dooglus
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June 05, 2014, 05:41:23 PM |
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What does generally a pretty bad idea mean ? As far as I can understand , the house edge should be equal at all levels and that would just be a lot less fun (as you have no chance of winning something substantial) , with the same amount of risk.
Is my understanding wrong ?
If you want to win 1 BTC, you could: a) risk 0.1 BTC at 9% for an 11x payout, or you could b) risk 10 BTC at 90% for a 1.1x payout. In each case you expect to lose 1% of the amount you risk, so b) costs about 100 times more than a) in terms of the amount you expect to lose, while only having a 10 times better chance of success. That makes 90% seem like a bad deal compared to 9%, even though they both have a 1% edge. Does that make sense?
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Just-Dice | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | Play or Invest | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | 1% House Edge |
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jjc326
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June 05, 2014, 05:49:31 PM |
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I do understand OP and it's worth a shot. You're thinking that even though people might be "winning" with an edge of like 1% or something, they'll keep playing until they lose. It is risly but if you could make it owrk that'd be great. You would have to stop bots because they wouldn't have "emotion" so that was a great point too.
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dooglus
Legendary
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June 05, 2014, 05:55:27 PM |
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Someone have a simulator to help me fully realize I'm wrong? I dunno how to create the formula for doing this quickly. 1,000 users have a $1,000 bankroll and must make 1,000 $25 bets with a 51% chance of 2x return, 49% chance of 0x return. The casino has an unlimited bankroll. The casino only loses if someone cashes out their winnings, which in this simulator, requires someone to make 1,000 $25 bets without their bankroll ever hitting $0. They get to keep whatever's left at the end of that.
I'll run that simulation and let you know how it goes.
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Just-Dice | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | Play or Invest | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | 1% House Edge |
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dooglus
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June 05, 2014, 06:11:30 PM |
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Someone have a simulator to help me fully realize I'm wrong? I dunno how to create the formula for doing this quickly. 1,000 users have a $1,000 bankroll and must make 1,000 $25 bets with a 51% chance of 2x return, 49% chance of 0x return. The casino has an unlimited bankroll. The casino only loses if someone cashes out their winnings, which in this simulator, requires someone to make 1,000 $25 bets without their bankroll ever hitting $0. They get to keep whatever's left at the end of that.
I'll run that simulation and let you know how it goes. OK, maybe I misunderstood your specification, but here are the results: I coded a simulation, ran it 6 times. The first time I ran it the first player busted and the 2nd player made 1000 bets without busting. The other 5 times the first player made 1000 bets without busting: player 1 won bet 1. balance = 1025 player 1 won bet 2. balance = 1050 player 1 lost bet 3. balance = 1025 player 1 lost bet 4. balance = 1000 player 1 won bet 5. balance = 1025 player 1 lost bet 6. balance = 1000 player 1 lost bet 7. balance = 975 player 1 won bet 8. balance = 1000 player 1 won bet 9. balance = 1025 player 1 lost bet 10. balance = 1000 [...] player 1 won bet 991. balance = 2475 player 1 lost bet 992. balance = 2450 player 1 lost bet 993. balance = 2425 player 1 lost bet 994. balance = 2400 player 1 lost bet 995. balance = 2375 player 1 won bet 996. balance = 2400 player 1 lost bet 997. balance = 2375 player 1 won bet 998. balance = 2400 player 1 won bet 999. balance = 2425 player 1 won bet 1000. balance = 2450 player 1 made 1000 bets without busting Here's the simulation code: #!/usr/bin/env python
import random, sys
players = 1000 bets_per_player = 1000 starting_balance = 1000 stake = 25
def roll(): return random.random() < 0.51
player = 1 while player <= players: balance = starting_balance bets = 0 while True: bets += 1 if roll(): balance += stake print "player %4d won bet %4d. balance = %4d" % (player, bets, balance) else: balance -= stake print "player %4d lost bet %4d. balance = %4d" % (player, bets, balance) if balance < stake: print "player %d bust after %d bets" % (player, bets) break if bets == bets_per_player: print "player %d made %d bets without busting" % (player, bets) sys.exit(0)
player += 1
print "all the players busted"
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Just-Dice | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | Play or Invest | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | 1% House Edge |
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a1choi
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June 05, 2014, 06:12:17 PM |
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What does generally a pretty bad idea mean ? As far as I can understand , the house edge should be equal at all levels and that would just be a lot less fun (as you have no chance of winning something substantial) , with the same amount of risk.
