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Subject : Question for Arnold Snyder- Playing Multiple Hands posted by MJ1 on Nov-15-2006 08:30pm |
Mr Snyder, Somebody posted a question similar to this one a while back but you never commented on it. I revised the conditions of the game and am hoping you could share your opinion on this matter. Which of the following options is the best for a 6D game, typical rules (DAS, DA2, RS3, 75%Pen) with 3 other players at the table? All options below assume optimal betting with a fixed kelly-factor and multiple hand wagers that are adjusted for covariance. a) To play one hand all the time... Increasing and decreasing the bets with the count.... b) To play two hands at a time every time.... Increasing and decreasing the bets with the count... c) To play one hand and if the count goes up play two hands and increase the bets, of course having the same bet on both. d) To play two hands and if the count goes up play only one hand and increase the bets... Now option a) clearly cannot be the best because conventional wisdom says to play two hands in positive counts when other players are at the table. The problem with Option b) is that the counter would be playing two hands in negative counts and therefore losing twice as much in negative and neutral counts. On a positive note, at least he will play an extra hand in positive counts....which can really boost SC0RE! Between option c) and option d), I am inclined to go with option d) because it has to do with the card eating effect. By playing two hands in neg and neutral counts, you burn through the neg and neutral counts faster and get to play more rounds in positive counts. Well Mr Snyder, what do YOU think? Thanks, MJ |
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Subject : Does ANYBODY have an opinion on this matter? posted by MJ1 on Nov-17-2006 02:41pm |
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Subject : It depends on how may... posted by zengrifter on Nov-17-2006 02:50pm |
| other spots are in play. zg |
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Subject : Need more info posted by ETFan on Nov-17-2006 07:04pm |
MJ1 wrote: > > Mr Snyder, > > Somebody posted a question similar to this one a while back but you never commented on it. I revised the conditions of the game and am hoping you could share your opinion on this matter. > > Which of the following options is the best for a 6D game, typical rules (DAS, DA2, RS3, 75%Pen) with 3 other players at the table? All options below assume optimal betting with a fixed kelly-factor and multiple hand wagers that are adjusted for covariance. > > a) To play one hand all the time... Increasing and decreasing the bets with the count.... > b) To play two hands at a time every time.... Increasing and decreasing the bets with the count... > c) To play one hand and if the count goes up play two hands and increase the bets, of course having the same bet on both. > d) To play two hands and if the count goes up play only one hand and increase the bets... It depends on how fast you play, and whether you're required to bet twice table minimum to play two hands. It also depends on whether there's someone standing next to you eager to grab your second spot. These things can be worked out very precisely. You just need the covariance between hands at a table (about 0.5 for two hands), number of players at the table, speed of all players (counters usually assume they play faster than other players, and can play two hands in less than twice the time for one hand), and bet spread -- including required minimums. But it's always better to play two hands in positive counts with others at the table, unless the edge is so tiny you can't afford the house minimumX2. You want to eat more cards in positive counts when others are competing for those same high cards. And if you play two hands pretty fast, and you're concernd about time under the eye, then it's better to play two hands in negative counts, unless you have to pay 2Xmin on each hand. But this is a much closer decision. I used to play a second spot, sometimes, just because there was some ploppie lurking behind ready to grab my spot. I had to protect my second spot for the positive counts. But this is very brazen. I was like that playing red chips. Now, I know some successful black chippers who like to play THREE hands all the time with wild, crazy looking bet jumps. But that's another story. $20 on one hand, $300 on the other two. That kind of thing. ;) ETF |
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Subject : Re: Need more info posted by MJ1 on Nov-18-2006 09:56am |
