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Comments for Derk's blog http://derk.badbeatscrew.com Tue, 30 Oct 2012 18:53:12 -0700 http://wordpress.org/?v=2.8.4 hourly 1 Comment on Breaking down the A9 call of Russell Thomas by Gideon http://derk.badbeatscrew.com/poker/breaking-down-the-a9-call-of-russell-thomas/comment-page-1/#comment-877 Gideon Tue, 30 Oct 2012 18:53:12 +0000 http://derk.badbeatscrew.com/?p=451#comment-877 Thanks for posting this... great read! This situation seems so unique within the ME context that I would feel like Balsiger's range is much harder to determine than in a "normal" tournament against an average competent reg. I could picture him shoving fairly wide (basically about a game-theory optimal range... or even wider if he thinks getting looked up is much less likely because of the stakes) or being really tight and only shoving a real value range (something like AJ+/66+) simply because the stakes are so high and pay jumps so significant... I guess knowing he got coaching from Timex, you have to lean towards him not being oddly tight there... and I guess you have to just range him as well as you can and go for it... really interesting spot though (for what would normally be a fairly standard spot)! Thanks for posting this… great read! This situation seems so unique within the ME context that I would feel like Balsiger’s range is much harder to determine than in a “normal” tournament against an average competent reg. I could picture him shoving fairly wide (basically about a game-theory optimal range… or even wider if he thinks getting looked up is much less likely because of the stakes) or being really tight and only shoving a real value range (something like AJ+/66+) simply because the stakes are so high and pay jumps so significant… I guess knowing he got coaching from Timex, you have to lean towards him not being oddly tight there… and I guess you have to just range him as well as you can and go for it… really interesting spot though (for what would normally be a fairly standard spot)!

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Comment on Gambling theory problem/puzzle solution by Matt http://derk.badbeatscrew.com/gambling/gambling-theory-problempuzzle-solution/comment-page-1/#comment-752 Matt Thu, 16 Jun 2011 20:38:45 +0000 http://derk.badbeatscrew.com/?p=393#comment-752 This was a neat thought experiment, and to play around with it I threw together a quick php script for simulation. http://codepad.org/HLQHF2S4 Your EV with $1 bets is of course -$12.50 . It looks like the EV when you bet $100 x25 is around -10.5. But for EV ignoring bonuses (contextual EV I'll call it) I'm just having it calculate the total amount wagered for 10k runthroughs and applying the .5% edge over that. When you calculate EV based on the amount actually won including bonuses (actual EV) it's a pretty standard $86-87 for $1 bets and it fluctuates quite a bit for $100. I've only eyeballed those stats but it seems to stay in the 90s although I've seen it plummet down to the 50s on some runs. That got me thinking about the bonus:buyin ratio, along with playthrough amount, and how it influences things if at all. Initially with the original problem I thought the higher contextual EV you get for risking bustso would be counter-balanced by the hit taken to your actual EV when you consider the substantial amount of times where you bust and lose advantage of the 25% bonus. That is to say, with the ~33% risk of ruin you get for betting $100, wouldn't the bonus money lost on those runs alter the overall outlook of the deposit bonus? So I experimented a little and made the buyin $100 and the deposit bonus $400 with the same playthrough req: would we see a different outcome in the simulation between $1 bets and $100? What about a $1 buyin and 499 bonus? Turns out, which makes sense now but didn't to me at first, that it doesn't seem to have much of an impact at all. Contextual EV is identical across the board (-12.5 vs. -10.5) of course, and overall EV ("I buyin for $1, gamble with 500, and come away with X") shows the same trends where the $1 bet has a very consistant range and the $100 bet is a bit wider. Unfortunately I don't have more time to spend on this, but my next step with simulating would be to generate a curve on total $ won, factoring in bonuses, because right now I'm just eyeballing results on 10k run throughs and its' still pretty swingy. I'd be interested to see how the bonus ratio influences things because it seems like it should. My thought now is that the smaller the bonus, the more you want to minimize your risk of ruin and the larger the bonus the more you want to gamble with it. Of course it could affect nothing and you're always better off taking the bigger gamble whether the bonus is $0 or 100x your buyin. This was a neat thought experiment, and to play around with it I threw together a quick php script for simulation.

http://codepad.org/HLQHF2S4

Your EV with $1 bets is of course -$12.50 . It looks like the EV when you bet $100 x25 is around -10.5. But for EV ignoring bonuses (contextual EV I’ll call it) I’m just having it calculate the total amount wagered for 10k runthroughs and applying the .5% edge over that. When you calculate EV based on the amount actually won including bonuses (actual EV) it’s a pretty standard $86-87 for $1 bets and it fluctuates quite a bit for $100. I’ve only eyeballed those stats but it seems to stay in the 90s although I’ve seen it plummet down to the 50s on some runs.

That got me thinking about the bonus:buyin ratio, along with playthrough amount, and how it influences things if at all. Initially with the original problem I thought the higher contextual EV you get for risking bustso would be counter-balanced by the hit taken to your actual EV when you consider the substantial amount of times where you bust and lose advantage of the 25% bonus. That is to say, with the ~33% risk of ruin you get for betting $100, wouldn’t the bonus money lost on those runs alter the overall outlook of the deposit bonus?