Is my understanding wrong ?
If you want to win 1 BTC, you could: a) risk 0.1 BTC at 9% for an 11x payout, or you could b) risk 10 BTC at 90% for a 1.1x payout. In each case you expect to lose 1% of the amount you risk, so b) costs about 100 times more than a) in terms of the amount you expect to lose, while only having a 10 times better chance of success. That makes 90% seem like a bad deal compared to 9%, even though they both have a 1% edge. Does that make sense? i guess my risk preferences are more risk averse than yours. i'd gladly risk the 100x for the 10x more chance of winning. 90% just seems a much better shot than 9%. but personally i'd be limited to only acting on the 0.1BTC bet because i don't have the bankroll for 10BTC bets.
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dooglus
Legendary
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June 05, 2014, 06:17:56 PM |
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I coded a simulation, ran it 6 times. The first time I ran it the first player busted and the 2nd player made 1000 bets without busting. The other 5 times the first player made 1000 bets without busting:
OK, so let's give the casino a better chance. Each player starts with just $25, and has to flat-bet $25 over and over until they either bust or make 1000 bets. Now the casino is bound to win, right? Wrong: player 1 lost bet 1. balance = 0 player 1 bust after 1 bets player 2 lost bet 1. balance = 0 player 2 bust after 1 bets player 3 lost bet 1. balance = 0 player 3 bust after 1 bets player 4 lost bet 1. balance = 0 player 4 bust after 1 bets player 5 lost bet 1. balance = 0 player 5 bust after 1 bets player 6 won bet 1. balance = 50 player 6 lost bet 2. balance = 25 player 6 lost bet 3. balance = 0 player 6 bust after 3 bets player 7 won bet 1. balance = 50 player 7 lost bet 2. balance = 25 player 7 won bet 3. balance = 50 player 7 lost bet 4. balance = 25 player 7 won bet 5. balance = 50 player 7 won bet 6. balance = 75 player 7 lost bet 7. balance = 50 player 7 lost bet 8. balance = 25 player 7 lost bet 9. balance = 0 player 7 bust after 9 bets player 8 lost bet 1. balance = 0 player 8 bust after 1 bets player 9 won bet 1. balance = 50 player 9 won bet 2. balance = 75 player 9 won bet 3. balance = 100 player 9 won bet 4. balance = 125 player 9 lost bet 5. balance = 100 player 9 won bet 6. balance = 125 player 9 lost bet 7. balance = 100 player 9 won bet 8. balance = 125 player 9 won bet 9. balance = 150 player 9 won bet 10. balance = 175 player 9 lost bet 11. balance = 150 player 9 lost bet 12. balance = 125 player 9 lost bet 13. balance = 100 player 9 lost bet 14. balance = 75 player 9 lost bet 15. balance = 50 player 9 won bet 16. balance = 75 player 9 lost bet 17. balance = 50 player 9 lost bet 18. balance = 25 player 9 won bet 19. balance = 50 player 9 lost bet 20. balance = 25 player 9 lost bet 21. balance = 0 player 9 bust after 21 bets player 10 lost bet 1. balance = 0 player 10 bust after 1 bets player 11 won bet 1. balance = 50 player 11 lost bet 2. balance = 25 player 11 lost bet 3. balance = 0 player 11 bust after 3 bets player 12 won bet 1. balance = 50 player 12 won bet 2. balance = 75 player 12 lost bet 3. balance = 50 player 12 lost bet 4. balance = 25 player 12 won bet 5. balance = 50 player 12 lost bet 6. balance = 25 player 12 lost bet 7. balance = 0 player 12 bust after 7 bets player 13 lost bet 1. balance = 0 player 13 bust after 1 bets player 14 won bet 1. balance = 50 player 14 lost bet 2. balance = 25 player 14 won bet 3. balance = 50 player 14 won bet 4. balance = 75 player 14 won bet 5. balance = 100 player 14 won bet 6. balance = 125 player 14 won bet 7. balance = 150 player 14 won bet 8. balance = 175 player 14 lost bet 9. balance = 150 player 14 won bet 10. balance = 175 [...] player 14 won bet 224. balance = 125 player 14 lost bet 225. balance = 100 player 14 lost bet 226. balance = 75 player 14 won bet 227. balance = 100 player 14 won bet 228. balance = 125 player 14 lost bet 229. balance = 100 player 14 lost bet 230. balance = 75 player 14 lost bet 231. balance = 50 player 14 lost bet 232. balance = 25 player 14 lost bet 233. balance = 0 player 14 bust after 233 bets player 15 won bet 1. balance = 50 player 15 won bet 2. balance = 75 player 15 won bet 3. balance = 100 player 15 lost bet 4. balance = 75 player 15 won bet 5. balance = 100 player 15 won bet 6. balance = 125 player 15 lost bet 7. balance = 100 player 15 won bet 8. balance = 125 player 15 won bet 9. balance = 150 player 15 lost bet 10. balance = 125 [...] player 15 lost bet 991. balance = 850 player 15 lost bet 992. balance = 825 player 15 lost bet 993. balance = 800 player 15 won bet 994. balance = 825 player 15 won bet 995. balance = 850 player 15 won bet 996. balance = 875 player 15 won bet 997. balance = 900 player 15 lost bet 998. balance = 875 player 15 lost bet 999. balance = 850 player 15 lost bet 1000. balance = 825 player 15 made 1000 bets without busting
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Just-Dice | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | Play or Invest | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | 1% House Edge |
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dooglus
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June 05, 2014, 06:21:40 PM |
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OK, so let's give the casino a better chance. Each player starts with just $25, and has to flat-bet $25 over and over until they either bust or make 1000 bets.
OK, still too easy for the player. What if we don't let them cash out until they've made a million bets, and still only let them start with enough to make a single bet? Still no good. It takes a few more players before one goes to the moon, but it still happens, and when it does he breaks the bank: player 1 lost bet 1. balance = 0 player 1 bust after 1 bets player 2 won bet 1. balance = 50 player 2 won bet 2. balance = 75 player 2 won bet 3. balance = 100 [...] player 2 won bet 18. balance = 225 player 2 won bet 19. balance = 250 player 2 won bet 20. balance = 275 player 2 lost bet 21. balance = 250 player 2 lost bet 22. balance = 225 [...] player 2 lost bet 51. balance = 50 player 2 lost bet 52. balance = 25 player 2 lost bet 53. balance = 0 player 2 bust after 53 bets player 3 lost bet 1. balance = 0 player 3 bust after 1 bets player 4 won bet 1. balance = 50 player 4 lost bet 2. balance = 25 player 4 lost bet 3. balance = 0 player 4 bust after 3 bets player 5 won bet 1. balance = 50 player 5 lost bet 2. balance = 25 player 5 lost bet 3. balance = 0 player 5 bust after 3 bets player 6 lost bet 1. balance = 0 player 6 bust after 1 bets player 7 lost bet 1. balance = 0 player 7 bust after 1 bets player 8 won bet 1. balance = 50 player 8 lost bet 2. balance = 25 player 8 won bet 3. balance = 50 player 8 lost bet 4. balance = 25 player 8 won bet 5. balance = 50 player 8 lost bet 6. balance = 25 player 8 won bet 7. balance = 50 player 8 lost bet 8. balance = 25 player 8 lost bet 9. balance = 0 player 8 bust after 9 bets player 9 won bet 1. balance = 50 player 9 lost bet 2. balance = 25 player 9 won bet 3. balance = 50 player 9 lost bet 4. balance = 25 player 9 lost bet 5. balance = 0 player 9 bust after 5 bets player 10 lost bet 1. balance = 0 player 10 bust after 1 bets player 11 lost bet 1. balance = 0 player 11 bust after 1 bets player 12 won bet 1. balance = 50 player 12 won bet 2. balance = 75 player 12 won bet 3. balance = 100 player 12 