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September 16th, 2011 at 7:15:19 PM
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I've seen Gamblers Bonus machines (United Coin Machine Co.) around town, usually at the local bars, 7-11's, and other convenience stores. I didn't pay them much mind, as they are typically short pay games without progressive jackpots. I did notice a neat feature, however - they offer bonuses much like a slot club without the need for a players card. All you have to do is log in to reap the rewards.

One day recently, I went in to a 7-11 to purchase a Slurpee, and noticed a pamphlet that outlined the benefits and promotions, one of which caught my eye. The tagline read, "Win up to $60,000 playing Four-Of-A-Kind Bingo with no additional bet," and it peaked my interest. The details and locations (throughout Nevada) can be found online. Go to www.gamblersbonus.com and click on Ways to Win; there's even a demo. The jist is that once you win your first quad, that rank is marked off, and you have 2000 hands to hit quads in each of the remaining 12 ranks. Clearly this is not a very likely venture, but this is gambling, is it not? Success will land you $60,000 while playing dollars, $15,000 while playing quarters, and $6,000 while playing nickels. This is independent of what you win or lose while playing the hands prior to the first quad and the 2000 hands after. Assuming that each of these offer the full royal with a 5-coin bet, note that the proportional bonus for nickels is double that of the bonus for the higher denominations.

It seems to me that you would play it straight until you get the first quad (in order to reduce the hold during these hands), and bend strongly in favor of quads for the next 2000, like you would when playing Shockwave but even more aggressively. Try creating a strategy by adding 2000 coins per coin bet to the payout for each quad. Now create another one by adding 24000 coins. The strategy changes drastically, without much increase to the probability of a quad.

I know that the average cycle for quads is usually between 400 and 450 hands depending on the game, so when playing without bending to the added value of this bonus the expected number of quads in 2000 hands would be between 4 and 5. Bending strongly only increases this to between 5 and 6. I seem to have a mental block against calculating the probability of hitting at least one quad in each of the 12 remaining ranks within 2000 trials. Any tips to get me started?

Just out of curiosity, any idea what the expected number of hands it would take to see at least one quad from each of the 13 ranks? It seems that this calculation might help with the one above...

Oh, and it doesn't matter to me which game you analyze, just so long as you describe your thought process and/or show your work, so that I can recreate it for any game type. Also, the different game types will pale in comparison when playing for the large premium for quads - I believe they will resemble one another more after each distinctly ranked quad.

All the best,

camapl

One day recently, I went in to a 7-11 to purchase a Slurpee, and noticed a pamphlet that outlined the benefits and promotions, one of which caught my eye. The tagline read, "Win up to $60,000 playing Four-Of-A-Kind Bingo with no additional bet," and it peaked my interest. The details and locations (throughout Nevada) can be found online. Go to www.gamblersbonus.com and click on Ways to Win; there's even a demo. The jist is that once you win your first quad, that rank is marked off, and you have 2000 hands to hit quads in each of the remaining 12 ranks. Clearly this is not a very likely venture, but this is gambling, is it not? Success will land you $60,000 while playing dollars, $15,000 while playing quarters, and $6,000 while playing nickels. This is independent of what you win or lose while playing the hands prior to the first quad and the 2000 hands after. Assuming that each of these offer the full royal with a 5-coin bet, note that the proportional bonus for nickels is double that of the bonus for the higher denominations.

It seems to me that you would play it straight until you get the first quad (in order to reduce the hold during these hands), and bend strongly in favor of quads for the next 2000, like you would when playing Shockwave but even more aggressively. Try creating a strategy by adding 2000 coins per coin bet to the payout for each quad. Now create another one by adding 24000 coins. The strategy changes drastically, without much increase to the probability of a quad.

I know that the average cycle for quads is usually between 400 and 450 hands depending on the game, so when playing without bending to the added value of this bonus the expected number of quads in 2000 hands would be between 4 and 5. Bending strongly only increases this to between 5 and 6. I seem to have a mental block against calculating the probability of hitting at least one quad in each of the 12 remaining ranks within 2000 trials. Any tips to get me started?

Just out of curiosity, any idea what the expected number of hands it would take to see at least one quad from each of the 13 ranks? It seems that this calculation might help with the one above...

Oh, and it doesn't matter to me which game you analyze, just so long as you describe your thought process and/or show your work, so that I can recreate it for any game type. Also, the different game types will pale in comparison when playing for the large premium for quads - I believe they will resemble one another more after each distinctly ranked quad.

All the best,

camapl

It’s a dog eat dog world.
…Or maybe it’s the other way around!

September 16th, 2011 at 11:06:35 PM
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2000 hands to hit 12 quads in each suit which pays 60,000:1. You can't really bend it much beyond 360:1 by discarding everything but the cards required.

it's a good Wizard question for "ask the wizard". So, you've got 2 things to overcome: the incredible amount of luck required to get 12 four of a kinds in 2000 hands and the even more incredible amount of luck to get 12 different ones.

it's a good Wizard question for "ask the wizard". So, you've got 2 things to overcome: the incredible amount of luck required to get 12 four of a kinds in 2000 hands and the even more incredible amount of luck to get 12 different ones.

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You want the truth! You can't handle the truth!

September 17th, 2011 at 7:57:54 AM
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.....

September 17th, 2011 at 6:18:23 PM
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Cycle of hitting any particular quads ranges from about 4200 to about 5700, depending on how hard you're going for it. (8888 in a jacks-or-better variant: around 5700. AAAA in Super Aces: around 4200.) Let's be really generous in assessing the promo and say it's 4000.

Odds of NOT hitting your particular quads on any given hand is 3999/4000. Odds of not hitting your particular quads in 2000 hands is (3999/4000)^2000 ~= 60.6%. Odds of hitting your particular quads is 100% - 60.6% = 39.4%.

Odds of hitting 12 particular quads in the same 2000-hand stretch is about (39.4%)^12 ~= 0.0014%. Value of the promo, at dollars, is $60000 * 0.0014% ~= $0.83. EV this adds to the game is $0.83 / (2000 * $5) ~= 0.0083%.

Nothing to write home about, to say the least.

Odds of NOT hitting your particular quads on any given hand is 3999/4000. Odds of not hitting your particular quads in 2000 hands is (3999/4000)^2000 ~= 60.6%. Odds of hitting your particular quads is 100% - 60.6% = 39.4%.

Odds of hitting 12 particular quads in the same 2000-hand stretch is about (39.4%)^12 ~= 0.0014%. Value of the promo, at dollars, is $60000 * 0.0014% ~= $0.83. EV this adds to the game is $0.83 / (2000 * $5) ~= 0.0083%.

Nothing to write home about, to say the least.

January 3rd, 2012 at 8:35:17 PM
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This has to be an interesting point in the bingo strategy point of view. I just hoped that things would be well soon in order to get things done in the future.

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