A few days ago, jack,jackson asked me to perform some simulations comparing HO2 and AO2 in various hand-held games.
For these simulations, I used 1/4 deck resolution, rounded deck estimation and rounded deck estimation. Both systems have full indices and an ace side-count. All simulations were for 1 Billion Rounds.
The systems were compared under two different types of SD and DD games. Each SD and DD game had two different pen varieties. Finally, each pen level had two different spreads. Thus, 32 different simulations are reported (although I had to do an additional sixteen to determine betting ramps that would make fair as fair a comparison as possible).
For the betting ramps, each system bets 1 unit on all hands below a certain true count and places its max bet on hands where the TC exceeds this critical value. Ideally, you want to have each system raise its bets when each system's TC predict that they have the exact same TBA for the hand (Total bet advantage; IOW, advantage related to the total bet for the hand). (How accurate this prediction is relates to the BC of the system). I did my best to make sure that each system raised its bets when their TC predicted that the next hand would offer a nearly equivalent TBA, though for some cases one system may have been raising its bets on hands offering a slightly lower TBA than the other system, thus overbetting relative to the other system. The TC at which each system ramps its bet is indicated for each set of conditions.
I provided the TBA, S.d. (per 100 hands) and Action (per 100 hands) as a means to compare the two systems. The latter two figures are reported in units. As you can see from the results, the system raising its bet on hands with a slightly lower predicted TBA, will have an advantage in the TBA criterion, but this will lead to a higher S.d. Clearly then, if a system has a higher TBA, but a lower S.d., then it is superior under those conditions, assuming perfect play.
I have highlighted the conditions green where the HO2's SOCRE is higher
Similarly, I have highlighted the conditions red where AO2's SCORE is higher
Disclaimer: Note that when a system is victorious, the victory is absolutely minuscule, even when perfect play is assumed. In practice, I'd wager that there is absolutely difference between these two systems under the conditions studied. Deciding which system is better for any given user should be determined by how well they can execute each system.
Here are the results:
https://docs.google.com/leaf?id=0B0cCldUn36hMNTEwZDc1ZWItMWIyNC00NzY4LWJjNGMtYjVlNjRiNmE5MWNk&hl=fr
Enjoy!
SP
For these simulations, I used 1/4 deck resolution, rounded deck estimation and rounded deck estimation. Both systems have full indices and an ace side-count. All simulations were for 1 Billion Rounds.
The systems were compared under two different types of SD and DD games. Each SD and DD game had two different pen varieties. Finally, each pen level had two different spreads. Thus, 32 different simulations are reported (although I had to do an additional sixteen to determine betting ramps that would make fair as fair a comparison as possible).
For the betting ramps, each system bets 1 unit on all hands below a certain true count and places its max bet on hands where the TC exceeds this critical value. Ideally, you want to have each system raise its bets when each system's TC predict that they have the exact same TBA for the hand (Total bet advantage; IOW, advantage related to the total bet for the hand). (How accurate this prediction is relates to the BC of the system). I did my best to make sure that each system raised its bets when their TC predicted that the next hand would offer a nearly equivalent TBA, though for some cases one system may have been raising its bets on hands offering a slightly lower TBA than the other system, thus overbetting relative to the other system. The TC at which each system ramps its bet is indicated for each set of conditions.
I provided the TBA, S.d. (per 100 hands) and Action (per 100 hands) as a means to compare the two systems. The latter two figures are reported in units. As you can see from the results, the system raising its bet on hands with a slightly lower predicted TBA, will have an advantage in the TBA criterion, but this will lead to a higher S.d. Clearly then, if a system has a higher TBA, but a lower S.d., then it is superior under those conditions, assuming perfect play.
I have highlighted the conditions green where the HO2's SOCRE is higher
Similarly, I have highlighted the conditions red where AO2's SCORE is higher
Disclaimer: Note that when a system is victorious, the victory is absolutely minuscule, even when perfect play is assumed. In practice, I'd wager that there is absolutely difference between these two systems under the conditions studied. Deciding which system is better for any given user should be determined by how well they can execute each system.
Here are the results:
https://docs.google.com/leaf?id=0B0cCldUn36hMNTEwZDc1ZWItMWIyNC00NzY4LWJjNGMtYjVlNjRiNmE5MWNk&hl=fr
Enjoy!
SP
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Is it safe to say the system with the higher TBA would also have a better score?