how many hands to get all 13 quads?

or how many quads total would be hit on average before all 13 different quads are hit?

and is it best to adjust your strategy when only the last quad is needed and add the bonus to the quad and play accordingly?

What do you get for hitting all 13?

Quote: CrystalMath

What do you get for hitting all 13?

By the way, excellent question waxvub!

CrystalMath, I can't speak for waxvub, but Boomtown Reno has an ongoing promotion for certain VP games at each casino. Once you have gotten all 13 quads (each must be verified and logged), there is a $125 bonus on guarters, $250 on half-dollars, or $500 on dollars with max bet (5-coin).

I have pondered the same question. My gut says 13 times the average of cycle length of each quad rank (or the sum of actual cycle lengths for each rank), assuming no strategy changes as you approach completion.

Just a guess but over 10k hands? on the promotion can you have multiple cards working assuming its a bingo card type of thing.

This isn't the exact answer because the probability of quads vary a little by rank:

Probability of any quad is roughly 1 in 425 at Jacks or Better.

So first quad: 425 hands on average, duh

Second quad: 12 ranks of 13 left so now 13*425/12 = 460.4166 hands on average

Third quad: 12 ranks of 13 left so now 13*425/11 = 502.27272 hands on average

and so on until:

Thirteenth quad: 1 rank of 13 left so now 13*425 = 5525 hands on average

Summing all the terms together:
425
460.4166666667
502.2727272727
552.5
613.8888888889
690.625
789.2857142857
920.8333333333
1105
1381.25
1841.6666666667
2762.5
5525

Total: ~17,570 hands.
This isn't the exact answer because the probability of quads vary a little by rank:

Probability of any quad is roughly 1 in 425 at Jacks or Better.

So first quad: 425 hands on average, duh

Second quad: 12 ranks of 13 left so now 13*425/12 = 460.4166 hands on average

Third quad: 12 ranks of 13 left so now 13*425/11 = 502.27272 hands on average

and so on until:

Thirteenth quad: 1 rank of 13 left so now 13*425 = 5525 hands on average

Summing all the terms together:
425
460.4166666667
502.2727272727
552.5
613.8888888889
690.625
789.2857142857
920.8333333333
1105
1381.25
1841.6666666667
2762.5
5525

Total: ~17,570 hands.

If completing the cycle wins you 100 betting units as camapl has suggested, then this promo adds roughly:
100/17,570 = 0.00569 = 0.569% to the machine's base return.

This promo is quite swingy though. Note the average number of hands to collect the very last quad is 5525. But the number of hands needed to collect the last quad 95% of the time is: (5524/5525)^N = 0.05

N = 16,550 just for collecting the last quad only with 95% confidence.

Quote: AxelWolf

Just a guess but over 10k hands? on the promotion can you have multiple cards working assuming its a bingo card type of thing.

Hey AxelWolf. Yes, you may have multiple sheets in progress at each of the three bars (each bar being separate from the other two) - don't think there is a limit on the number of sheets you can have in play. (I may be thinking of the Gambler's Bonus promotion seen at some 7-Elevens, etc., as I know that had a limit of like 2 or 3?)

Obviously this would alter the expected cycle length, as you don't need to complete one set before pursuing another. I'd be curious to see some calculations/methodology for the average cycle lengths of both a single trial and that of the ongoing case.

Quote: tringlomane

Total: ~17,570 hands.

Thank you tringlomane! My guess would have resulted in merely the 5525 hands. I believe your estimate of 17.5K is sound even without accounting for the different likelihoods of quads, as accounting for order would over-complicate the calculation!

Given that it is impossible to complete this in a single hand (unlikely minimum would be 13), would it be mathematically correct to take the reciprocal of the 17.5K cycle length in order to devise a probability of success for any hand? I am also interested in the probability of hitting all 13 quads in X hands.

Quote: tringlomane

If completing the cycle wins you 100 betting units as camapl has suggested, then this promo adds roughly:
100/17,570 = 0.00569 = 0.569% to the machine's base return.

Not a bad addition to long term if they offered JOB 9/6! Unfortunately, they do not, at least not to my knowledge, at the bars.

