Hi All Using Joep’s secret bet tourney teaser as a basis can you prove mathematically what the best bet for BR1 is assuming that BR2 makes a perfectly random bet somewhere between $500-$25000 with 500 bet increments. Here’s a reminder: Final hand, BR2 to act first BR2 – $40,000 – Secret bet BR1 - $46000 – No secret bet As well as proving what the best bet for BR1 is can you demonstrate what the worst bet is? As the title says this is a somewhat abstract exercise and so assume that neither player will double or surrender. Cheers Reachy
Unless I'm really missing something here, this seems pretty basic so maybe this is a trick question. OK, I'll bite, the best bet for BR1 is to take the low. By betting $500 to $5,500, BR1 guarantees the low. Since you said no doubling or surrendering, the exact amount is not critical but a bet of $500 provides a little leeway in case BR2 decides to get sneaky and bet small hoping BR1 will bet enough to give the low to BR2 if BR1 loses. Since BR2's bet is secret, I see no value in betting more than the minimum because a bet of say $5,500 does no good if BR2 bets large. So I'll say BR1's best bet is $500. As for the worst bet, who cares. I don't make a study of bonehead plays and I try to keep them out of my toolbox. Now Reachy, since you started this you can't abandon it. I expect sometime in the near future you will post the correct answer.
Br1 I like 11.5K if BR2 is a strong player or timid player, or 22.5K for any other player. With 11.5K you can surrender to force BR2 get paid. You can double down for the high if your chance of winning that is better than BR2's chance of losing. With most players, especially the freeroll poker players, a 22.5 bet has such a good chance of correlating BR2 that it gives you a better chance of winning than taking the absolute low does.
I would think... 500 is best. There really is no "correct answer" given that BR2s bet is secret. Thats what I hate about secret bets. Too much guessing involved. But you know for sure you have the low and possibly can endure a swing with the 500. The secret bet is a great advantage though for BR2. I still believe his best bet is 17,500 as I said in the other post. Also not much time to think in the heat of battle though. If I were BR1, maybe its best to think of BR2s optimal bet and match it? In this case, BR1 bets 17,500 as is suspected of BR2. My 2 cents, Rounder
Monkeysystem, You have to rethink your bet. When Reachy posted the problem he said: Ya, I know, this takes all the fun out but that's the restrictions we are under for this exercise.
Under Reachy's criteria, I like a bet of $5500. It gives BR1 the lose/push outcome, and automatically correlates with as much of BR2's random bet spread as possible. (If BR2 bet anywhere between $500 and $11,000, then BR1 has high and low.) If surrender was allowed, I like $11,500 better for BR1.
Attention Span Oops, not paying attention in class. I had the same problem in high school! If surrender isn't allowed I like 5.5K against strong players and timid players, and 22.5K against other types of players.
Hypothetical You can actually "prove" what the right bet is in this situation. I may not have explained myself clearly in my orginal post so I'll try now. The key point is that BR2 bets perfectly randomly so is as likely to bet 13500 as 500 or 2200 or any other number between 500 and 25000. With that information you can calculate exactly what the best bet for BR1 is. If you have the inclination can you tell me what the probability of succes is with the "best" bet and how much better than other bets it is? The reason I asked the question is because some people say that they use a "random" wager amount when they place a secret bet so as to be unpredicatable. Cheers Reachy
Random People (Or Chimps) The betting range in EBJ is 500 to 25K in increments of 500. Thus, there are fifty bets possible in EBJ. There are one hundred bets possible on the final table. BR2 could bet 500 through 11K, 11.5K, or 12K through 25K. 500 through 11K is twenty three possibilities. 11.5K is one possibility. 12K through 25K is twenty six possibilities. If BR1 bets 5.5K there is a 23/50 chance of a correlation, a 1/50 chance of a tiebreaker if both win, and a 26/50 chance of having the low. Any bet higher than 5.5K gives BR2 possibilities for getting the low, which weakens BR1's chances of winning. Any bet lower than 5.5K reduces BR1's number of possibilities for getting the high-low correlation, which reduces their chances of winning. 5.5K is the best bet in this scenario.
You da man/chimp! That's the answer I got also (so it must be right )! Ken got it earlier though. Incidentally did you calculate the probability for success? Cheers Reachy
I would submit that any "probability for success" calculation is theory only and cannot be used with any reliability in a live tournament game. The assumption is that out of the 50 possible bets by BR2, he will pick one at random without any other considerations. This is a false premise. For example, BR2 will most likely never bet $24,500 - he'll just bet the $25,000. By the same token, he will most likely never bet $14,500 - he'll bet $14,000 or $15,000. And so on, and so on, and so on. In summary, the human mind is not capable of pure random selection. Other circumstances always enter the picture.
Hence the thread title I did qualify the teaser by calling it "abstract betting theory" and I did say it was "hypothetical" in another post. You are right, nobody could be totally random nor would they want to be. It was just meant to be a bit of fun really. I don't have my calculations to hand but if I remember rightly BR1's chance of success in this hypothetical scenario betting 5500 is 70.2%. Betting 500 had a theoretical probability of just under 66%. I did figure the probabilty for other key bets but I can't remember them. Cheers Reachy
Using Wong's Table 4 for Best Bet Using Wong's Table 4 for Win, Push, Lose probabilities for 2 players for all bets for BR2 (500 to 25000) I get a success rate for BR1 (with a bet of 5,500) of 70.08%. This assumes that tied probabilities are half a win. Some success rates for other BR1 bets follow below BR1 Bet.........% Win ..500............66.48 1000............66.84 1500............67.20 ............................ ............................ 5000............69.72 5500............70.08 6000............68.06 ............................ ............................ 24000............59.45 24500............58.83 25000............58.21 ........................BlueLight
Beat me to it! I was just about to do that Bluelight! I concur with your numbers except that I classified a tie as a loss for BR1. Cheers Reachy