won bet 4. balance = 125 player 12 lost bet 5. balance = 100 player 12 won bet 6. balance = 125 player 12 lost bet 7. balance = 100 player 12 won bet 8. balance = 125 player 12 won bet 9. balance = 150 player 12 won bet 10. balance = 175 player 12 won bet 11. balance = 200 player 12 won bet 12. balance = 225 player 12 won bet 13. balance = 250 player 12 lost bet 14. balance = 225 player 12 lost bet 15. balance = 200 player 12 lost bet 16. balance = 175 player 12 lost bet 17. balance = 150 player 12 lost bet 18. balance = 125 player 12 won bet 19. balance = 150 player 12 won bet 20. balance = 175 player 12 lost bet 21. balance = 150 player 12 lost bet 22. balance = 125 player 12 lost bet 23. balance = 100 player 12 won bet 24. balance = 125 player 12 won bet 25. balance = 150 player 12 lost bet 26. balance = 125 player 12 lost bet 27. balance = 100 player 12 lost bet 28. balance = 75 player 12 lost bet 29. balance = 50 player 12 lost bet 30. balance = 25 player 12 won bet 31. balance = 50 player 12 lost bet 32. balance = 25 player 12 won bet 33. balance = 50 player 12 lost bet 34. balance = 25 player 12 lost bet 35. balance = 0 player 12 bust after 35 bets player 13 lost bet 1. balance = 0 player 13 bust after 1 bets player 14 lost bet 1. balance = 0 player 14 bust after 1 bets player 15 lost bet 1. balance = 0 player 15 bust after 1 bets player 16 won bet 1. balance = 50 player 16 won bet 2. balance = 75 player 16 lost bet 3. balance = 50 player 16 lost bet 4. balance = 25 player 16 lost bet 5. balance = 0 player 16 bust after 5 bets player 17 lost bet 1. balance = 0 player 17 bust after 1 bets player 18 lost bet 1. balance = 0 player 18 bust after 1 bets player 19 lost bet 1. balance = 0 player 19 bust after 1 bets player 20 won bet 1. balance = 50 player 20 lost bet 2. balance = 25 player 20 won bet 3. balance = 50 player 20 lost bet 4. balance = 25 player 20 lost bet 5. balance = 0 player 20 bust after 5 bets player 21 lost bet 1. balance = 0 player 21 bust after 1 bets player 22 won bet 1. balance = 50 player 22 won bet 2. balance = 75 player 22 lost bet 3. balance = 50 player 22 won bet 4. balance = 75 player 22 lost bet 5. balance = 50 player 22 lost bet 6. balance = 25 player 22 won bet 7. balance = 50 player 22 won bet 8. balance = 75 player 22 lost bet 9. balance = 50 player 22 lost bet 10. balance = 25 player 22 won bet 11. balance = 50 player 22 lost bet 12. balance = 25 player 22 won bet 13. balance = 50 player 22 lost bet 14. balance = 25 player 22 lost bet 15. balance = 0 player 22 bust after 15 bets player 23 lost bet 1. balance = 0 player 23 bust after 1 bets player 24 won bet 1. balance = 50 player 24 lost bet 2. balance = 25 player 24 won bet 3. balance = 50 player 24 won bet 4. balance = 75 player 24 won bet 5. balance = 100 player 24 won bet 6. balance = 125 player 24 won bet 7. balance = 150 player 24 lost bet 8. balance = 125 player 24 lost bet 9. balance = 100 player 24 lost bet 10. balance = 75 player 24 lost bet 11. balance = 50 player 24 lost bet 12. balance = 25 player 24 lost bet 13. balance = 0 player 24 bust after 13 bets player 25 won bet 1. balance = 50 player 25 lost bet 2. balance = 25 player 25 lost bet 3. balance = 0 player 25 bust after 3 bets player 26 lost bet 1. balance = 0 player 26 bust after 1 bets player 27 lost bet 1. balance = 0 player 27 bust after 1 bets player 28 lost bet 1. balance = 0 player 28 bust after 1 bets player 29 lost bet 1. balance = 0 player 29 bust after 1 bets player 30 lost bet 1. balance = 0 player 30 bust after 1 bets player 31 won bet 1. balance = 50 player 31 won bet 2. balance = 75 player 31 won bet 3. balance = 100 player 31 won bet 4. balance = 125 player 31 lost bet 5. balance = 100 player 31 won bet 6. balance = 125 player 