So I experimented a little and made the buyin $100 and the deposit bonus $400 with the same playthrough req: would we see a different outcome in the simulation between $1 bets and $100? What about a $1 buyin and 499 bonus? Turns out, which makes sense now but didn’t to me at first, that it doesn’t seem to have much of an impact at all. Contextual EV is identical across the board (-12.5 vs. -10.5) of course, and overall EV (”I buyin for $1, gamble with 500, and come away with X”) shows the same trends where the $1 bet has a very consistant range and the $100 bet is a bit wider.

Unfortunately I don’t have more time to spend on this, but my next step with simulating would be to generate a curve on total $ won, factoring in bonuses, because right now I’m just eyeballing results on 10k run throughs and its’ still pretty swingy. I’d be interested to see how the bonus ratio influences things because it seems like it should. My thought now is that the smaller the bonus, the more you want to minimize your risk of ruin and the larger the bonus the more you want to gamble with it. Of course it could affect nothing and you’re always better off taking the bigger gamble whether the bonus is $0 or 100x your buyin.

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Comment on Gambling theory problem/puzzle solution by EngineerSean http://derk.badbeatscrew.com/gambling/gambling-theory-problempuzzle-solution/comment-page-1/#comment-729 EngineerSean Wed, 01 Jun 2011 19:40:29 +0000 http://derk.badbeatscrew.com/?p=393#comment-729 It figures that the answer to this problem is not trying to maintain your bankroll for as long as possible but rather how fast you can go busto. With your $500 on a table with no maximum bet, and you bet your entire bankroll or the remaining amount to clear, you can expect to go busto 75% of the time, end up with $3000.95 12.5% of the time, and end up with $975.05 12.5% of the time, giving you an expected value of $496. I think the fact that the maximum bet was $100 instead of infinity was a good way to throw people off, very good thought experiment. It figures that the answer to this problem is not trying to maintain your bankroll for as long as possible but rather how fast you can go busto. With your $500 on a table with no maximum bet, and you bet your entire bankroll or the remaining amount to clear, you can expect to go busto 75% of the time, end up with $3000.95 12.5% of the time, and end up with $975.05 12.5% of the time, giving you an expected value of $496. I think the fact that the maximum bet was $100 instead of infinity was a good way to throw people off, very good thought experiment.

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Comment on Variance in SNGs by Derk’s blog » Blog Archive » Gambling theory problem/puzzle solution http://derk.badbeatscrew.com/poker/variance-in-sngs/comment-page-1/#comment-728 Derk’s blog » Blog Archive » Gambling theory problem/puzzle solution Wed, 01 Jun 2011 19:13:11 +0000 http://derk.badbeatscrew.com/?p=356#comment-728 [...] is pretty easy to write a Monte Carlo simulation for, and I did, similar to what I did for my megapost on variance in SNGs. In practice the result for the $1 bets is indeed around $87.50 per bonus but for the maximum bet [...] [...] is pretty easy to write a Monte Carlo simulation for, and I did, similar to what I did for my megapost on variance in SNGs. In practice the result for the $1 bets is indeed around $87.50 per bonus but for the maximum bet [...]

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Comment on Should you ever fold aces? by Derk’s blog » Blog Archive » Gambling theory problem/puzzle solution http://derk.badbeatscrew.com/poker/should-you-ever-fold-aces/comment-page-1/#comment-727 Derk’s blog » Blog Archive » Gambling theory problem/puzzle solution Wed, 01 Jun 2011 19:11:27 +0000 http://derk.badbeatscrew.com/?p=20#comment-727 [...] As a general method of reasoning, when you have a lot of possible options and it wouldn’t help or would take too long to think about individual cases, it helps to look at things like extreme cases, boundary conditions, and infinite iterations. This is very useful in fields like math and engineering. If you watch my videos on Poker VT or read some of my other blog posts, you’ll see me saying things like “Even if this guy called with 100% of his hands, it would be a good push” or “Even if you have AA you should fold.” [...] [...] As a general method of reasoning, when you have a lot of possible options and it wouldn’t help or would take too long to think about individual cases, it helps to look at things like extreme cases, boundary conditions, and infinite iterations. This is very useful in fields like math and engineering. If you watch my videos on Poker VT or read some of my other blog posts, you’ll see me saying things like “Even if this guy called with 100% of his hands, it would be a good push” or “Even if you have AA you should fold.” [...]

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Comment on Interesting gambling theory question/puzzle by Derk’s blog » Blog Archive » Gambling theory problem/puzzle solution http://derk.badbeatscrew.com/gambling/interesting-gambling-theory-question/comment-page-1/#comment-726 Derk’s blog » Blog Archive » Gambling theory problem/puzzle solution Wed, 01 Jun 2011 19:09:03 +0000 http://derk.badbeatscrew.com/?p=378#comment-726 [...] originally posted a problem about a week ago here and an update with a hint here. If you haven’t read those, please do and give it a try before [...] [...] originally posted a problem about a week ago here and an update with a hint here. If you haven’t read those, please do and give it a try before [...]

