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Subject:
Theoretical vs. Actual House Advantage
Category: Science > Math Asked by: ramblergh-ga List Price: $15.00 |
Posted:
16 Nov 2005 12:43 PST
Expires: 16 Dec 2005 12:43 PST Question ID: 593887 |
1)If I were starting a casino online or offline (not sure if it matters) and I wanted make financial projections 3 years out. Would I be using the Theoretical vs. Actual House Advantage in my calculation. How would it work? |
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There is no answer at this time. |
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Subject:
Re: Theoretical vs. Actual House Advantage
From: mr_f-ga on 20 Nov 2005 04:03 PST |
Making a financial projection would be based off the theoretical house advantage (T.H.A). Although this T.H.A might be less that the A.H.A., because some players know how to 'count-cards' and proper betting strategies for table games. The T.H.A and A.H.A is static with regards to slot machines, because there is no strategy, and all probabilities are fixed. The Actual House Advantage could be computed by setting the limit as t -> +inf as the T.H.A. In other words, the longer your time frame, the closer your A.H.A will be to the T.H.A. You could view your A.H.A as stochastic ( random but with direction ), and this direction would be similar to (but likely greater than) the T.H.A. I say greater than, because inexperienced players who do not use optimum betting strategies, as well as players under the influence of alchole give the house a slightly greater edge. Craps may be a 49.29% chance of winning for the player, but as soon as an inexperienced player starts throwing bets down, the house will obtain a greater edge. Concluding, the A.H.A is a stochastic process which will have the same direction as the T.H.A, but is likely to be slightly higher than the T.H.A. As a financial model over 3 years, you would always want to use your theoretical house advantage, as that would pose the 'worst-case-scenerio' ( every player betting the best ). As far as the theory behind the house advange is, you would need to consider the proportions of people playing slot machines, and the different table games. T.H.A is larger if larger proportions of your clients are playing slot machines. The T.H.A. could be written as: numberofpeopleincasino*P(X=slot_player)*T.H.A(for slots) + numberofpeopleincasino*P(X=crapsplayer)*T.H.A(for craps) ... Where {X} contains all types of games in casino, P(X=slot_player) + P(X=crap_player) + ... + P(X=nongambler) = 1 (if they are all independent events, but it is likely you would have to use some sort of inclusion-exclusion formula). With appropriate theory, the Theoretical House Advantage would be close to the Actual House Advantage. For some periods of time the Actual House Advantage might be much different from the Theoretical House Advantage because it is a stochastic process, but a good theoretical model would contain some sort of random walk, and could explain all A.H.A. to company owners. The advantage to using a theoretical model for the house advantage as opposed to an 'actual' is you only need to crunch the numbers once. The actual house advantage would be ever changing ( stochastic ), but close to the theoretical. Hopefully this helps you make your choice, (theoretical). Mr_F |
Subject:
Re: Theoretical vs. Actual House Advantage
From: ramblergh-ga on 20 Nov 2005 06:57 PST |
But let me ask you how is that in vegas we see the hold for the house is anywhere between 14-20 percent over extended period of time, when we know and like you say that over time the AHA and THA get closer and closer. Thanks Joshua |
Subject:
Re: Theoretical vs. Actual House Advantage
From: mr_f-ga on 20 Nov 2005 18:11 PST |
Let me rephrase your statement and you tell me if I am answering the right question here. Over the long run, how come vegas casino's holds are between 14-20% and not a fixed number close to the T.H.A? This would be accounted for by the fact the A.H.A is a stochastic process, as well as the realization that different casino's would host different types of people. Some casinos might have alot more slot machines (thus more slot players), so there A.H.A would be greater than other casino's (or less than if they decide they like to pay out more often... which is unlikely). The Theoretical House Advantage would be casino specific, using proportions of people playing different games combined with the probabilities of winning in those events. Also some casino's have slightly different 'table' rules. (Eg. Hit on soft 17 in blackjack), some casinos might also take a different rake from poker games, would would contribute to the house. The theoretical house advantage is not universal for all casino's but rather very specific to individual casinos. If the data for the A.H.A is there and computed, you could figure out all the important statistical variables (STD, VAR.. etc) and apply that to a financial model, which would be much simpler. The issue is, if your not modeling financial projection of an existing casino, it would be incorrect to fudge data to get an A.H.A.. Unless you knew the house edge on the slot machines, and all the different table styles, and your casino did _EXACTLY_ the same thing, in the same demograph, which is unlikely, and probably wont be as correct a T.H.A model. The best approach would be having a Theoretical House Advantage _MODEL_, in which you adjusted it after the first month with regards to the proportions of people playing what. Or you could just use average of the daily house advantage. (which would approach the true house advantage with a larger time period because of the central limit theorem) Mr_F |
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