31 lost bet 7. balance = 100 player 31 lost bet 8. balance = 75 player 31 lost bet 9. balance = 50 player 31 lost bet 10. balance = 25 [...] player 31 lost bet 999991. balance = 502750 player 31 lost bet 999992. balance = 502725 player 31 lost bet 999993. balance = 502700 player 31 lost bet 999994. balance = 502675 player 31 lost bet 999995. balance = 502650 player 31 won bet 999996. balance = 502675 player 31 won bet 999997. balance = 502700 player 31 lost bet 999998. balance = 502675 player 31 won bet 999999. balance = 502700 player 31 lost bet 1000000. balance = 502675 player 31 made 1000000 bets without busting
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Just-Dice | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | Play or Invest | ██ ██████████ ██████████████████ ██████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████████████ ██████████████████████ ██████████████ ██████ | 1% House Edge |
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Kluge (OP)
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June 06, 2014, 02:17:00 AM |
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Yay! Thank you, dooglus. I'll run it 50 times, average what the house earns, then do that set of fifty 9 more times. Tonight's my last night of free time for a while. Time well spent, IMO. ![Cheesy](https://bitcointalk.org/Smileys/default/cheesy.gif) ETA: Actually, I'll do EV neutral, since there's still a fair chance I'll get some doubt benefit if variance is with me. ![Grin](https://bitcointalk.org/Smileys/default/grin.gif)
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Kluge (OP)
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June 06, 2014, 04:40:44 AM |
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Game rules: 1000 players bet 1000 times in a game where they have a 50% chance of winning each bet (actually I think they have a 49.999999999% chance or whatever - Idunno exactly how random works, tbh). They each have a starting balance of 1 unit and must bet 1 unit. (changed from original so there's less 0s to write) Set rules: One game must be played 50 times. Results of 10 sets: https://docs.google.com/spreadsheets/d/1KR_Wd9Z7K1YfWCsOgiq0KyRF7lD4dYaBnbW99BkSbSY/pubhtmlConclusion: House ended up very slightly (each game and set, the house seemed likely to lose, but rarely won huge) - nothing abnormal. Theory's definitely bunk, and I've now paid my debt to rationality by manually typing all those numbers in. Script run (only "real" change is to print "casino profit" after each game so I don't have to think): #!/usr/bin/env python
import random, sys
players = 1000 bets_per_player = 1000 starting_balance = 1 stake = 1
def roll(): return random.random() < 0.50
player = 1 while player <= players: balance = starting_balance bets = 0 while True: bets += 1 if roll(): balance += stake print "player %4d won bet %4d. balance = %4d" % (player, bets, balance) else: balance -= stake print "player %4d lost bet %4d. balance = %4d" % (player, bets, balance) if balance < stake: print "player %d bust after %d bets" % (player, bets) break if bets == bets_per_player: print "player %d made %d bets without busting" % (player, bets) print "casino profit is %d" % (player-balance) sys.exit(0)
player += 1
print "all the players busted"
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jambola2
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June 06, 2014, 06:17:02 AM |
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What does generally a pretty bad idea mean ? As far as I can understand , the house edge should be equal at all levels and that would just be a lot less fun (as you have no chance of winning something substantial) , with the same amount of risk.
Is my understanding wrong ?
