diff --git a/L1Trigger/L1TGlobal/interface/GlobalBoard.h b/L1Trigger/L1TGlobal/interface/GlobalBoard.h
index 4bb167f4f76ff..a353ab300f466 100644
--- a/L1Trigger/L1TGlobal/interface/GlobalBoard.h
+++ b/L1Trigger/L1TGlobal/interface/GlobalBoard.h
@@ -169,24 +169,22 @@ namespace l1t {
     static const std::vector<double> semirandomNumber(const edm::Event& iEvent,
                               const std::vector<double>& prescaleFactorsAlgoTrig) {
         std::vector<double> out(prescaleFactorsAlgoTrig.size(), 1.);
-        //pick a random number from a combination of run and lumi numbers (same number for different threads)
-        //Option A) multi-thread reproducible
-/*        std::srand(0);*/
-/*        std::srand(std::rand()+iEvent.id().run());*/
-/*        std::srand(std::rand()+iEvent.id().luminosityBlock());*/
-/*        const double semirandom = std::rand(); */*/
-        //Option B) multi-thread non-reproducible
-        const double semirandom = iEvent.id().event() + iEvent.id().run() + iEvent.id().luminosityBlock();
+        //pick a random number from a combination of run, lumi, event numbers (different number for different threads)
+        std::srand(0);
+        std::srand(std::rand()+iEvent.id().run());
+        std::srand(std::rand()+iEvent.id().luminosityBlock());
+        //this causes different semirandomNumber number for different threads
+        std::srand(std::rand()+iEvent.id().event()); //reminder: different threads have different initial event number
+        const double semirandom = std::rand(); 
         for ( size_t i = 0; i< prescaleFactorsAlgoTrig.size(); i++)
         {
             const double ps = prescaleFactorsAlgoTrig.at(i);
-            if (ps==0 || ps==1) {  //do not touch ps = 0 or 1
+            if (ps==0 || ps==1) {  //do not touch ps = 0 and ps = 1
                 out[i] = ps;
             }
             else { //replace ps with a semirandom number between [1,ps]
                 out[i] = semirandom - floor(semirandom/ps)*ps;
                 if(out[i]==0) out[i] = ps;
-                //std::cout<< out[i] <<"\t" << ps <<"\t" << semirandom << std::endl;
                 assert(out[i]>0);
                 assert(out[i]<=ps);
             }
@@ -224,6 +222,7 @@ namespace l1t {
     void setBxLast(int bx);
 
     void setResetPSCountersEachLumiSec(bool val) { m_resetPSCountersEachLumiSec = val; }
+    void setSemiRandomInitialPSCounters(bool val) { m_semiRandomInitialPSCounters = val; }
 
   public:
     inline void setVerbosity(const int verbosity) { m_verbosity = verbosity; }
@@ -295,9 +294,12 @@ namespace l1t {
     // Information about board
     int m_uGtBoardNumber;
     bool m_uGtFinalBoard;
-
+    
     //whether we reset the prescales each lumi or not
     bool m_resetPSCountersEachLumiSec = true;
+    
+    // start the PS counter from a random value between [1,PS] instead of PS
+    bool m_semiRandomInitialPSCounters = false;
   };
 
 }  // namespace l1t
diff --git a/L1Trigger/L1TGlobal/plugins/L1TGlobalProducer.cc b/L1Trigger/L1TGlobal/plugins/L1TGlobalProducer.cc
index 1fa464f17fed5..1550439d427b5 100644
--- a/L1Trigger/L1TGlobal/plugins/L1TGlobalProducer.cc
+++ b/L1Trigger/L1TGlobal/plugins/L1TGlobalProducer.cc
@@ -69,6 +69,7 @@ void L1TGlobalProducer::fillDescriptions(edm::ConfigurationDescriptions& descrip
   // switch for muon showers in Run-3
   desc.add<bool>("useMuonShowers", false);
   desc.add<bool>("resetPSCountersEachLumiSec", true);
+  desc.add<bool>("semiRandomInitialPSCounters", false);
   // These parameters have well defined  default values and are not currently
   // part of the L1T/HLT interface.  They can be cleaned up or updated at will:
   desc.add<bool>("ProduceL1GtDaqRecord", true);
@@ -116,6 +117,7 @@ L1TGlobalProducer::L1TGlobalProducer(const edm::ParameterSet& parSet)
       m_requireMenuToMatchAlgoBlkInput(parSet.getParameter<bool>("RequireMenuToMatchAlgoBlkInput")),
       m_algoblkInputTag(parSet.getParameter<edm::InputTag>("AlgoBlkInputTag")),
       m_resetPSCountersEachLumiSec(parSet.getParameter<bool>("resetPSCountersEachLumiSec")),
+      m_semiRandomInitialPSCounters(parSet.getParameter<bool>("semiRandomInitialPSCounters")),
       m_useMuonShowers(parSet.getParameter<bool>("useMuonShowers")) {
   m_egInputToken = consumes<BXVector<EGamma>>(m_egInputTag);
   m_tauInputToken = consumes<BXVector<Tau>>(m_tauInputTag);
@@ -197,6 +199,7 @@ L1TGlobalProducer::L1TGlobalProducer(const edm::ParameterSet& parSet)
   m_uGtBrd = std::make_unique<GlobalBoard>();
   m_uGtBrd->setVerbosity(m_verbosity);
   m_uGtBrd->setResetPSCountersEachLumiSec(m_resetPSCountersEachLumiSec);
+  m_uGtBrd->setSemiRandomInitialPSCounters(m_semiRandomInitialPSCounters);
 
