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#61
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Yes I realized this, but I wanted a general question. So I should remove the simple cases and just get to the point: numbers in R[0,1], you get N numbers total, optimal strategy?
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#62
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Yes, the more focused question is better. [img]/images/graemlins/grin.gif[/img]
For N=10... (10) will be a real number on [0,1] on (9), you would stand on any number > 0.5. Your EV for the stand is given by (9) - 0.5 So if (9) is .8, your EV on the stand is +0.3. On (9): Stand on all numbers greater than 0.5 Integrating on (9) = [0 1] we see that the total EV of your option on (9) is going to be +0.125. now for strategy on (8). Your immediate EV on the stand is again (8) - 0.5. You also have an option which is worth +0.125, that you give up if you stand. Therefore your adjusted EV on stand is (8) - 0.5 - 0.125 On (8), stand on all numbers greater than .625 Again, you calculate the integral from [0 1] and we conclude that the added value of our option on (8) is about .070 Using recursion, our strategy is determined to be: Stand (7) > 0.695 Stand (6) > 0.742 Stand (5) > 0.775 Stand (4) > 0.800 Stand (3) > 0.819 Stand (2) > 0.835 Stand (1) > 0.848 Obviously this method works for any N. |
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#63
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I am a "for fun" sports better. I have a 10 Leg Parlay Card (cost $10) with 5 winners in, 5 games to go. (pays $ 6,000 - I know parlays are sucker bets)
Games left: South Carolina -6, game on 12/29, Michigan +1, game on 01/01, Boise State +8, game on 01/01, LSU -9, game on 01/03, Ohio State -8, 01/08. At what point do I start to bet the other side to insure a "win". What amount? thanks, Kathy |
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#64
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oops originally addressed wrong! Try this please.
I am a "for fun" sports better. I have a 10 Leg Parlay Card (cost $10) with 5 winners in, 5 games to go. (pays $ 6,000 - I know parlays are sucker bets) Games left: South Carolina -6, game on 12/29, Michigan +1, game on 01/01, Boise State +8, game on 01/01, LSU -9, game on 01/03, Ohio State -8, 01/08. At what point do I start to bet the other side to insure a "win". What amount? thanks, Kathy |
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#65
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Variance is a b!tch, but how big of a downswing in limit holdem would convince you that variance is not the main factor? Rather, the problem is you suck. -300bb? -500bb? -4000bb?
i recently posed the following question: how big of a bankroll do you need to play 6max 100/200 online limit holdem. Answers i've seen range from 300bb to 4000bb! |
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#66
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How many consecutive times does someone have to win the lottery to make it more likely that they are a time traveler than they're very lucky?
Assume the probability they are cheating or the lottery is rigged in some way is zero. |
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#67
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[ QUOTE ]
None of the questions are turning me on. I'm not sure why. [/ QUOTE ] Perhaps all of these questions are more than 16 years old. |
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#68
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[ QUOTE ]
oops originally addressed wrong! Try this please. I am a "for fun" sports better. I have a 10 Leg Parlay Card (cost $10) with 5 winners in, 5 games to go. (pays $ 6,000 - I know parlays are sucker bets) Games left: South Carolina -6, game on 12/29, Michigan +1, game on 01/01, Boise State +8, game on 01/01, LSU -9, game on 01/03, Ohio State -8, 01/08. At what point do I start to bet the other side to insure a "win". What amount? thanks, Kathy [/ QUOTE ] Hedging for "for fun" bettors. So you have this bet. Your bet is equivalent to "g6 AND g7 AND g8 AND g9 AND g10." Now suppose all these games are sequential -- the Michigan and Boise State games might overlap, but whatever. Suppose all your sides are coinflips to come in. Then you have a (1/2)^5 chance of getting $6000. Otherwise you get $0. (Doesn't matter what you paid for it, plus it'll make you sick.) So your EV right now is $187.50. Consider the South Carolina game. If you WIN this game, your EV goes to $375. If you lose, it goes to zero. The difference between these two numbers is called the *delta* that this game has on your bet. Delta is like your risk on this game. You can make other bets to increase your delta on this game. For example, you could bet $110 to win $100 on South Carolina -6. That would increase your delta by $210. But what you're talking about is "hedging," which is the process of reducing your delta. Say you want to reduce your delta from $375 to zero; that is, you want to lock up the profit you've already made and take no more risk (except for line movement risk in the other games, which you can't hedge easily). Then you need to make a bet such that the difference between South Carolina losing the bet and winning the bet is $375. So supposing you can get the same spread at -110, you would bet $196.43 to win $178.57. Now whatever happens, you have zeroed out your risk. If SC wins, then your parlay goes up in value to $375, but you lose 196.43, for a total of 178.57. If SC loses, you win your bet for 178.57, but your parlay goes to zero. The downside of this is that you have to pay juice on each game to hedge - here you lose 187.50 - 178.57 = 8.93 in juice. These amounts will get larger if your parlay bet wins. You don't have to completely hedge out your risk, of course. You could make a smaller bet, thus hoping that SC will win, while having less riding on the outcome. So you just have to decide how much you want to have riding on this game. Then reduce your delta by hedging such that your delta is equal to the amount of risk you want. Jerrod |
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#69
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When all things are considered, which of the following would be the easiest way make money gambling long-term (lets say $50,000/yr):
1. Playing poker; 2. Counting cards at blackjack; or 3. Sports betting. As a person relatively new to gambling I have been giving this some thought. Here are some of my thoughts which you guys can expound on and perhaps David can give his thoughts. With Poker the competition is the nine or so players you are against at this moment. You get to select your competition, and can leave at anytime. If you are a winner you will get no heat from the casino and can play as often as you like. The rake or time charge is competitive with sports betting but substantially higher than playing basic blackjack. Learning to play winning poker at decent limits is a very difficult undertaking. Learning to count cards and keep up with the dealer must be significantly easier than learning to play winning poker. But if you do this you will eventually get heat from casino’s and be ask to leave. So you must be able to count under the watchful eye of a casino, which is a very difficult undertaking. With Sports betting your direct competition is the professional odds-makers and their limitless resources. Indirectly, you are also competing with the general public to whom they offer their lines. You must overcome a vig of 4.5%, quite steep by poker or blackjack standards. Beating the sports books is a very difficult undertaking. So my question is: how would you rank these gambling pursuits for making money long-term, from easiest to most difficult. |
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#70
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[ QUOTE ]
[ QUOTE ] None of the questions are turning me on. I'm not sure why. [/ QUOTE ] Perhaps all of these questions are more than 16 years old. [/ QUOTE ] A++ |
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