If you want to win 1 BTC, you could: a) risk 0.1 BTC at 9% for an 11x payout, or you could b) risk 10 BTC at 90% for a 1.1x payout. In each case you expect to lose 1% of the amount you risk, so b) costs about 100 times more than a) in terms of the amount you expect to lose, while only having a 10 times better chance of success. That makes 90% seem like a bad deal compared to 9%, even though they both have a 1% edge. Does that make sense? Well , I first expected it to still work , because you could just bet at 90% with 0.1 BTC over and over. 0.1 * (1.1)^25 = 1.083 BTC So , taking the same percentage of 90% chance of winning, (90/100)^ 25 = 7.17% of winning What you said makes sense now that I have calculated it , but why does this happen ? You have a lesser chance of winning and also a lesser amount of winnings , does this mean a bet with lesser chances of winning is always better ?
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No longer active on bitcointalk, however, you can still reach me via PMs if needed.
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Light
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June 06, 2014, 06:25:37 AM |
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Well , I first expected it to still work , because you could just bet at 90% with 0.1 BTC over and over.
0.1 * (1.1)^25 = 1.083 BTC
So , taking the same percentage of 90% chance of winning,
(90/100)^ 25 = 7.17% of winning
What you said makes sense now that I have calculated it , but why does this happen ?
You have a lesser chance of winning and also a lesser amount of winnings , does this mean a bet with lesser chances of winning is always better ?
It's because when you accept those odds and gamble you effectively reduce your bet by 1% (this is true over an n case scenario where n approaches infinity). Hence, mathematically it is better to bet in smaller amounts as you 'lose' less from the edge. You don't notice this as in comparison to the number of bets you make the losses you get from the 1% are tiny. Maybe after something like 50 million bets that 1% would be clearer but over the short term variance wins out.
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jambola2
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June 06, 2014, 08:33:06 AM |
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Well , I first expected it to still work , because you could just bet at 90% with 0.1 BTC over and over.
0.1 * (1.1)^25 = 1.083 BTC
So , taking the same percentage of 90% chance of winning,
(90/100)^ 25 = 7.17% of winning
What you said makes sense now that I have calculated it , but why does this happen ?
You have a lesser chance of winning and also a lesser amount of winnings , does this mean a bet with lesser chances of winning is always better ?
It's because when you accept those odds and gamble you effectively reduce your bet by 1% (this is true over an n case scenario where n approaches infinity). Hence, mathematically it is better to bet in smaller amounts as you 'lose' less from the edge. You don't notice this as in comparison to the number of bets you make the losses you get from the 1% are tiny. Maybe after something like 50 million bets that 1% would be clearer but over the short term variance wins out. So , if you are betting in an attempt to win something , it is best to bet all you can afford to bet at once ? Does this imply that the martingale strategy is worse than a normal strategy ?
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No longer active on bitcointalk, however, you can still reach me via PMs if needed.
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Salmon1989
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June 06, 2014, 08:56:38 AM |
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Well , I first expected it to still work , because you could just bet at 90% with 0.1 BTC over and over.
0.1 * (1.1)^25 = 1.083 BTC
So , taking the same percentage of 90% chance of winning,
(90/100)^ 25 = 7.17% of winning
What you said makes sense now that I have calculated it , but why does this happen ?
You have a lesser chance of winning and also a lesser amount of winnings , does this mean a bet with lesser chances of winning is always better ?
It's because when you accept those odds and gamble you effectively reduce your bet by 1% (this is true over an n case scenario where n approaches infinity). Hence, mathematically it is better to bet in smaller amounts as you 'lose' less from the edge. You don't notice this as in comparison to the number of bets you make the losses you get from the 1% are tiny. Maybe after something like 50 million bets that 1% would be clearer but over the short term variance wins out. So , if you are betting in an attempt to win something , it is best to bet all you can afford to bet at once ? Does this imply that the martingale strategy is worse than a normal strategy ? Yes and yes. With "1% house edge", statistically speaking, you should expect to lose 1% of your total wagered amount.
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dooglus
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June 06, 2014, 09:05:59 AM |
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So , if you are betting in an attempt to win something , it is best to bet all you can afford to bet at once ?
Does this imply that the martingale strategy is worse than a normal strategy ?
Yes and yes. I hesitate to mention this, but if you carefully pick your martingale strategy it is more effective than a single large bet at achieving your goal (whatever that goal is).