   // initialize cached IDs
 
diff --git a/L1Trigger/L1TGlobal/plugins/L1TGlobalProducer.h b/L1Trigger/L1TGlobal/plugins/L1TGlobalProducer.h
index 80d2c20c66813..22e0f4af1bc6b 100644
--- a/L1Trigger/L1TGlobal/plugins/L1TGlobalProducer.h
+++ b/L1Trigger/L1TGlobal/plugins/L1TGlobalProducer.h
@@ -188,6 +188,8 @@ class L1TGlobalProducer : public edm::stream::EDProducer<> {
 
   //disables reseting the prescale counters each lumisection (needed for offline)
   bool m_resetPSCountersEachLumiSec;
+  // start the PS counter from a random value between [1,PS] instead of PS
+  bool m_semiRandomInitialPSCounters;
   // switch to load muon showers in the global board
   bool m_useMuonShowers;
 };
diff --git a/L1Trigger/L1TGlobal/src/GlobalBoard.cc b/L1Trigger/L1TGlobal/src/GlobalBoard.cc
index ec3339b54ae83..a2d78222143c8 100644
--- a/L1Trigger/L1TGlobal/src/GlobalBoard.cc
+++ b/L1Trigger/L1TGlobal/src/GlobalBoard.cc
@@ -973,8 +973,14 @@ void l1t::GlobalBoard::runFDL(edm::Event& iEvent,
     // prescale counters: numberPhysTriggers counters per bunch cross
     m_prescaleCounterAlgoTrig.reserve(numberPhysTriggers * totalBxInEvent);
 
+
     for (int iBxInEvent = 0; iBxInEvent <= totalBxInEvent; ++iBxInEvent) {
-      m_prescaleCounterAlgoTrig.push_back(semirandomNumber(iEvent, prescaleFactorsAlgoTrig));
+      if (m_semiRandomInitialPSCounters){
+          m_prescaleCounterAlgoTrig.push_back(semirandomNumber(iEvent, prescaleFactorsAlgoTrig));
+      }
+      else{
+          m_prescaleCounterAlgoTrig.push_back(prescaleFactorsAlgoTrig);
+      }
     }
     m_firstEv = false;
     m_currentLumi = iEvent.luminosityBlock();
@@ -984,7 +990,12 @@ void l1t::GlobalBoard::runFDL(edm::Event& iEvent,
   if (m_firstEvLumiSegment || (m_currentLumi != iEvent.luminosityBlock() && m_resetPSCountersEachLumiSec)) {
     m_prescaleCounterAlgoTrig.clear();
     for (int iBxInEvent = 0; iBxInEvent <= totalBxInEvent; ++iBxInEvent) {
-      m_prescaleCounterAlgoTrig.push_back(semirandomNumber(iEvent, prescaleFactorsAlgoTrig));
+      if (m_semiRandomInitialPSCounters){
+          m_prescaleCounterAlgoTrig.push_back(semirandomNumber(iEvent, prescaleFactorsAlgoTrig));
+      }
+      else{
+          m_prescaleCounterAlgoTrig.push_back(prescaleFactorsAlgoTrig);
+      }
     }
     m_firstEvLumiSegment = false;
     m_currentLumi = iEvent.luminosityBlock();