> It depends on how fast you play, and whether you're required to bet twice table minimum to play two hands. It also depends on whether there's someone standing next to you eager to grab your second spot. Thanks for responding ETF. Let me try and provide the additional information you requested and perhaps you can help me (and other like minded players) figure out the best course of action. * I can play fairly fast...nearly 150% faster than the average ploppy...not really sure what my speed has to do with it though. * I do NOT have to bet twice the table minimum to play 2 hands. * Other players are eager to take the second spot. > These things can be worked out very precisely. You just need the covariance between hands at a table (about 0.5 for two hands), number of players at the table, speed of all players (counters usually assume they play faster than other players, and can play two hands in less than twice the time for one hand), and bet spread -- including required minimums. * Like I stated before, 3 other players at the table beside me. * The speed of the other players is the speed of the avg ploppy. Assume 50 rounds/Hr. * Spreading from 1 to 20 (on one hand or both hands). * Table minimum is $10/Hand. > But it's always better to play two hands in positive counts with others at the table, unless the edge is so tiny you can't afford the house minimumX2. You want to eat more cards in positive counts when others are competing for those same high cards. > And if you play two hands pretty fast, and you're concernd about time under the eye, then it's better to play two hands in negative counts, unless you have to pay 2Xmin on each hand. But this is a much closer decision. So your saying the best option for these conditions is to ALWAYS play 2 hands in both positive and negative counts. This way I am assured two spots for the high counts. BTW, can PowerSim be used to figure out the optimal bets for switching back and forth between 1 hand in neg and neutral counts and 2 hands in positive counts? MJ |
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Subject : card eating posted by ArnoldSnyder on Nov-20-2006 12:23pm |
| This is an area where many players have a misunderstanding. Optimally, playing two (or even three) hands in positive counts and one (or even none) in negative counts would provide the highest percentage and dollar return. Card eating is a valid strategy only if you use a monster betting spread. For instance, at a table with $25 minimums and $2500 maximums, if you could eat cards at the minimum and spread up to the max on your high counts, the card eating would cost little and it would speed up the game, which would work in your favor. Many players, however, cannot get away with such a big spread (or they don't have the bankroll to use such a spread). To make card eating a valid approach, the cards would have to be eaten by a confederate (like a wife or girlfriend) who can play multiple hands at the minimum with little suspicion. If you're using a more typical 1-8 or 1-12 spread, then card eating is probably going to take too big of a chunk out of your win rate to be an optimal strategy to employ by yourself. |
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Subject : Re: card eating posted by T.Hopper on Nov-24-2006 05:25pm |
| I like playing multiple hands in neutral counts. You burn up more cards per round at minimal price in EV. |
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Subject : What I have to do posted by ETFan on Nov-22-2006 04:07pm |
MJ1, This is a little math puzzle, and I have to clear out a couple hours where I can write it all out in excruciating detail. I've done this kind of puzzle before, and it comes out different each time, depending on the parameters you start with. Speed is definitely a factor. I can tell you, with the conditions you've layed out, some top authorities would come out on opposite sides. I think Schlessinger and Snyder would come out on one side, while MathProf and DD' would come out the other way. I won't tell you how I'm guessing until I do the math. ;) PowerSim gives you the raw data to answer these questions, but it takes a little scribbling to get from there to here. You can do the comparison more directly with some simulators, but that would take a little programming with PowerSim in its current form. But I would regard the question of how much to bet on two hands in positive EV counts as long settled math. There were articles on this in Blackjack Forum, oh I don't know, 15 years ago? You bet to keep the same Risk Of Ruin. When you do that, the total bet on two hands isn't double what you'd bet on one hand. It's 146% of what you'd bet on one hand. So if you'd normally bet 1 x $100, you'd want to bet $73 on each of two hands. So it would improve your take home pay by 46% per hour, EXCEPT that it does take a little longer to play two hands... I'll try to get to it on Friday. ETF MJ1 wrote: > > > It depends on how fast you