tot_no_point,(double)tot_no_point/(double)count);	printf("total jackpots\t%I64i\t%f\n",tot_jackpot,(double)tot_jackpot/(double)count);	for (i=0; i<=5; i++)		printf("%i wins\t%I64i\t%f\n",i,wins_array,(double)wins_array/(double)count);}`
It's not whether you win or lose; it's whether or not you had a good bet.