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05-30-2012, 06:39 PM   #16
veteran

Join Date: Jun 2011
Posts: 2,273
Re: Progressive Question

Quote:
 Originally Posted by random_person Am I correct in thinking that the math for the strategy for this machine is the same as the strategy for the average jackpot?
Yes, for strategy purposes, I would assume this is the best course of action. If this is not technically optimal, I am almost certain it is the best practical approximation we can make. Optimal strategy may not be tied to the average jackpot if strategy errors are significantly more severe in one particular direction.

We can briefly explore this idea through example. Let's say there are two jackpots, one at 1500 credits and one at 1580.4 credits. So the average jackpot is 1540.2 credits. We are dealt A A K T 4. At 1540.2 credits we are indifferent to either holding AA or AKT suited. At 1500, holding AA is superior by 0.03719 credits, while at 1580.4 credits, holding AKT suited is superior by 0.03719 credits. So, yep, using the strategy for the average jackpot is definitely best.

Like you say, when the average jackpot is above \$1944 (1555 credits), then the machine becomes +EV. And then to answer your other question what is the expected +EV value if you only play the machine when the average jackpot is \$1944 or higher? Well, the easiest way to estimate this is to determine the average number of hands it will take you to hit a royal. Unfortunately oyal probabilities change as the oyal payouts increase.

But studying various game states, the probability of hitting a royal in any given hand is roughly 1 in 32,300 when the machine is between 100% and 101% return. So we would see about 3230 deals on average before getting a royal. And would gain 3c x 3290 = \$96.90 from the royal payout that you end up hitting on average while chasing it. So this adds \$96.90/\$1.25/32,300 ~ 0.24% return on average. Now in this scenario, the machine may still be +EV even after you hit a royal if that royal's jackpot that was hit was lower than average. But I'm just indicating what the average return would be if you just chased until you hit any royal.

Generally speaking, going back to your OP, if this machine consistently adds 3 cents per hand played to the progressive royal bank, this machine basically depends on player error to turn a profit.

05-30-2012, 11:53 PM   #17
centurion

Join Date: Aug 2011
Posts: 121
Re: Progressive Question

Quote:
 Originally Posted by tringlomane Yes, for strategy purposes, I would assume this is the best course of action. If this is not technically optimal, I am almost certain it is the best practical approximation we can make. Optimal strategy may not be tied to the average jackpot if strategy errors are significantly more severe in one particular direction. We can briefly explore this idea through example. Let's say there are two jackpots, one at 1500 credits and one at 1580.4 credits. So the average jackpot is 1540.2 credits. We are dealt A A K T 4. At 1540.2 credits we are indifferent to either holding AA or AKT suited. At 1500, holding AA is superior by 0.03719 credits, while at 1580.4 credits, holding AKT suited is superior by 0.03719 credits. So, yep, using the strategy for the average jackpot is definitely best. Like you say, when the average jackpot is above \$1944 (1555 credits), then the machine becomes +EV. And then to answer your other question what is the expected +EV value if you only play the machine when the average jackpot is \$1944 or higher? Well, the easiest way to estimate this is to determine the average number of hands it will take you to hit a royal. Unfortunately oyal probabilities change as the oyal payouts increase. But studying various game states, the probability of hitting a royal in any given hand is roughly 1 in 32,300 when the machine is between 100% and 101% return. So we would see about 3230 deals on average before getting a royal. And would gain 3c x 3290 = \$96.90 from the royal payout that you end up hitting on average while chasing it. So this adds \$96.90/\$1.25/32,300 ~ 0.24% return on average. Now in this scenario, the machine may still be +EV even after you hit a royal if that royal's jackpot that was hit was lower than average. But I'm just indicating what the average return would be if you just chased until you hit any royal. Generally speaking, going back to your OP, if this machine consistently adds 3 cents per hand played to the progressive royal bank, this machine basically depends on player error to turn a profit.
I agree with everything you said here. I think to justify the optimal strategy being the same you just have to appeal to the linearity of expectations. Because E(aX+bY)=aE(X)+bE(Y), the average jackpot is a sufficient statistic for the optimal strategy on any hand.

Your calculation was similar to one approach I took to calculating the answer. The problem is that multiple royals are possible, and probably account for a substantial amount of extra equity. I'm just waiting for VPgenius to stop giving me error messages so I can work out the probabilities of the different numbers of royals.

I think the optimal strategy for monopolizing the bank is some cutoff rule where you play until the royal is below some number, but I don't think this is solvable in closed form. I think I would have to run simulations to find that rule. My bet is that it might be below the 1944 cutoff mark but it might not be.

Of course monopolizing the machine until you hit a dealt royal would be impossible. You would get kicked out far before then.

 05-31-2012, 12:03 AM #18 veteran   Join Date: Jun 2011 Posts: 2,273 Re: Progressive Question Monopolizing the machine shouldn't negatively effect your EV as long as each hand's jackpot increases 3 cents for every hand missed whether you play it our not.
05-31-2012, 04:40 AM   #19
centurion

Join Date: Aug 2011
Posts: 121
Re: Progressive Question

Quote:
 Originally Posted by tringlomane Monopolizing the machine shouldn't negatively effect your EV as long as each hand's jackpot increases 3 cents for every hand missed whether you play it our not.
I think it does. Imagine you play the machine by yourself until the jackpot reaches some value where everyone in the casino gets excited and seven others join you in competition for the jackpot. They are taking 7/8 of your extra built up ev

05-31-2012, 05:37 PM   #20
Mod Werewolf Game MVP

Join Date: Feb 2009
Location: New England
Posts: 3,677
Re: Progressive Question

Quote:
 Originally Posted by tringlomane Unfortunately royal probabilities change as the royal payouts increase.
Can you explain this? I would think the probability of hitting a royal remains constant regardless of the progressive size. Or do you mean an increasing progressive draws more people to it, so your chances of hitting it decrease due to competition?

05-31-2012, 10:26 PM   #21
centurion

Join Date: Aug 2011
Posts: 121
Re: Progressive Question

Quote:
 Originally Posted by Lattimer Can you explain this? I would think the probability of hitting a royal remains constant regardless of the progressive size. Or do you mean an increasing progressive draws more people to it, so your chances of hitting it decrease due to competition?
He is talking about strategy adjustments. For example qj suited and akqj are close in ev around a 1944 jackpot. At lower jackpots the akqj is better while the qj is at higher. If the royal is high enough, then 3 to a royal becomes better than a pair of aces. The result is that optimal strategy gives you a royal one in 40000 hands at a 1000 dollar jackpot and one in 33000 hands at 1944.

 05-31-2012, 11:08 PM #22 Mod Werewolf Game MVP     Join Date: Feb 2009 Location: New England Posts: 3,677 Re: Progressive Question Right, that makes sense.

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