play, and whether you're required to bet twice table minimum to play two hands. It also depends on whether there's someone standing next to you eager to grab your second spot. > > Thanks for responding ETF. Let me try and provide the additional information you requested and perhaps you can help me (and other like minded players) figure out the best course of action. > * I can play fairly fast...nearly 150% faster than the average ploppy...not really sure what my speed has to do with it though. > * I do NOT have to bet twice the table minimum to play 2 hands. > * Other players are eager to take the second spot. > > > These things can be worked out very precisely. You just need the covariance between hands at a table (about 0.5 for two hands), number of players at the table, speed of all players (counters usually assume they play faster than other players, and can play two hands in less than twice the time for one hand), and bet spread -- including required minimums. > > * Like I stated before, 3 other players at the table beside me. > * The speed of the other players is the speed of the avg ploppy. Assume 50 rounds/Hr. > * Spreading from 1 to 20 (on one hand or both hands). > * Table minimum is $10/Hand. > > > But it's always better to play two hands in positive counts with others at the table, unless the edge is so tiny you can't afford the house minimumX2. You want to eat more cards in positive counts when others are competing for those same high cards. > > > And if you play two hands pretty fast, and you're concernd about time under the eye, then it's better to play two hands in negative counts, unless you have to pay 2Xmin on each hand. But this is a much closer decision. > > So your saying the best option for these conditions is to ALWAYS play 2 hands in both positive and negative counts. This way I am assured two spots for the high counts. > > BTW, can PowerSim be used to figure out the optimal bets for switching back and forth between 1 hand in neg and neutral counts and 2 hands in positive counts? > > MJ > > > |
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Subject : Some numbers -- or check my math, PLEASE! posted by ETFan on Nov-27-2006 05:16am |
| I'll check it myself again tomorrow. Here's how it looks to me today ... You say I should assume 50 rounds per hour. This is very slow. It couldn't be 50 rounds per hour with one player at the table, so I'm going to assume you mean 50 rounds per hour with 4 civilians (I prefer that term to ploppy) at the table. I'm further going to assume, though you didn't specify, that the dealer takes just as long as a civilian to play his hand, and another equal parcel of time to deal plus make the payoffs. So there are 6 actions that take place each round, and each takes an equal amount of time. It's easy to see that each separate action is 12 seconds long. 12 x 6 x 50 = 3600 seconds = 1 hour. You also say that you play about 150% faster than a civilian. That means it takes you 8 seconds to play a hand. You don't say anything about how much faster you can play two hands, so I'll just assume a second hand uses up another 8 seconds. A $10 to $200 spread at a 6D DAS 75% pen spread brings in a little over $0.20 a round overall, playing one spot. I'm assuming H17. A quick sim with PowerSim gives an EV of -$0.11 per hand in negative counts, and $1.03 per hand in positive counts. I'm rounding these numbers off, since this is strictly intended as a "ballpark" calculation. The negative counts occur 72.7% of the time, and the posiives, 27.3%. When you add it all up, it comes to $0.2012 per hand. Now you'll get in a little more than 50 rounds per hour, playing with 3 civilians, since you play a little faster. With the numbers above, it will take 68 seconds for a round, so we have 3600/68 = 52.94 rounds per hour. Total EV playing one spot = $0.20122 x 52.94 = $10.65 an hour. (I wouldn't travel too far to get to this game.) Now we'll see what happens to the EV when the counter plays two spots all the time with the same 3 civilians playing along. As I mentioned in my previous post, it's well established that the counter should bet approximately 73% as much on each of two hands in the positive counts to keep the same risk of ruin (because of covariance). Therefore, on each round in positive counts, the counter will not average $1.03, but $1.03 x 146% = $1.504. In negative counts he still bets the minimum, so he loses 2 x $0.11 = $0.22. The percentage of positive vs. negative rounds stays the same here, but the number of rounds per hour changes. Each round takes 5 x 12 secs + 2 x 8 secs = 76 seconds. Rounds per hour = 3600/76 = 47.368, and total EV per hour = ($1.5038 x 27.3% - $0.22 x 72.7%) x 47.368 = $11.87. Purists will object that I've changed the bet spread for the two hand case. Alright, lets