The Snake Bar (near the pit) has a $1 progressive with Bonus 8/5 (RF from $4K, SF $250, 4A $400), Deuces 25/15/9/4/4 (RF), Double Bonus 9/7/5 (RF), and Double Double 9/6 (RF). The meters aren't the fastest I've seen, but including the bonus for quads, Bonus 8/5 is a play regardless of the progressive values. (Assuming you can last the duration of the bonus!)

Best game I have found with this promo at Gambler's Bonus is 9/5 JOB. I think the cash back is .2% plus they send random text bounce backs. Unless you are going to drink a lot I doubt it is still close enough to 100% to be worth it.

Quote: tringlomane

Total: ~17,570 hands.

While tringlomane's answer contains the average requirement for the first instance of getting each quad, I would think that the cycle length comes down as you continue playing for subsequent sets (at a Boomtown Reno bar). In 17.5K hand, you would expect to have hit an average of about 41 quads in order to get exactly one complete set of 13. After you claim your first prize, you would have about 28 unclaimed quads remaining to use towards completing your next set. On average, wouldn't that require only enough hands to hit any 13 more quads, or ~5525 more hands? It seems that this would be the case for every set once the first is complete. Now you are looking at a 100/5525 (or ~1.81%) bonus. Another way to determine the return, would be to add 7.6923 (or 100/13) to the value of each of the quad payouts. Again, this is only correct once the first set is complete!

If you're allowed to have multiple lists of quads to collect, then the average number of hands needed to complete a cycle will definitely be less than 17.5k each. But it won't be quite as low as ~5525 per list unless you do this promo for eternity, or if there is a limit on collection lists active at any given time. If anyone plans to put a royal cycle or more worth of hands into this, I wouldn't be surprised if the promo was worth at least 1% on the return. I would have to make a rough sim to get a better idea though, and it's late, and I leave for Vegas on Wed. :)

Quote: tringlomane

But it won't be quite as low as ~5525 per list unless you do this promo for eternity, or if there is a limit on collection lists active at any given time.

Something else occurred to me. Quads that are more likely (like A's & faces on most games and 2's-4's in bonus games) would not all be useful in the long run, as the other ranks would eventually fall too far behind. You would need to adjust (reduce) the value of the promo for these more likely ranks, as you would eventually, and periodically, need to skip certain select 4oK hits

Quote:

I would have to make a rough sim to get a better idea though, and it's late, and I leave for Vegas on Wed. :)

Would love to see your results... Have an awesome trip!

Ok so I am thanking all of you that you found where the wiz already figured this out and this is what I was thinking about 15 to 20 k of hands and he and you all said it is 17.5k hands. Not very difficult to do in less than 20hrs where as I play at about 1100 hands an hour. You all must understand that I have lived and played VP in vegas for over 15 years so it is not hard for me to have an 8 hour session playing around 7500 hands for sure. So 250 dollars on 17.5 k hands will get me how many total quads? about 36 or so right? so lets say 39 quads total will get me my 13 for the 250 which we break it down to the third which is roughly 6.50 added to the quad which is substantial on a progressive royal that is not hard to pick up at 1250 to 1750 which will put me at 1 - 2 % winner which equates to about 10 dollars an hour average with not alot of variance. Now if they change this to get to the 416 payout for the cycle it will boost up the quad to around 10 dollars which is 40 quarters extra at 165 coins and it is pretty good with the card, mailers and other perks like comps and what not.

I know you might not think 10 - 15 dollars an hour is much but when your playing quarters on lightning speed machines on a smaller BR its pretty good. My point was that its a good win and I am older now so I don't put in the 12 to 15 hr sessions but I know a few people who still do.

Now after re-reading that post that you guys directed me to I find out that it puts roughly a half a percent on the game which is great on JoB or even Full Pay Bonus Poker Deluxe making the game break even from jump street not adding the progressive royal and other perks!

Thanks to all who found that post because I was having some trouble searching it out. I must of been searching the wrong site or keywords

You missed the old days about 10 yrs ago when the quarters paid about 50 dollars an hour on the Gamblers Bonus. This play is roughly about .5% to 1% return which is great these days!

Sorry that I do not really want to post where this is located since it has been pretty unknown for almost 7 months now but it is 9/6 JoB and 9/6 Bonus Poker Deluxe. Happy Hunting though to all of you who like to scout!