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Comment on Theory problem update by Derk’s blog » Blog Archive » Gambling theory problem/puzzle solution http://derk.badbeatscrew.com/gambling/theory-problem-update/comment-page-1/#comment-725 Derk’s blog » Blog Archive » Gambling theory problem/puzzle solution Wed, 01 Jun 2011 19:08:04 +0000 http://derk.badbeatscrew.com/?p=384#comment-725 [...] originally posted a problem about a week ago here and an update with a hint here. If you haven’t read those, please do and give it a try before reading the [...] [...] originally posted a problem about a week ago here and an update with a hint here. If you haven’t read those, please do and give it a try before reading the [...]

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Comment on Theory problem update by EngineerSean http://derk.badbeatscrew.com/gambling/theory-problem-update/comment-page-1/#comment-724 EngineerSean Tue, 31 May 2011 13:43:13 +0000 http://derk.badbeatscrew.com/?p=384#comment-724 Also it seems clear that if you are claiming that Martingaling has the same EV as betting $1 every time (a claim that I just verified and it's true) then Martingaling is certainly not the correct answer, since your chance of going to zero is far greater and we're only concerned with doing $2500 worth of volume, even if the median value of all possible bankrolls is higher by Martingaling than by just betting $1 every time. Also I made a mistake above, I meant $87.50 in profit, not $88.50, but the numbers don't significantly change. If you haven't Martingaled for breakfast in Vegas I highly recommend it. Free breakfast buffet never tasted so good. Also it seems clear that if you are claiming that Martingaling has the same EV as betting $1 every time (a claim that I just verified and it’s true) then Martingaling is certainly not the correct answer, since your chance of going to zero is far greater and we’re only concerned with doing $2500 worth of volume, even if the median value of all possible bankrolls is higher by Martingaling than by just betting $1 every time. Also I made a mistake above, I meant $87.50 in profit, not $88.50, but the numbers don’t significantly change.

If you haven’t Martingaled for breakfast in Vegas I highly recommend it. Free breakfast buffet never tasted so good.

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Comment on Theory problem update by EngineerSean http://derk.badbeatscrew.com/gambling/theory-problem-update/comment-page-1/#comment-722 EngineerSean Tue, 31 May 2011 13:24:41 +0000 http://derk.badbeatscrew.com/?p=384#comment-722 It's obviously a percentage of your current bankroll, which is a Kelly problem. Unfortunately the Kelly criterion states that you only bet if you have an edge. In $2500 of play, and EV of half a cent lost per dollar of play, your EV is -$12.50. With your $100 bonus, however, you expect to win $88.50 over $2500 of play, which means that you now have a 3.5% edge. Kelly criterion states that you bet f = (bp - q)/b, where f = percentage of bankroll you bet, b = odds if you win, p = probability of winning, and q = probability of losing b = 1.035 (Our expected value is 3.5% so we expect to get $1.035 back for every dollar we bet) p = 0.5 q = 0.5 bp = 0.5015 bp - q = .0015 (bp - q) / b = ~0.0014 = f So you would want to bet 14 cents for every hundred dollars in your current bankroll, or $1, whichever is greater. This assumes you want to make the full Kelly bet. Betting any more than that increases risk of ruin without increasing your chance of clearing the $100 bonus. It’s obviously a percentage of your current bankroll, which is a Kelly problem. Unfortunately the Kelly criterion states that you only bet if you have an edge. In $2500 of play, and EV of half a cent lost per dollar of play, your EV is -$12.50. With your $100 bonus, however, you expect to win $88.50 over $2500 of play, which means that you now have a 3.5% edge.

Kelly criterion states that you bet f = (bp – q)/b, where f = percentage of bankroll you bet, b = odds if you win, p = probability of winning, and q = probability of losing

b = 1.035 (Our expected value is 3.5% so we expect to get $1.035 back for every dollar we bet)
p = 0.5
q = 0.5

bp = 0.5015
bp – q = .0015
(bp – q) / b = ~0.0014 = f

So you would want to bet 14 cents for every hundred dollars in your current bankroll, or $1, whichever is greater. This assumes you want to make the full Kelly bet. Betting any more than that increases risk of ruin without increasing your chance of clearing the $100 bonus.

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Comment on Theory problem update by rouliroul http://derk.badbeatscrew.com/gambling/theory-problem-update/comment-page-1/#comment-720 rouliroul Tue, 31 May 2011 04:07:53 +0000 http://derk.badbeatscrew.com/?p=384#comment-720 I'm in the "It doesn't matter camp" I don't see how its not a valid solution to the problem. The problem is: "How much should we bet to maximize EV, and why? Does it even matter? If so, why? If not, why not?" The answer is the size of the bet won't change the EV, it will only increase or decrease variance. So it doesn't matter. I’m in the “It doesn’t matter camp” I don’t see how its not a valid solution to the problem. The problem is: “How much should we bet to maximize EV, and why? Does it even matter? If so, why? If not, why not?”

The answer is the size of the bet won’t change the EV, it will only increase or decrease variance. So it doesn’t matter.

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