assume the table minimum is actually $5, and the counter is able to juggle his $5 and $10 bets so they average out to $7.30 per hand in negative counts. EV per round in negative counts is then 146% x (-$.11) = -$0.1606. You plug that in place of the -$0.22 in the formula above, you come out with EV per hour = $13.92. A nice little 31% gain over playing one spot at all times, with no increase in risk of ruin. That was the easy part. ;) Now, for playing two spots in positive counts and one spot in negs. To work out the card eating effect, the guiding principle is that the percentage of cards with positive vs. negative counts is the same as that original 27.3% vs. 72.7%. That's all cards to everybody. However, the percentage of cards you actually receive in plus or minus territory will change because you're varying the number of hands. For this ballpark estimate, I'm going to assume that the average number of cards per hand in negative territory is the same as the average number of cards in positive territory, and also that the dealer's average hand has the same number cards as an average player hand. Neither of these assumptions are true, but they're close enough to get a picture of what's happening. So! In positive counts, the counter plays two hands and gets 2/6 of the +EV cards. In negative counts, he plays one hand and gets 1/5 of the -EV cards. Out of every 100 cards dealt, he gets 2/6 x 27.3 = 9.1 plus count cards, and 1/5 x 72.7 = 14.54 minus count cards. The other players and the dealer get the other 76.36 cards. 9.1 + 14.54 + 76.36 = 100. Say a hand consists of C cards. We can see the counter gets 9.1/C hands in positive territory, and 14.54/C hands in negative tundra. Since one round = 2 plus hands, and one round = 1 neg hand, the counter gets 4.55/C plus rounds versus 14.54/C negative rounds. Don't fret about what 0.55 of a card is. These numbers are all averages. I just refuse to say "an average of" X number of cards over and over and over. !Whew! Now, it doesn't really matter what C is (2.8?). What's important is the ratio 4.55/14.54. For this ratio to hold, the percentage of plus/minus count rounds must be: 23.83%/76.17%. So in terms of rounds (as opposed to cards or hands) the percentage of plus counts has gone down. This is a subtle point that aft gangs agley! So we know 23.83 percent of the time counter is playing two hands and the round takes 2 x 8 secs + 5 x 12 secs = 76 seconds. And 76.17% of the time the round takes 1 x 8 secs + 5 x 12 secs = 68 seconds. So your average round takes 68 x 76.17% + 76 x 23.83% = 69.91 seconds, and we're getting in 51.50 rounds per hour. 12.27 of those rounds are positive and 39.23 of them are negative. Again, our EV on each positive round is $1.03 x 146% = $1.5038. In negative counts, if he still bets the $10 minimum, he loses 11 cents. Overall EV per hour = 12.27 x $1.5038 - 39.23 x $0.11 = $14.14. Once again, purists will object. OK, to make the bet spread purely equal, counter must average a $14.6 bet on the negative rounds, and his EV on each such round is -0.1606. EV per hour = 12.27 x $1.5038 - 39.23 x $0.1606 = $12.15. So we have five EVs to compare: 1) Play one hand at all times: $10.65 2) Play two hands at 73% in positives and two hands at 100% ($10 x 2) in negatives: $11.87 3) Play two hands at 73% in positives and two hands at 73% (averaging $7.30 x 2) in negatives: $13.92 Same Risk of Ruin and bet spread as case 1). 4) Play two hands at 73% in positives and one hand at 100% ($10 x 1) in negatives: $14.14. Same RoR as cases 1) and 3) 5) Play two hands at 73% in positives and one hand at 146% in negatives: $12.15. Same bet spread as cases 1) and 3). Make of it what you will. Personally, I like case 3). It's very close to case 4), and case 4) technically has a larger bet spread than case 3), though we can argue about which looks better to the eye in the sky. Also, you mentioned people lurking behind, anxious to steal your extra spot. Also, if you can play the second spot a just weeeee bit faster than the first spot -- say 7 seconds instead of 8 -- number 3) will come out on top. Maybe you can do a one hand signal (a swooping wave) if you want to stand on both hands. I don't believe my simplifying assumptions affected the results substantially, though it's possible 3) and 4) might trade places in a well structured sim. My analysis here doesn't touch on T-Hoppers suggestion to play two hands only at certain negative counts. However I will say that when a TC truly goes in the tank, the best option is ZERO hands. And the more you Wong out on negs, the better the calculation looks for playing two hands on all remaining negs. Still, if you're in a crowded casino where sitting out til the shuffle is not allowed, there may come a point where it makes sense to drop to one hand. Also, if your civilian buddies get fast all of a sudden, I wouldn't rule out 4) -- or even 5) if you're a purist. Finally, interpretation of these numbers really depends on your point of view. If you truly feel that you LIKE to play blackjack, and if the game goes a little slower, why you might just play a little LONGER(!), well then, 4) and 5) gain some ground. Maybe you only care how much you win in an evening, and you believe in limiting exposure before the eye to a certain number of hands, rather than a certain number of minutes. That's a defensible attitude for a red/low green player, but it's inconceivable to a pro. ETF |