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Salmon1989
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June 06, 2014, 09:09:43 AM |
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So , if you are betting in an attempt to win something , it is best to bet all you can afford to bet at once ?
Does this imply that the martingale strategy is worse than a normal strategy ?
Yes and yes. I hesitate to mention this, but if you carefully pick your martingale strategy it is more effective than a single large bet at achieving your goal (whatever that goal is). Say, my target is to double my initial deposit. Is it really possible to use martingale (or whatever strategy) to achieve the goal with higher than 49.5% success rate (one single bet)?
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dooglus
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June 07, 2014, 05:32:15 AM Last edit: June 07, 2014, 05:49:35 AM by dooglus |
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Say, my target is to double my initial deposit. Is it really possible to use martingale (or whatever strategy) to achieve the goal with higher than 49.5% success rate (one single bet)?
Yes. And you're the first person who responded in such an open manner. Everyone else just tells me I'm wrong. ![Smiley](https://bitcointalk.org/Smileys/default/smiley.gif) The trick is to split up your bet (the amount you were going to risk in a single bet) into a series of amounts which sum to a the same, and which form a sequence such that you can bet the smallest amount, and if it wins, you make the same as if you bet the whole amount at 49.5% (so you'll be betting with a smaller chance, and higher payout multiplier). And if it loses, you want betting the 2nd amount to cover the first loss and make the same net profit. Etc. If you can find such a sequence (and you always can, though it can involve some hairy math depending on the length of the sequence you're looking for) then the amount you expect to risk is less than your whole amount (since there's a non-zero chance that you will win before the last bet, and stop at that point), and so the amount you expect to lose, being 1% of the amount you risk, is less than when you make the single bet. Here's a very simple example: you have 1 BTC and want to double it. * you could bet it all at 49.5%, and succeed in doubling up with probability 0.495 * or you could bet 0.41421356 BTC at 28.99642866% with payout multiplier 3.41421356x, and if you lose, bet the rest at the same chance. If you win either bet, you double up, else you lose. Your chance of doubling up is 0.4958492857 - a little higher than the 0.495 you have with the single bet. Cool, huh? That's breaking the single bet up into a sequence of length 2. If you break it up into more, smaller bets, then the probability of success increases further. The more steps, the closer to 0.5 your probability of success gets. You'll be limited by real-life barriers, like the invisibility indivisibility of the satoshi, and the limit of 4 decimal places on the chance at JD. But in theory you can get arbitrarily close to 0.5. I think. ![Smiley](https://bitcointalk.org/Smileys/default/smiley.gif)
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Rigon
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June 07, 2014, 05:35:41 AM |
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Only EV plus games are PVP games where players can win and not the house.
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a1choi
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June 07, 2014, 05:45:10 AM |
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You'll be limited by real-life barriers, like the invisibility of the satoshi, and the limit of 4 decimal places on the chance at JD. But in theory you can get arbitrarily close to 0.5. I think. ![Smiley](https://bitcointalk.org/Smileys/default/smiley.gif) cool! i didn't know there was a 4 dec limit on chance. good to know. Also, can you explain more about the invisibility of the satoshi? never heard that term until now.
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dooglus
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June 07, 2014, 05:46:19 AM |
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Only EV plus games are PVP games where players can win and not the house.
Except https://bitcointalk.org/index.php?topic=639787.msg7141055#msg7141055
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dooglus
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June 07, 2014, 05:48:35 AM |
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You'll be limited by real-life barriers, like the invisibility of the satoshi, and the limit of 4 decimal places on the chance at JD. But in theory you can get arbitrarily close to 0.5. I think. ![Smiley](https://bitcointalk.org/Smileys/default/smiley.gif) Also, can you explain more about the invisibility of the satoshi? never heard that term until now. Oh, I meant in divisibility. As is there's nothing between 0 BTC and 1 satoshi. Sorry - it's been a long day... I expect at some point you're going to be wanting bet 0.01 satoshi at 0.00001% if you keep breaking down the martingale into ever more steps. Neither of which (tiny stake nor tiny chance) is possible.
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