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Subject : Wow, thanks for running the numbers (nt) posted by EZrhino on Nov-28-2006 04:37am |
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Subject : One weak assumption posted by ETFan on Nov-28-2006 09:08pm |
| I was worried because I didn't include time for the dealer to shuffle. But on reflection, it's reasonable to include that as part of the time to play each hand. It's more reasonable to do it that way than to have it add time each round, for example. After all, a shuffle tends to occur after some given number of hands for a given penetration. There is one other slightly weak assumption: I'm giving the dealer the same 12 seconds to deal each round and make the payoffs regardless of the number of hands in play. We could just assume the dealer tends to joke around more with four spots in play instead of five. I'm not going to rework the calculation based on these little nits, unless there's an enormous groundswell. ;) The really accurate way to work this out is to do a simulation with hard numbers for each timed variable. I'm not aware of a simulator set up to do this. I'll have to try to set up PowerSim to do this. Hopefully sometime before Christmas. ETF |
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Subject : wait, what about increasing minimums? posted by EZrhino on Nov-29-2006 04:41am |
ETF, I just reread, and thought about the case where the player is playing the table minimum (let's say $10), and then, in order to play two spots, would need to play double at each spot (2x$20). This is the role that I'm personally familiar with. My guess is that, unless the player already has a min bet comfortably above the table minimum, then this would really, really, really hurt the effective spread and EV. |
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Subject : Of course it would posted by ETFan on Nov-29-2006 03:16pm |
| You just take the new bets and plug them into the equations I laid out. The pertinent part is: << Therefore, on each round in positive counts, the counter will not average $1.03, but $1.03 x 146% = $1.504. In negative counts he still bets the minimum, so he loses 2 x $0.11 = $0.22. The percentage of positive vs. negative rounds stays the same here, but the number of rounds per hour changes. Each round takes 5 x 12 secs + 2 x 8 secs = 76 seconds. Rounds per hour = 3600/76 = 47.368, and total EV per hour = ($1.5038 x 27.3% - $0.22 x 72.7%) x 47.368 = $11.87. >> If you have to bet $20 x 2 on negs, this becomes: << Therefore, on each round in positive counts, the counter will not average $1.03, but $1.03 x 146% = $1.504. In negative counts he bets twice the minimum, so he loses 2 x $0.22 = $0.44. The percentage of positive vs. negative rounds stays the same here, but the number of rounds per hour changes. Each round takes 5 x 12 secs + 2 x 8 secs = 76 seconds. Rounds per hour = 3600/76 = 47.368, and total EV per hour = ($1.5038 x 27.3% - $0.44 x 72.7%) x 47.368 = $4.29. >> Ie. less than half of what you can make just playing one hand. And in fact, it's even worse. By overbetting on negs, you've increased your risk of ruin, and you should actually bet less on high counts to compensate -- which drags down the EV even more. I was not putting up my post as "the final answer" to whether one should play two hands. As I tried to explain in previous posts, it very much depends on the specific details. There is no "one size fits all" answer. ETF |
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Subject : Playing multiple hands to eat cards posted by T.Hopper on Nov-29-2006 04:17pm |
The best time to do this is when you are heads up, and the count is between about +/-1 TC. Playing more hands increases the count variance per round, decreasing the time it takes to get to either a - count worth sitting out the rest of the shoe, or a + count worth making more than a minimum bet. Of course when you are within 2-3 rounds of the cut card the strategy might be different. |
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Subject : Thanks ETF! posted by MJ1 on Dec-02-2006 08:26am |
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